diff --git a/bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb b/bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb
index eacb186ebd8f839d198c6fa739b93475f9e55257..8c23489eb65bbbb8796eb0ac4a75d53b6a1b306e 100644
--- a/bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb
+++ b/bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb
@@ -370,7 +370,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.8"
+ "version": "3.9.1"
},
"toc": {
"base_numbering": 1,
diff --git a/fig/Cars.gif b/fig/Cars.gif
new file mode 100644
index 0000000000000000000000000000000000000000..71a60969eb0b2e9e915c7c756b1a9a1c07091702
Binary files /dev/null and b/fig/Cars.gif differ
diff --git a/index.ipynb b/index.ipynb
index 17b8272b0c64213aadc6c1265e70d158ff399059..386c97b050a9b443363e09e5a2c6976fa76ddc94 100644
--- a/index.ipynb
+++ b/index.ipynb
@@ -62,7 +62,7 @@
"|-|-|-------|------| \n",
"|  |  |  |  | \n",
"|  | [](pull_out/pull_out.ipynb) | | [](mkappa/mkappa.ipynb) |\n",
- "|  | [](tension/fragmentation.ipynb) | [](bending/bending_3pt.ipynb) |  |"
+ "|  | [](pull_out/fragmentation.ipynb) | [](bending/bending_3pt.ipynb) |  |"
]
},
{
@@ -129,47 +129,88 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 1\n",
+ "## **Tour 1**: Introduction\n",
"\n",
- " - 1.1 A roadmap through the BMCS landscape\n",
- " - 1.2 Introduction to Jupyter Web Apps and notebooks (mathematics and mechanics support)\n",
- " - 1.3 [Example Elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)"
+ "### 1.1 A roadmap through the BMCS landscape\n",
+ "### 1.2 Introduction to Jupyter Web Apps and notebooks\n",
+ "Not only static slides and videos but also the possibility to interactively put your fingers on the theory in terms of prepared interactive applications is used throughout the course. Basic information how to \n",
+ "use the `jupyter` notebooks are summarized here:</br>\n",
+ "[**Web Apps:** first steps](link)\n",
+ "\n",
+ "### 1.3 Interactive computational environment\n",
+ "\n",
+ "To demonstrate the theory on examples that can be interactively modified, let us consider an elementary case of mixture rule to determine the effective stiffness of an elastic composite </br>\n",
+ "[**Mixture rule**: example elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 2\n",
- "\n",
- "### Material and cross-section\n",
+ "## **Tour 2:** Constant bond - pull-out, crack bridge, fragmentation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.1 - Pull-out from rigid matrix - test setup and theory\n",
"\n",
- "- 2.1 [Pull-out of long fiber from rigid matrix](bmcs_course/2_1_PO_LF_LM_RG.ipynb)\n",
- "- 2.2 [Pull-out of long fiber from long elastic matrix](bmcs_course/2_2_PO_LF_LM_EL.ipynb)\n",
- "- 2.3 [Pull-out of short fiber from rigid matrix](bmcs_course/2_3_PO_SF_M_RG.ipynb)\n",
- "- 2.4 [Crack-bridge behavior]\n",
+ "Using the analytical solution of the pullout problem assuming constant bond-slip law, elastic fiber and rigid matrix, we first explore the fundamental relations between the measured pull-out curve of a steel-rebar from the concrete matrix:</br> \n",
+ "[**Pull-out:** analytical constant-bond model](pull_out/2_1_1_PO_observation.ipynb)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.2 - Classification of pullout configurations with constant bond stress\n",
"\n",
- "### Cross section and structure \n",
+ "Include further configurations of a pull-out to show the differences in their behavior, learning the correspondence between the shape of the pull-out curve and the distribution of slip, shear, fiber and matrix strain and stresses depending on a particular configuration, i.e. elastic matrix, short fiber, short matrix and clamped fiber:</br> \n",
+ "[**Pull-out:** extended analytical constant-bond models - short / long / elastic / clamped](pull_out/2_2_1_PO_configuration_explorer.ipynb)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.3 - Multiple cracking\n",
"\n",
- "- 2.6 [Anchorage]\n",
- "- 2.7 [Multiple cracking]"
+ "The crack-bridging action of a fiber within a composite loaded in tension is a key to understanding the behavior of brittle-matrix composites. By putting crack bridges in a series, we can directly simulate a tensile test and predict the test response in terms of the stress-strain and crack spacing curves. This helps us to study and understand the relation between reinforcement ratio, bond strength, matrix strenth and the tensile response of the composite:\n",
+ "</br>\n",
+ "[**Multiple cracking:** tensile response of a composite](pull_out/fragmentation.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 3\n",
- "- 3.1 [Pull-out with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb) \n",
- "- 3.2 [EXTRA - Newton iterative scheme](extras/newton_method.ipynb)\n",
- "- 3.2 [EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb)"
+ "## **Tour 3:** Non-linear bond-slip law\n",
+ "\n",
+ "### 3.1 - Pull-out with softening and hardening bond behavior\n",
+ "\n",
+ "The shape of the bond-slip law is distinguished into hardening and softening leading to a completely different pull-out behavior. A numerical model of the pull-out test is used to visualize the debonding process</br>\n",
+ "[**Pull-out**: with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb) \n",
+ "\n",
+ "### 3.2 - Anchorage failure mechanisms\n",
+ "\n",
+ "With the developed understanding, we address the questions related to design rules: What is the necessary bond length to avoid (or to guarantee) a fiber pull-out (fiber rupture). At which distance can we expect a matrix crack to appear?</br>\n",
+ "[**Anchorage**: pull-out, fiber rupture, matrix crack](pull_out/)\n",
+ "\n",
+ "supportive material [EXTRA - Newton iterative scheme](extras/newton_method.ipynb), [EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 4\n",
+ "## **Tour 4:** Unloading and reloading\n",
+ "\n",
+ "### 4.1 - Reversible and irreversible behavior\n",
+ "\n",
+ "Non-linear behavior can be described by nonlinear functions as we did so far. However,\n",
+ "this description cannot capture the irreversible changes within the material structure.\n",
+ "To demonstrate this, let us revisit the pull-out test and unload.</br>\n",
"\n",
"- 4.1 [Unloading with multi-linear bond-slip law](bmcs_course/4_1_PO_multilinear_unloading.ipynb)\n",
"- 4.2 [Basic concept of plasticity, ideal and isotropic hardening](bmcs_course/4_2_BS_EP_SH_I_A.ipynb) \n",
@@ -181,7 +222,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 5\n",
+ "## **Tour 5**\n",
"- 5.1 [Damage initiation, damage evolution, 2D bond behavior](bmcs_course/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb)\n",
"- 5.2 [Pull out simulation using damage model](bmcs_course/5_2_PO_DM_FRP_N.ipynb)"
]
@@ -190,7 +231,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 6\n",
+ "## **Tour 6**\n",
"\n",
"- 6.1 Crack propagation"
]
@@ -199,10 +240,17 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Tour 7\n",
+ "## **Tour 7**\n",
"\n",
"- 7.1 Beam bending "
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
}
],
"metadata": {
diff --git a/pull_out/2_1_1_PO_observation.ipynb b/pull_out/2_1_1_PO_observation.ipynb
index eeb42e6c346ada1dc703c8c5c487660e73a54428..fff565a1c317c81a68293c99a9acd2d68ecd9f03 100644
--- a/pull_out/2_1_1_PO_observation.ipynb
+++ b/pull_out/2_1_1_PO_observation.ipynb
@@ -8,10 +8,11 @@
}
},
"source": [
- "# Example 2.1: PO-ELF-RLM\n",
- "Pull-out of a elastic long fiber (ELF) from rigid long matrix (RLG)\n",
+ "# 2.1 Pull-out of elastic fiber from rigid matrix \n",
"\n",
- "[Video - pullout with constant bond](add link)"
+ "PO-ELF-RLM = Pull Out - Elastic Long Fiber - Rigid Long Matrix\n",
+ "\n",
+ "[Moodle Video - pullout with constant bond](https://moodle.rwth-aachen.de/mod/page/view.php?id=551807)"
]
},
{
@@ -101,6 +102,17 @@
"cell_type": "code",
"execution_count": 8,
"metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "from pull_out import PO_ELF_RLM\n",
+ "po = PO_ELF_RLM(E_f=E_f, L_b=L_b, p=p_b, A_f=A_f, w_max=w_max)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
"outputs": [
{
"data": {
@@ -118,10 +130,6 @@
}
],
"source": [
- "%matplotlib widget\n",
- "from pull_out import PullOutAModel, PO_ELF_RLM_Symb\n",
- "po = PullOutAModel(symb_class=PO_ELF_RLM_Symb)\n",
- "po.trait_set(E_f=E_f, L_b=L_b, p=p_b, A_f=A_f, w_max=w_max)\n",
"po.interact()"
]
},
diff --git a/pull_out/2_1_2_PO_ELF_RLM.ipynb b/pull_out/2_1_2_PO_ELF_RLM.ipynb
index ebdbfd94b6f6966e53b3967cdd6fdacb6eb72422..efb16a5f92833947fb49677e702eb91a10f462a0 100644
--- a/pull_out/2_1_2_PO_ELF_RLM.ipynb
+++ b/pull_out/2_1_2_PO_ELF_RLM.ipynb
@@ -11,7 +11,7 @@
"# 2.1: PO_ELF_RLM\n",
"Pull-out (PO) of a elastic long fiber (ELF) from rigid long matrix (RLG)\n",
"\n",
- "[Video - pullout with constant bond](add link)"
+ "[Video - pullout with constant bond](https://moodle.rwth-aachen.de/mod/page/view.php?id=551807)"
]
},
{
@@ -42,13 +42,13 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "6bd568cf0dcb405dab9d65a1c9cec7e7",
+ "model_id": "bdd635c9105c4f6f918df5add1749f9e",
"version_major": 2,
"version_minor": 0
},
@@ -61,7 +61,7 @@
},
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 5 Axes>"
]
diff --git a/pull_out/2_2_1_PO_configuration_explorer.ipynb b/pull_out/2_2_1_PO_configuration_explorer.ipynb
index 0c07a2628c7ccc79d03118f57f2f2658380ed417..6380db65426b5bacc4f42402cd1c1c3f872c455c 100644
--- a/pull_out/2_2_1_PO_configuration_explorer.ipynb
+++ b/pull_out/2_2_1_PO_configuration_explorer.ipynb
@@ -57,7 +57,7 @@
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
@@ -78,13 +78,13 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "20ea5982ea244b4e92001563041b091a",
+ "model_id": "752d9298bc6d445e8be3087cc05b203e",
"version_major": 2,
"version_minor": 0
},
@@ -98,7 +98,7 @@
],
"source": [
"from pull_out import PO_ELF_RLM\n",
- "po_explorer = PO_ELF_RLM()\n",
+ "po_explorer = PO_ELF_RLM(E_f=1, E_m=1, tau=1, p=1, A_m=1, A_f=1, w_max=0.5, L_b=1, t=0.5)\n",
"po_explorer.interact()"
]
},
@@ -116,13 +116,24 @@
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "from pull_out import PO_ELF_ELM\n",
+ "po_explorer = PO_ELF_ELM(E_f=1, E_m=1, tau=1, p=1, A_m=1, A_f=1, w_max=0.5, L_b=1, t=0.5)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "da7a56b5a18a4cf9aeb55d9bbfbf3e6e",
+ "model_id": "fb5075e8fc0d45a0a818d2c738151e70",
"version_major": 2,
"version_minor": 0
},
@@ -135,8 +146,6 @@
}
],
"source": [
- "from pull_out import PO_ELF_ELM\n",
- "po_explorer = PO_ELF_ELM()\n",
"po_explorer.interact()"
]
},
@@ -154,13 +163,24 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "from pull_out import PO_ESF_RLM\n",
+ "po_explorer = PO_ESF_RLM(E_f=2, E_m=1, tau=1, A_f=1, A_m=1, p=1, L_b=1, w_max=1.3, t=0.26)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "e9f9b17af07d4a9caf27e0be8d6d25f6",
+ "model_id": "c1209be4e9e74ba39404245ae8b56139",
"version_major": 2,
"version_minor": 0
},
@@ -173,8 +193,6 @@
}
],
"source": [
- "from pull_out import PO_ESF_RLM\n",
- "po_explorer = PO_ESF_RLM()\n",
"po_explorer.interact()"
]
},
@@ -192,13 +210,13 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "5bd0c7317f274ebcbc01b002dc51cea4",
+ "model_id": "f25966d36cda4d418f8485a111b70c5a",
"version_major": 2,
"version_minor": 0
},
@@ -211,8 +229,9 @@
}
],
"source": [
+ "%matplotlib widget\n",
"from pull_out import CB_ELF_ELM\n",
- "po_explorer = CB_ELF_ELM()\n",
+ "po_explorer = CB_ELF_ELM(E_f=2, E_m=1, tau=1, A_f=1, A_m=1, p=1, L_b=1, w_max=1.3, t=0.7)\n",
"po_explorer.interact()"
]
},
@@ -224,7 +243,7 @@
}
},
"source": [
- "## Let's learn from the model\n",
+ "# Let's learn from the model\n",
"\n",
"Exercise the relation between $P$ and $\\tau(x)$ and between $w$ and $\\varepsilon(x)$.\n",
"\n",
@@ -247,9 +266,9 @@
],
"metadata": {
"kernelspec": {
- "display_name": "base",
+ "display_name": "Python 3",
"language": "python",
- "name": "base"
+ "name": "python3"
},
"language_info": {
"codemirror_mode": {
@@ -261,7 +280,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.1"
+ "version": "3.8.8"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/2_2_2_PO_ELF_ELM.ipynb b/pull_out/2_2_2_PO_ELF_ELM.ipynb
index a0c22d1ff0604d6b8a6b7978918065a79e41387a..2c36fdbbaf171b1558338d329c99a744ba19fbbd 100644
--- a/pull_out/2_2_2_PO_ELF_ELM.ipynb
+++ b/pull_out/2_2_2_PO_ELF_ELM.ipynb
@@ -21,7 +21,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "f5349eba7f0640ddb3b5163deefe0ee2",
+ "model_id": "93b6825917414c54a9da1652b435142f",
"version_major": 2,
"version_minor": 0
},
@@ -227,7 +227,7 @@
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -255,7 +255,7 @@
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -313,7 +313,7 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -332,7 +332,7 @@
"âŽA_\\mathrm{f} A_\\mathrm{m} ⎠"
]
},
- "execution_count": 3,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -371,7 +371,7 @@
},
{
"cell_type": "code",
- "execution_count": 4,
+ "execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -390,7 +390,7 @@
"⎠A_\\mathrm{f} A_\\mathrm{m} ⎠"
]
},
- "execution_count": 4,
+ "execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@@ -419,7 +419,7 @@
},
{
"cell_type": "code",
- "execution_count": 5,
+ "execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -440,7 +440,7 @@
"⎠E_\\mathrm{f} E_\\mathrm{m} ⎠"
]
},
- "execution_count": 5,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -483,7 +483,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -508,7 +508,7 @@
"m{m}⋅E_\\mathrm{m}⎠"
]
},
- "execution_count": 6,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -558,7 +558,32 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$\\displaystyle \\left\\{A_\\mathrm{f} C = P, A_\\mathrm{m} D = - P\\right\\}$"
+ ],
+ "text/plain": [
+ "{A_\\mathrm{f}â‹…C = P, A_\\mathrm{m}â‹…D = -P}"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "eq_CD = {sp.Eq(sig_f.subs({x:0}) * A_f, P),sp.Eq(sig_m.subs({x:0}) * A_m, -P)}\n",
+ "eq_CD"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -567,27 +592,24 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\left( \\left\\{ C : \\frac{P}{A_\\mathrm{f}}\\right\\}, \\ \\left\\{ D : - \\frac{P}{A_\\mathrm{m}}\\right\\}\\right)$"
+ "$\\displaystyle \\left\\{ C : \\frac{P}{A_\\mathrm{f}}, \\ D : - \\frac{P}{A_\\mathrm{m}}\\right\\}$"
],
"text/plain": [
- "⎛⎧ P ⎫ ⎧ -P ⎫⎞\n",
- "⎜⎨C: ────────────⎬, ⎨D: ────────────⎬⎟\n",
- "âŽâŽ© A_\\mathrm{f}⎠⎩ A_\\mathrm{m}âŽâŽ "
+ "⎧ P -P ⎫\n",
+ "⎨C: ────────────, D: ────────────⎬\n",
+ "⎩ A_\\mathrm{f} A_\\mathrm{m}âŽ"
]
},
- "execution_count": 7,
+ "execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "eq_C = {P - sig_f.subs({x:0}) * A_f}\n",
- "C_subs = sp.solve(eq_C,C) \n",
- "eq_D = {P + sig_m.subs({x:0}) * A_m}\n",
- "D_subs = sp.solve(eq_D,D) \n",
- "C_subs, D_subs # display the result"
+ "CD_subs = sp.solve(eq_CD,{C,D})\n",
+ "CD_subs"
]
},
{
@@ -633,7 +655,7 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 30,
"metadata": {},
"outputs": [
{
@@ -646,13 +668,13 @@
"{F: 0}"
]
},
- "execution_count": 8,
+ "execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "F_subs = sp.solve({u_m.subs(x,0) - 0}, F)\n",
+ "F_subs = sp.solve({sp.Eq(u_m.subs(x,0),0)}, F)\n",
"F_subs"
]
},
@@ -669,7 +691,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 31,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -702,7 +724,7 @@
" âŽ"
]
},
- "execution_count": 9,
+ "execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@@ -726,7 +748,7 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 32,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -747,7 +769,7 @@
"⎩ E_\\mathrm{m} E_\\mathrm{f} âŽ"
]
},
- "execution_count": 10,
+ "execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@@ -759,7 +781,7 @@
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 33,
"metadata": {},
"outputs": [
{
@@ -774,7 +796,7 @@
"⎩ \\bar{\\tau}â‹…pâŽ"
]
},
- "execution_count": 11,
+ "execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
@@ -799,7 +821,7 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 34,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -832,7 +854,7 @@
" âŽ"
]
},
- "execution_count": 21,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -855,7 +877,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 35,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -891,7 +913,7 @@
"athrm{m}⋅E_\\mathrm{m}⎠"
]
},
- "execution_count": 13,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -918,7 +940,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 36,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -938,7 +960,7 @@
"⎠2 2 ⎠"
]
},
- "execution_count": 14,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -961,7 +983,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 37,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -977,7 +999,7 @@
" 0.18 , 0.095, -0. ]))"
]
},
- "execution_count": 15,
+ "execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@@ -1002,7 +1024,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 38,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1045,7 +1067,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 39,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1055,7 +1077,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "4b412cac4b20455f8c8d04c32293b3a5",
+ "model_id": "6b1488df0f6f4b5f8e958252f9fc5cdc",
"version_major": 2,
"version_minor": 0
},
@@ -1092,7 +1114,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 40,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1101,7 +1123,7 @@
"outputs": [
{
"data": {
- "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGIAAAAyCAYAAACnKw75AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGC0lEQVR4Ae2c7XHUMBCGEyYFhFABRwd8VEDogI8KgA5g8u/+ZaAD6ABCB4EKCHQAVABDB+F9dFrFkiWdL3fJMZZ3Rpa0WsnWu95dWfbd7vn5+U6N5vP5TO3vkFH5UU12aosREF53xfmidKzy27g1rt2Iq3FNnV+J88Nzn8StU20ZAsLvu2TA7UjlH0rc1FnaLVmEOr1RDxTxUuX32d4jY2qezBerP/RT+6z8ry/vKz9QOlN6LVnj++ZyJln6Yhko4p7qP1PprCIkyIWcKr1X+WXaaex1zRl//V35vXSu4oHLfaXbKq+qjF/qd6Z+PRdfck2vuQB1aFEJ+HXowyLrHYmX3OEvei0VhlcanuVQZTtH6FFSBBaBWbZIXbeUmz/uBbq1yFY6mnLtHKFzTxHSFtqGBpvdQnw0R+c2hAOBNkfmVgzUnEyJZ5jeSQV6iugI/OmUWyoWvYGUQxuJYF1SVA2rIqZ7tV6ttQlc890E5EDi446Il4+Vnqj+KTRuqDApIgaSux16ILBZvhvxLHUqnlvEGHOT+aSIGE2LD9f+8FqLEfEltlHDIi7j+9dGZ1KEh1Bux+LDVpbtkyIu7mWLD1Ggvmi+2tKkiAt8n1GUZWzFIpoP1gL+RPjPlJxrUh2LYIVU3baWzEZpUsR8fu0rpJwGJ9eUQ2ULvEkRWwBdpzxIT5tTBP4Ssg2qRW06ro2A4o5hup8OllPEVpdx6QWOsM4Do2EcppcL1kdq/SntDV7GSRYrYh8Gjf9WYlPs8ZCVh2TYx/msvJWXUMea74nm+0IpvIKOLEIN7msNCdqeu4p1Uh+0+03pjcpsD7PsYxzqPRMUP5BvR4m8emyCNGduUhTwTmXm7igoQkzAe6r0UOXey+2FeHyUHECzDkcB3T6UsSospEi+/aby3rvhYqcRNGi+WD/K+Kayc1N7KgAmdzTu4abyVYitYvp/TDox+KA9e52zqqzuuP5a+RqCcw4l3h+EjTyV6x9yDR01kdO4uwmrWpU8X8fw8IibOo5ihBj7SoOB0SBYEAoMfRhDPExu43s2/jxrWY/GWAkwzeMqCdzcW7sbTE7J3qH+Utl2IasXIDkAJ4W7zXdAOTtqHxzsfb+mMuFDKMCtY7FvuzECv4WL+aKGEERUX0ZfEwG2DJxyNA4rp1XGSoYaZ1WY4NL5HId47LAKimDKYqIMTAVNVUmymBWDBKDFY3DqZ0oQrxy7QXzB9Ue14QrPlYhRTZDmSvzki0JihFMCE48UAUOEydz1HRyjcnioNsB+pYSWUQBL3wN4yj8oFUkyKBNFmeKKsiNqsI/3wjMEc4uCtZ+s+XYAtbJvijMPZG73MseLO/uaxrD4lG0fIROLCJZg88tZhLkSAvFEG0RAN51hahiH0XMWERrHXhAwxLTSLsIftRMzr4KIwxG1rgj8dOSrI3SusZJzTdd4+ulUhkCzFiG3w6ruSMn8tmFiuW1g7kiWAIsL42EXd0UfeNADpeeS+etqlzw0aRECjaU2n9WzumPLhNUheUiS6X488Eh12+Zn62ZGu5ch8C597pJMlZqzCIHHXf1VediUVHlHqbekBDnxZ8hTFlHml0Shr+q8T8G61qLmLALAu0CqjGJqboXVkwGPbPqQ6p6DJFNycYMU1JwiMqjwYVlxp1gAOyUpt5iQPuQ6RZpcZvxBrEkRi988DNliIVhHL7u8FaCg9H3MIPC7Qk0rQkDOBAaBNxsfukCpDOCpNfBAiMW4/SPll6a9Ss+DSttYmvgFUG+7IZ2cv/NxQeGJWDzqLH/Zyq7FmHS4bL2miGyHkTF5BmC3eRlhDRAfRNgKiSCd/fG6k8wfijd3TxFoV4lh1loF5K/j/+JqnkN3iS0+4JpS97TKpAzTngWVYgQnO9SFWsdVTjZGWSxiHQUYJmZZ6RI4+2KIThZ88IFNk78ZCerFJe4QgPw44MlzTG9xkLUIL8gjPm/eCGhNkp87n+9A/MMMq6SVSf3wLDZO1h1m/xTFzqQBCEzsyzT55yiGwzq5MMQd2YKAPavsKq2qCC5AHTFLN5DKpZcoiE6UICC8WOJiCUv/OOsfhRHlgze2wCgAAAAASUVORK5CYII=\n",
+ "image/png": "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\n",
"text/latex": [
"$\\displaystyle \\left\\{ a : - \\frac{P}{\\bar{\\tau} p}\\right\\}$"
],
@@ -1111,7 +1133,7 @@
"⎩ \\bar{\\tau}â‹…pâŽ"
]
},
- "execution_count": 18,
+ "execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
@@ -1152,7 +1174,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 41,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1181,7 +1203,7 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 42,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1190,3184 +1212,726 @@
"outputs": [
{
"data": {
- "application/javascript": [
- "/* Put everything inside the global mpl namespace */\n",
- "window.mpl = {};\n",
- "\n",
- "\n",
- "mpl.get_websocket_type = function() {\n",
- " if (typeof(WebSocket) !== 'undefined') {\n",
- " return WebSocket;\n",
- " } else if (typeof(MozWebSocket) !== 'undefined') {\n",
- " return MozWebSocket;\n",
- " } else {\n",
- " alert('Your browser does not have WebSocket support. ' +\n",
- " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
- " 'Firefox 4 and 5 are also supported but you ' +\n",
- " 'have to enable WebSockets in about:config.');\n",
- " };\n",
- "}\n",
- "\n",
- "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
- " this.id = figure_id;\n",
- "\n",
- " this.ws = websocket;\n",
- "\n",
- " this.supports_binary = (this.ws.binaryType != undefined);\n",
- "\n",
- " if (!this.supports_binary) {\n",
- " var warnings = document.getElementById(\"mpl-warnings\");\n",
- " if (warnings) {\n",
- " warnings.style.display = 'block';\n",
- " warnings.textContent = (\n",
- " \"This browser does not support binary websocket messages. \" +\n",
- " \"Performance may be slow.\");\n",
- " }\n",
- " }\n",
- "\n",
- " this.imageObj = new Image();\n",
- "\n",
- " this.context = undefined;\n",
- " this.message = undefined;\n",
- " this.canvas = undefined;\n",
- " this.rubberband_canvas = undefined;\n",
- " this.rubberband_context = undefined;\n",
- " this.format_dropdown = undefined;\n",
- "\n",
- " this.image_mode = 'full';\n",
- "\n",
- " this.root = $('<div/>');\n",
- " this._root_extra_style(this.root)\n",
- " this.root.attr('style', 'display: inline-block');\n",
- "\n",
- " $(parent_element).append(this.root);\n",
- "\n",
- " this._init_header(this);\n",
- " this._init_canvas(this);\n",
- " this._init_toolbar(this);\n",
- "\n",
- " var fig = this;\n",
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "e7fd268310cf4b1ab2242a859ad39818",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, '$u$ [mm]')"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "u_fa_x_range = get_u_fa_x(x_range, 1)\n",
+ "u_ma_x_range = get_u_ma_x(x_range, 1)\n",
+ "fig, (ax_u2) = plt.subplots(1,1, figsize=(6,3), tight_layout=True)\n",
+ "line_u_f, = ax_u2.plot(x_range, u_fa_x_range, color='black');\n",
+ "line_u_m, = ax_u2.plot(x_range, u_ma_x_range, color='green');\n",
+ "ax_u2.set_xlabel('x [mm]'); ax_u2.set_ylabel('$u$ [mm]')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Evaluate strains and stresses\n",
+ "With the known displacements at hand, we can directly calculate the strains as\n",
+ "\\begin{align}\n",
+ "\\varepsilon_\\mathrm{f} &= \\frac{\\mathrm{d} u_\\mathrm{f}}{ \\mathrm{d} x} \\\\\n",
+ "\\varepsilon_\\mathrm{m} &= \\frac{\\mathrm{d} u_\\mathrm{m}}{ \\mathrm{d} x} \\\\\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/latex": [
+ "$\\displaystyle \\left( \\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\\\frac{P + \\bar{\\tau} p x}{A_\\mathrm{f} E_\\mathrm{f}} & \\text{otherwise} \\end{cases}, \\ \\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\- \\frac{P + \\bar{\\tau} p x}{A_\\mathrm{m} E_\\mathrm{m}} & \\text{otherwise} \\end{cases}\\right)$"
+ ],
+ "text/plain": [
+ "⎛⎧ -P ⎧ \n",
+ "⎜⎪ 0 for x ≤ ──────────── ⎪ 0 \n",
+ "⎜⎪ \\bar{\\tau}⋅p ⎪ \n",
+ "⎜⎨ , ⎨ \n",
+ "⎜⎪ P + \\bar{\\tau}⋅p⋅x ⎪ -(P + \\bar{\\tau}⋅p⋅x) \n",
+ "⎜⎪───────────────────────── otherwise ⎪───────────────────────── \n",
+ "âŽâŽ©A_\\mathrm{f}â‹…E_\\mathrm{f} ⎩A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
"\n",
- " this.waiting = false;\n",
+ " -P ⎞\n",
+ " for x ≤ ────────────⎟\n",
+ " \\bar{\\tau}⋅p⎟\n",
+ " ⎟\n",
+ " ⎟\n",
+ " otherwise ⎟\n",
+ " ⎠"
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "eps_f_x = sp.diff(u_fa_x,x)\n",
+ "eps_m_x = sp.diff(u_ma_x,x)\n",
+ "sp.simplify(eps_f_x), sp.simplify(eps_m_x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The stresses along the fiber are given as\n",
+ "\\begin{align}\n",
+ "\\sigma_\\mathrm{f} &= \\frac{\\varepsilon_\\mathrm{f}}{ E_\\mathrm{f} }, \\;\n",
+ "\\sigma_\\mathrm{m} = \\frac{\\varepsilon_\\mathrm{m}}{ E_\\mathrm{f} }\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/latex": [
+ "$\\displaystyle \\left( E_\\mathrm{f} \\left(\\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\\\frac{P}{A_\\mathrm{f} E_\\mathrm{f}} + \\frac{\\bar{\\tau} p x}{A_\\mathrm{f} E_\\mathrm{f}} & \\text{otherwise} \\end{cases}\\right), \\ E_\\mathrm{m} \\left(\\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\- \\frac{P}{A_\\mathrm{m} E_\\mathrm{m}} - \\frac{\\bar{\\tau} p x}{A_\\mathrm{m} E_\\mathrm{m}} & \\text{otherwise} \\end{cases}\\right)\\right)$"
+ ],
+ "text/plain": [
+ "⎛ ⎛⎧ \n",
+ "⎜ ⎜⎪ 0 for x ≤\n",
+ "⎜ ⎜⎪ \n",
+ "⎜E_\\mathrm{f}⋅⎜⎨ \n",
+ "⎜ ⎜⎪ P \\bar{\\tau}⋅p⋅x \n",
+ "⎜ ⎜⎪───────────────────────── + ───────────────────────── ot\n",
+ "⎠âŽâŽ©A_\\mathrm{f}â‹…E_\\mathrm{f} A_\\mathrm{f}â‹…E_\\mathrm{f} \n",
"\n",
- " this.ws.onopen = function () {\n",
- " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
- " fig.send_message(\"send_image_mode\", {});\n",
- " if (mpl.ratio != 1) {\n",
- " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
- " }\n",
- " fig.send_message(\"refresh\", {});\n",
- " }\n",
+ " -P ⎞ ⎛⎧ \n",
+ " ────────────⎟ ⎜⎪ 0 \n",
+ " \\bar{\\tau}⋅p⎟ ⎜⎪ \n",
+ " ⎟, E_\\mathrm{m}⋅⎜⎨ \n",
+ " ⎟ ⎜⎪ P \\bar{\\tau}⋅\n",
+ "herwise ⎟ ⎜⎪- ───────────────────────── - ─────────────────\n",
+ " ⎠âŽâŽ© A_\\mathrm{m}â‹…E_\\mathrm{m} A_\\mathrm{m}â‹…E_\\m\n",
"\n",
- " this.imageObj.onload = function() {\n",
- " if (fig.image_mode == 'full') {\n",
- " // Full images could contain transparency (where diff images\n",
- " // almost always do), so we need to clear the canvas so that\n",
- " // there is no ghosting.\n",
- " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
- " }\n",
- " fig.context.drawImage(fig.imageObj, 0, 0);\n",
- " };\n",
- "\n",
- " this.imageObj.onunload = function() {\n",
- " fig.ws.close();\n",
- " }\n",
- "\n",
- " this.ws.onmessage = this._make_on_message_function(this);\n",
- "\n",
- " this.ondownload = ondownload;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_header = function() {\n",
- " var titlebar = $(\n",
- " '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
- " 'ui-helper-clearfix\"/>');\n",
- " var titletext = $(\n",
- " '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
- " 'text-align: center; padding: 3px;\"/>');\n",
- " titlebar.append(titletext)\n",
- " this.root.append(titlebar);\n",
- " this.header = titletext[0];\n",
- "}\n",
- "\n",
- "\n",
- "\n",
- "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
- "\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
- "\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_canvas = function() {\n",
- " var fig = this;\n",
- "\n",
- " var canvas_div = $('<div/>');\n",
- "\n",
- " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
- "\n",
- " function canvas_keyboard_event(event) {\n",
- " return fig.key_event(event, event['data']);\n",
- " }\n",
- "\n",
- " canvas_div.keydown('key_press', canvas_keyboard_event);\n",
- " canvas_div.keyup('key_release', canvas_keyboard_event);\n",
- " this.canvas_div = canvas_div\n",
- " this._canvas_extra_style(canvas_div)\n",
- " this.root.append(canvas_div);\n",
- "\n",
- " var canvas = $('<canvas/>');\n",
- " canvas.addClass('mpl-canvas');\n",
- " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
- "\n",
- " this.canvas = canvas[0];\n",
- " this.context = canvas[0].getContext(\"2d\");\n",
- "\n",
- " var backingStore = this.context.backingStorePixelRatio ||\n",
- "\tthis.context.webkitBackingStorePixelRatio ||\n",
- "\tthis.context.mozBackingStorePixelRatio ||\n",
- "\tthis.context.msBackingStorePixelRatio ||\n",
- "\tthis.context.oBackingStorePixelRatio ||\n",
- "\tthis.context.backingStorePixelRatio || 1;\n",
- "\n",
- " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
- "\n",
- " var rubberband = $('<canvas/>');\n",
- " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
- "\n",
- " var pass_mouse_events = true;\n",
- "\n",
- " canvas_div.resizable({\n",
- " start: function(event, ui) {\n",
- " pass_mouse_events = false;\n",
- " },\n",
- " resize: function(event, ui) {\n",
- " fig.request_resize(ui.size.width, ui.size.height);\n",
- " },\n",
- " stop: function(event, ui) {\n",
- " pass_mouse_events = true;\n",
- " fig.request_resize(ui.size.width, ui.size.height);\n",
- " },\n",
- " });\n",
- "\n",
- " function mouse_event_fn(event) {\n",
- " if (pass_mouse_events)\n",
- " return fig.mouse_event(event, event['data']);\n",
- " }\n",
- "\n",
- " rubberband.mousedown('button_press', mouse_event_fn);\n",
- " rubberband.mouseup('button_release', mouse_event_fn);\n",
- " // Throttle sequential mouse events to 1 every 20ms.\n",
- " rubberband.mousemove('motion_notify', mouse_event_fn);\n",
- "\n",
- " rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
- " rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
- "\n",
- " canvas_div.on(\"wheel\", function (event) {\n",
- " event = event.originalEvent;\n",
- " event['data'] = 'scroll'\n",
- " if (event.deltaY < 0) {\n",
- " event.step = 1;\n",
- " } else {\n",
- " event.step = -1;\n",
- " }\n",
- " mouse_event_fn(event);\n",
- " });\n",
- "\n",
- " canvas_div.append(canvas);\n",
- " canvas_div.append(rubberband);\n",
- "\n",
- " this.rubberband = rubberband;\n",
- " this.rubberband_canvas = rubberband[0];\n",
- " this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
- " this.rubberband_context.strokeStyle = \"#000000\";\n",
- "\n",
- " this._resize_canvas = function(width, height) {\n",
- " // Keep the size of the canvas, canvas container, and rubber band\n",
- " // canvas in synch.\n",
- " canvas_div.css('width', width)\n",
- " canvas_div.css('height', height)\n",
- "\n",
- " canvas.attr('width', width * mpl.ratio);\n",
- " canvas.attr('height', height * mpl.ratio);\n",
- " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
- "\n",
- " rubberband.attr('width', width);\n",
- " rubberband.attr('height', height);\n",
- " }\n",
- "\n",
- " // Set the figure to an initial 600x600px, this will subsequently be updated\n",
- " // upon first draw.\n",
- " this._resize_canvas(600, 600);\n",
- "\n",
- " // Disable right mouse context menu.\n",
- " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
- " return false;\n",
- " });\n",
- "\n",
- " function set_focus () {\n",
- " canvas.focus();\n",
- " canvas_div.focus();\n",
- " }\n",
- "\n",
- " window.setTimeout(set_focus, 100);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('<div/>');\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items) {\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) {\n",
- " // put a spacer in here.\n",
- " continue;\n",
- " }\n",
- " var button = $('<button/>');\n",
- " button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
- " 'ui-button-icon-only');\n",
- " button.attr('role', 'button');\n",
- " button.attr('aria-disabled', 'false');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- "\n",
- " var icon_img = $('<span/>');\n",
- " icon_img.addClass('ui-button-icon-primary ui-icon');\n",
- " icon_img.addClass(image);\n",
- " icon_img.addClass('ui-corner-all');\n",
- "\n",
- " var tooltip_span = $('<span/>');\n",
- " tooltip_span.addClass('ui-button-text');\n",
- " tooltip_span.html(tooltip);\n",
- "\n",
- " button.append(icon_img);\n",
- " button.append(tooltip_span);\n",
- "\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " var fmt_picker_span = $('<span/>');\n",
- "\n",
- " var fmt_picker = $('<select/>');\n",
- " fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
- " fmt_picker_span.append(fmt_picker);\n",
- " nav_element.append(fmt_picker_span);\n",
- " this.format_dropdown = fmt_picker[0];\n",
- "\n",
- " for (var ind in mpl.extensions) {\n",
- " var fmt = mpl.extensions[ind];\n",
- " var option = $(\n",
- " '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
- " fmt_picker.append(option);\n",
- " }\n",
- "\n",
- " // Add hover states to the ui-buttons\n",
- " $( \".ui-button\" ).hover(\n",
- " function() { $(this).addClass(\"ui-state-hover\");},\n",
- " function() { $(this).removeClass(\"ui-state-hover\");}\n",
- " );\n",
- "\n",
- " var status_bar = $('<span class=\"mpl-message\"/>');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
- " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
- " // which will in turn request a refresh of the image.\n",
- " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_message = function(type, properties) {\n",
- " properties['type'] = type;\n",
- " properties['figure_id'] = this.id;\n",
- " this.ws.send(JSON.stringify(properties));\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_draw_message = function() {\n",
- " if (!this.waiting) {\n",
- " this.waiting = true;\n",
- " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
- " }\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " var format_dropdown = fig.format_dropdown;\n",
- " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
- " fig.ondownload(fig, format);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
- " var size = msg['size'];\n",
- " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
- " fig._resize_canvas(size[0], size[1]);\n",
- " fig.send_message(\"refresh\", {});\n",
- " };\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
- " var x0 = msg['x0'] / mpl.ratio;\n",
- " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
- " var x1 = msg['x1'] / mpl.ratio;\n",
- " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
- " x0 = Math.floor(x0) + 0.5;\n",
- " y0 = Math.floor(y0) + 0.5;\n",
- " x1 = Math.floor(x1) + 0.5;\n",
- " y1 = Math.floor(y1) + 0.5;\n",
- " var min_x = Math.min(x0, x1);\n",
- " var min_y = Math.min(y0, y1);\n",
- " var width = Math.abs(x1 - x0);\n",
- " var height = Math.abs(y1 - y0);\n",
- "\n",
- " fig.rubberband_context.clearRect(\n",
- " 0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
- "\n",
- " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
- " // Updates the figure title.\n",
- " fig.header.textContent = msg['label'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
- " var cursor = msg['cursor'];\n",
- " switch(cursor)\n",
- " {\n",
- " case 0:\n",
- " cursor = 'pointer';\n",
- " break;\n",
- " case 1:\n",
- " cursor = 'default';\n",
- " break;\n",
- " case 2:\n",
- " cursor = 'crosshair';\n",
- " break;\n",
- " case 3:\n",
- " cursor = 'move';\n",
- " break;\n",
- " }\n",
- " fig.rubberband_canvas.style.cursor = cursor;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
- " fig.message.textContent = msg['message'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
- " // Request the server to send over a new figure.\n",
- " fig.send_draw_message();\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
- " fig.image_mode = msg['mode'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Called whenever the canvas gets updated.\n",
- " this.send_message(\"ack\", {});\n",
- "}\n",
- "\n",
- "// A function to construct a web socket function for onmessage handling.\n",
- "// Called in the figure constructor.\n",
- "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
- " return function socket_on_message(evt) {\n",
- " if (evt.data instanceof Blob) {\n",
- " /* FIXME: We get \"Resource interpreted as Image but\n",
- " * transferred with MIME type text/plain:\" errors on\n",
- " * Chrome. But how to set the MIME type? It doesn't seem\n",
- " * to be part of the websocket stream */\n",
- " evt.data.type = \"image/png\";\n",
- "\n",
- " /* Free the memory for the previous frames */\n",
- " if (fig.imageObj.src) {\n",
- " (window.URL || window.webkitURL).revokeObjectURL(\n",
- " fig.imageObj.src);\n",
- " }\n",
- "\n",
- " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
- " evt.data);\n",
- " fig.updated_canvas_event();\n",
- " fig.waiting = false;\n",
- " return;\n",
- " }\n",
- " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
- " fig.imageObj.src = evt.data;\n",
- " fig.updated_canvas_event();\n",
- " fig.waiting = false;\n",
- " return;\n",
- " }\n",
- "\n",
- " var msg = JSON.parse(evt.data);\n",
- " var msg_type = msg['type'];\n",
- "\n",
- " // Call the \"handle_{type}\" callback, which takes\n",
- " // the figure and JSON message as its only arguments.\n",
- " try {\n",
- " var callback = fig[\"handle_\" + msg_type];\n",
- " } catch (e) {\n",
- " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
- " return;\n",
- " }\n",
- "\n",
- " if (callback) {\n",
- " try {\n",
- " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
- " callback(fig, msg);\n",
- " } catch (e) {\n",
- " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
- " }\n",
- " }\n",
- " };\n",
- "}\n",
- "\n",
- "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
- "mpl.findpos = function(e) {\n",
- " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
- " var targ;\n",
- " if (!e)\n",
- " e = window.event;\n",
- " if (e.target)\n",
- " targ = e.target;\n",
- " else if (e.srcElement)\n",
- " targ = e.srcElement;\n",
- " if (targ.nodeType == 3) // defeat Safari bug\n",
- " targ = targ.parentNode;\n",
- "\n",
- " // jQuery normalizes the pageX and pageY\n",
- " // pageX,Y are the mouse positions relative to the document\n",
- " // offset() returns the position of the element relative to the document\n",
- " var x = e.pageX - $(targ).offset().left;\n",
- " var y = e.pageY - $(targ).offset().top;\n",
- "\n",
- " return {\"x\": x, \"y\": y};\n",
- "};\n",
- "\n",
- "/*\n",
- " * return a copy of an object with only non-object keys\n",
- " * we need this to avoid circular references\n",
- " * http://stackoverflow.com/a/24161582/3208463\n",
- " */\n",
- "function simpleKeys (original) {\n",
- " return Object.keys(original).reduce(function (obj, key) {\n",
- " if (typeof original[key] !== 'object')\n",
- " obj[key] = original[key]\n",
- " return obj;\n",
- " }, {});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.mouse_event = function(event, name) {\n",
- " var canvas_pos = mpl.findpos(event)\n",
- "\n",
- " if (name === 'button_press')\n",
- " {\n",
- " this.canvas.focus();\n",
- " this.canvas_div.focus();\n",
- " }\n",
- "\n",
- " var x = canvas_pos.x * mpl.ratio;\n",
- " var y = canvas_pos.y * mpl.ratio;\n",
- "\n",
- " this.send_message(name, {x: x, y: y, button: event.button,\n",
- " step: event.step,\n",
- " guiEvent: simpleKeys(event)});\n",
- "\n",
- " /* This prevents the web browser from automatically changing to\n",
- " * the text insertion cursor when the button is pressed. We want\n",
- " * to control all of the cursor setting manually through the\n",
- " * 'cursor' event from matplotlib */\n",
- " event.preventDefault();\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " // Handle any extra behaviour associated with a key event\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.key_event = function(event, name) {\n",
- "\n",
- " // Prevent repeat events\n",
- " if (name == 'key_press')\n",
- " {\n",
- " if (event.which === this._key)\n",
- " return;\n",
- " else\n",
- " this._key = event.which;\n",
- " }\n",
- " if (name == 'key_release')\n",
- " this._key = null;\n",
- "\n",
- " var value = '';\n",
- " if (event.ctrlKey && event.which != 17)\n",
- " value += \"ctrl+\";\n",
- " if (event.altKey && event.which != 18)\n",
- " value += \"alt+\";\n",
- " if (event.shiftKey && event.which != 16)\n",
- " value += \"shift+\";\n",
- "\n",
- " value += 'k';\n",
- " value += event.which.toString();\n",
- "\n",
- " this._key_event_extra(event, name);\n",
- "\n",
- " this.send_message(name, {key: value,\n",
- " guiEvent: simpleKeys(event)});\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
- " if (name == 'download') {\n",
- " this.handle_save(this, null);\n",
- " } else {\n",
- " this.send_message(\"toolbar_button\", {name: name});\n",
- " }\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
- " this.message.textContent = tooltip;\n",
- "};\n",
- "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
- "\n",
- "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
- "\n",
- "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
- " // Create a \"websocket\"-like object which calls the given IPython comm\n",
- " // object with the appropriate methods. Currently this is a non binary\n",
- " // socket, so there is still some room for performance tuning.\n",
- " var ws = {};\n",
- "\n",
- " ws.close = function() {\n",
- " comm.close()\n",
- " };\n",
- " ws.send = function(m) {\n",
- " //console.log('sending', m);\n",
- " comm.send(m);\n",
- " };\n",
- " // Register the callback with on_msg.\n",
- " comm.on_msg(function(msg) {\n",
- " //console.log('receiving', msg['content']['data'], msg);\n",
- " // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
- " ws.onmessage(msg['content']['data'])\n",
- " });\n",
- " return ws;\n",
- "}\n",
- "\n",
- "mpl.mpl_figure_comm = function(comm, msg) {\n",
- " // This is the function which gets called when the mpl process\n",
- " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
- "\n",
- " var id = msg.content.data.id;\n",
- " // Get hold of the div created by the display call when the Comm\n",
- " // socket was opened in Python.\n",
- " var element = $(\"#\" + id);\n",
- " var ws_proxy = comm_websocket_adapter(comm)\n",
- "\n",
- " function ondownload(figure, format) {\n",
- " window.open(figure.imageObj.src);\n",
- " }\n",
- "\n",
- " var fig = new mpl.figure(id, ws_proxy,\n",
- " ondownload,\n",
- " element.get(0));\n",
- "\n",
- " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
- " // web socket which is closed, not our websocket->open comm proxy.\n",
- " ws_proxy.onopen();\n",
- "\n",
- " fig.parent_element = element.get(0);\n",
- " fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
- " if (!fig.cell_info) {\n",
- " console.error(\"Failed to find cell for figure\", id, fig);\n",
- " return;\n",
- " }\n",
- "\n",
- " var output_index = fig.cell_info[2]\n",
- " var cell = fig.cell_info[0];\n",
- "\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
- " var width = fig.canvas.width/mpl.ratio\n",
- " fig.root.unbind('remove')\n",
- "\n",
- " // Update the output cell to use the data from the current canvas.\n",
- " fig.push_to_output();\n",
- " var dataURL = fig.canvas.toDataURL();\n",
- " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
- " // the notebook keyboard shortcuts fail.\n",
- " IPython.keyboard_manager.enable()\n",
- " $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
- " fig.close_ws(fig, msg);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.close_ws = function(fig, msg){\n",
- " fig.send_message('closing', msg);\n",
- " // fig.ws.close()\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
- " // Turn the data on the canvas into data in the output cell.\n",
- " var width = this.canvas.width/mpl.ratio\n",
- " var dataURL = this.canvas.toDataURL();\n",
- " this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Tell IPython that the notebook contents must change.\n",
- " IPython.notebook.set_dirty(true);\n",
- " this.send_message(\"ack\", {});\n",
- " var fig = this;\n",
- " // Wait a second, then push the new image to the DOM so\n",
- " // that it is saved nicely (might be nice to debounce this).\n",
- " setTimeout(function () { fig.push_to_output() }, 1000);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('<div/>');\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items){\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) { continue; };\n",
- "\n",
- " var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " // Add the status bar.\n",
- " var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "\n",
- " // Add the close button to the window.\n",
- " var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
- " var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
- " button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
- " button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
- " buttongrp.append(button);\n",
- " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
- " titlebar.prepend(buttongrp);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._root_extra_style = function(el){\n",
- " var fig = this\n",
- " el.on(\"remove\", function(){\n",
- "\tfig.close_ws(fig, {});\n",
- " });\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._canvas_extra_style = function(el){\n",
- " // this is important to make the div 'focusable\n",
- " el.attr('tabindex', 0)\n",
- " // reach out to IPython and tell the keyboard manager to turn it's self\n",
- " // off when our div gets focus\n",
- "\n",
- " // location in version 3\n",
- " if (IPython.notebook.keyboard_manager) {\n",
- " IPython.notebook.keyboard_manager.register_events(el);\n",
- " }\n",
- " else {\n",
- " // location in version 2\n",
- " IPython.keyboard_manager.register_events(el);\n",
- " }\n",
- "\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " var manager = IPython.notebook.keyboard_manager;\n",
- " if (!manager)\n",
- " manager = IPython.keyboard_manager;\n",
- "\n",
- " // Check for shift+enter\n",
- " if (event.shiftKey && event.which == 13) {\n",
- " this.canvas_div.blur();\n",
- " // select the cell after this one\n",
- " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
- " IPython.notebook.select(index + 1);\n",
- " }\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " fig.ondownload(fig, null);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.find_output_cell = function(html_output) {\n",
- " // Return the cell and output element which can be found *uniquely* in the notebook.\n",
- " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
- " // IPython event is triggered only after the cells have been serialised, which for\n",
- " // our purposes (turning an active figure into a static one), is too late.\n",
- " var cells = IPython.notebook.get_cells();\n",
- " var ncells = cells.length;\n",
- " for (var i=0; i<ncells; i++) {\n",
- " var cell = cells[i];\n",
- " if (cell.cell_type === 'code'){\n",
- " for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
- " var data = cell.output_area.outputs[j];\n",
- " if (data.data) {\n",
- " // IPython >= 3 moved mimebundle to data attribute of output\n",
- " data = data.data;\n",
- " }\n",
- " if (data['text/html'] == html_output) {\n",
- " return [cell, data, j];\n",
- " }\n",
- " }\n",
- " }\n",
- " }\n",
- "}\n",
- "\n",
- "// Register the function which deals with the matplotlib target/channel.\n",
- "// The kernel may be null if the page has been refreshed.\n",
- "if (IPython.notebook.kernel != null) {\n",
- " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
- "}\n"
- ],
- "text/plain": [
- "<IPython.core.display.Javascript object>"
- ]
- },
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- "output_type": "display_data"
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\" width=\"600\">"
- ],
- "text/plain": [
- "<IPython.core.display.HTML object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "810fcc171837490cb945ca003d270e20",
- "version_major": 2,
- "version_minor": 0
- },
- "text/plain": [
- "interactive(children=(FloatSlider(value=0.0, description='P', max=1.0, step=0.05), Output()), _dom_classes=('w…"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "u_fa_x_range = get_u_fa_x(x_range, 1)\n",
- "u_ma_x_range = get_u_ma_x(x_range, 1)\n",
- "fig, (ax_u2) = plt.subplots(1,1, figsize=(6,3), tight_layout=True)\n",
- "line_u_f, = ax_u2.plot(x_range, u_fa_x_range, color='black');\n",
- "line_u_m, = ax_u2.plot(x_range, u_ma_x_range, color='green');\n",
- "ax_u2.set_xlabel('x [mm]'); ax_u2.set_ylabel('$u$ [mm]')\n",
- "def update(P):\n",
- " line_u_f.set_ydata(get_u_fa_x(x_range, P))\n",
- " line_u_m.set_ydata(get_u_ma_x(x_range, P))\n",
- "ipw.interact(update, P=ipw.FloatSlider(min=0, max=1, step=0.05));"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "### Evaluate strains and stresses\n",
- "With the known displacements at hand, we can directly calculate the strains as\n",
- "\\begin{align}\n",
- "\\varepsilon_\\mathrm{f} &= \\frac{\\mathrm{d} u_\\mathrm{f}}{ \\mathrm{d} x} \\\\\n",
- "\\varepsilon_\\mathrm{m} &= \\frac{\\mathrm{d} u_\\mathrm{m}}{ \\mathrm{d} x} \\\\\n",
- "\\end{align}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/latex": [
- "$\\displaystyle \\left( \\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\\\frac{P + \\bar{\\tau} p x}{A_\\mathrm{f} E_\\mathrm{f}} & \\text{otherwise} \\end{cases}, \\ \\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\- \\frac{P + \\bar{\\tau} p x}{A_\\mathrm{m} E_\\mathrm{m}} & \\text{otherwise} \\end{cases}\\right)$"
- ],
- "text/plain": [
- "⎛⎧ -P ⎧ \n",
- "⎜⎪ 0 for x ≤ ──────────── ⎪ 0 \n",
- "⎜⎪ \\bar{\\tau}⋅p ⎪ \n",
- "⎜⎨ , ⎨ \n",
- "⎜⎪ P + \\bar{\\tau}⋅p⋅x ⎪ -(P + \\bar{\\tau}⋅p⋅x) \n",
- "⎜⎪───────────────────────── otherwise ⎪───────────────────────── \n",
- "âŽâŽ©A_\\mathrm{f}â‹…E_\\mathrm{f} ⎩A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
- "\n",
- " -P ⎞\n",
- " for x ≤ ────────────⎟\n",
- " \\bar{\\tau}⋅p⎟\n",
- " ⎟\n",
- " ⎟\n",
- " otherwise ⎟\n",
- " ⎠"
- ]
- },
- "execution_count": 21,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "eps_f_x = sp.diff(u_fa_x,x)\n",
- "eps_m_x = sp.diff(u_ma_x,x)\n",
- "sp.simplify(eps_f_x), sp.simplify(eps_m_x)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "The stresses along the fiber are given as\n",
- "\\begin{align}\n",
- "\\sigma_\\mathrm{f} &= \\frac{\\varepsilon_\\mathrm{f}}{ E_\\mathrm{f} }, \\;\n",
- "\\sigma_\\mathrm{m} = \\frac{\\varepsilon_\\mathrm{m}}{ E_\\mathrm{f} }\n",
- "\\end{align}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/latex": [
- "$\\displaystyle \\left( E_\\mathrm{f} \\left(\\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\\\frac{P}{A_\\mathrm{f} E_\\mathrm{f}} + \\frac{\\bar{\\tau} p x}{A_\\mathrm{f} E_\\mathrm{f}} & \\text{otherwise} \\end{cases}\\right), \\ E_\\mathrm{m} \\left(\\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\- \\frac{P}{A_\\mathrm{m} E_\\mathrm{m}} - \\frac{\\bar{\\tau} p x}{A_\\mathrm{m} E_\\mathrm{m}} & \\text{otherwise} \\end{cases}\\right)\\right)$"
- ],
- "text/plain": [
- "⎛ ⎛⎧ \n",
- "⎜ ⎜⎪ 0 for x ≤\n",
- "⎜ ⎜⎪ \n",
- "⎜E_\\mathrm{f}⋅⎜⎨ \n",
- "⎜ ⎜⎪ P \\bar{\\tau}⋅p⋅x \n",
- "⎜ ⎜⎪───────────────────────── + ───────────────────────── ot\n",
- "⎠âŽâŽ©A_\\mathrm{f}â‹…E_\\mathrm{f} A_\\mathrm{f}â‹…E_\\mathrm{f} \n",
- "\n",
- " -P ⎞ ⎛⎧ \n",
- " ────────────⎟ ⎜⎪ 0 \n",
- " \\bar{\\tau}⋅p⎟ ⎜⎪ \n",
- " ⎟, E_\\mathrm{m}⋅⎜⎨ \n",
- " ⎟ ⎜⎪ P \\bar{\\tau}⋅\n",
- "herwise ⎟ ⎜⎪- ───────────────────────── - ─────────────────\n",
- " ⎠âŽâŽ© A_\\mathrm{m}â‹…E_\\mathrm{m} A_\\mathrm{m}â‹…E_\\m\n",
- "\n",
- " -P ⎞⎞\n",
- " for x ≤ ────────────⎟⎟\n",
- " \\bar{\\tau}⋅p⎟⎟\n",
- " ⎟⎟\n",
- "p⋅x ⎟⎟\n",
- "──────── otherwise ⎟⎟\n",
- "athrm{m} ⎠⎠"
- ]
- },
- "execution_count": 23,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "sig_f_x = E_f * eps_f_x\n",
- "sig_m_x = E_m * eps_m_x\n",
- "sig_f_x, sig_m_x"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "The profile of shear stress along the bond zone is obtained as\n",
- "\\begin{align}\n",
- " \\tau = \\frac{\\mathrm{d} \\sigma}{\\mathrm{d} x}\n",
- "\\end{align}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
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- "text/latex": [
- "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\\\bar{\\tau} & \\text{otherwise} \\end{cases}$"
- ],
- "text/plain": [
- "⎧ -P \n",
- "⎪ 0 for x ≤ ────────────\n",
- "⎨ \\bar{\\tau}⋅p\n",
- "⎪ \n",
- "⎩\\bar{\\tau} otherwise "
- ]
- },
- "execution_count": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "tau_x = sig_f_x.diff(x) * A_f / p\n",
- "sp.simplify(tau_x)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "### Plot the strains and stresses\n",
- "Similarly to the callable function `get_u_fa_x` let us define the functions for the strains and stresses using the `sp.lambdify` generator "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [],
- "source": [
- "get_eps_f_x = sp.lambdify((x, P), eps_f_x.subs(data_f))\n",
- "get_eps_m_x = sp.lambdify((x, P), eps_m_x.subs(data_f))\n",
- "get_sig_f_x = sp.lambdify((x, P), sig_f_x.subs(data_f))\n",
- "get_sig_m_x = sp.lambdify((x, P), sig_m_x.subs(data_f))\n",
- "get_tau_x = sp.lambdify((x, P), tau_x.subs(data_f))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "To make the code for plotting shorter let us define a general procedure plotting and filling the curves and attaching the labels to a specified subplot in one call "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 26,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "outputs": [
- {
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- "\n",
- "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
- " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
- " // which will in turn request a refresh of the image.\n",
- " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_message = function(type, properties) {\n",
- " properties['type'] = type;\n",
- " properties['figure_id'] = this.id;\n",
- " this.ws.send(JSON.stringify(properties));\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_draw_message = function() {\n",
- " if (!this.waiting) {\n",
- " this.waiting = true;\n",
- " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
- " }\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " var format_dropdown = fig.format_dropdown;\n",
- " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
- " fig.ondownload(fig, format);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
- " var size = msg['size'];\n",
- " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
- " fig._resize_canvas(size[0], size[1]);\n",
- " fig.send_message(\"refresh\", {});\n",
- " };\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
- " var x0 = msg['x0'] / mpl.ratio;\n",
- " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
- " var x1 = msg['x1'] / mpl.ratio;\n",
- " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
- " x0 = Math.floor(x0) + 0.5;\n",
- " y0 = Math.floor(y0) + 0.5;\n",
- " x1 = Math.floor(x1) + 0.5;\n",
- " y1 = Math.floor(y1) + 0.5;\n",
- " var min_x = Math.min(x0, x1);\n",
- " var min_y = Math.min(y0, y1);\n",
- " var width = Math.abs(x1 - x0);\n",
- " var height = Math.abs(y1 - y0);\n",
- "\n",
- " fig.rubberband_context.clearRect(\n",
- " 0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
- "\n",
- " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
- " // Updates the figure title.\n",
- " fig.header.textContent = msg['label'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
- " var cursor = msg['cursor'];\n",
- " switch(cursor)\n",
- " {\n",
- " case 0:\n",
- " cursor = 'pointer';\n",
- " break;\n",
- " case 1:\n",
- " cursor = 'default';\n",
- " break;\n",
- " case 2:\n",
- " cursor = 'crosshair';\n",
- " break;\n",
- " case 3:\n",
- " cursor = 'move';\n",
- " break;\n",
- " }\n",
- " fig.rubberband_canvas.style.cursor = cursor;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
- " fig.message.textContent = msg['message'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
- " // Request the server to send over a new figure.\n",
- " fig.send_draw_message();\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
- " fig.image_mode = msg['mode'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Called whenever the canvas gets updated.\n",
- " this.send_message(\"ack\", {});\n",
- "}\n",
- "\n",
- "// A function to construct a web socket function for onmessage handling.\n",
- "// Called in the figure constructor.\n",
- "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
- " return function socket_on_message(evt) {\n",
- " if (evt.data instanceof Blob) {\n",
- " /* FIXME: We get \"Resource interpreted as Image but\n",
- " * transferred with MIME type text/plain:\" errors on\n",
- " * Chrome. But how to set the MIME type? It doesn't seem\n",
- " * to be part of the websocket stream */\n",
- " evt.data.type = \"image/png\";\n",
- "\n",
- " /* Free the memory for the previous frames */\n",
- " if (fig.imageObj.src) {\n",
- " (window.URL || window.webkitURL).revokeObjectURL(\n",
- " fig.imageObj.src);\n",
- " }\n",
- "\n",
- " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
- " evt.data);\n",
- " fig.updated_canvas_event();\n",
- " fig.waiting = false;\n",
- " return;\n",
- " }\n",
- " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
- " fig.imageObj.src = evt.data;\n",
- " fig.updated_canvas_event();\n",
- " fig.waiting = false;\n",
- " return;\n",
- " }\n",
- "\n",
- " var msg = JSON.parse(evt.data);\n",
- " var msg_type = msg['type'];\n",
- "\n",
- " // Call the \"handle_{type}\" callback, which takes\n",
- " // the figure and JSON message as its only arguments.\n",
- " try {\n",
- " var callback = fig[\"handle_\" + msg_type];\n",
- " } catch (e) {\n",
- " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
- " return;\n",
- " }\n",
- "\n",
- " if (callback) {\n",
- " try {\n",
- " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
- " callback(fig, msg);\n",
- " } catch (e) {\n",
- " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
- " }\n",
- " }\n",
- " };\n",
- "}\n",
- "\n",
- "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
- "mpl.findpos = function(e) {\n",
- " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
- " var targ;\n",
- " if (!e)\n",
- " e = window.event;\n",
- " if (e.target)\n",
- " targ = e.target;\n",
- " else if (e.srcElement)\n",
- " targ = e.srcElement;\n",
- " if (targ.nodeType == 3) // defeat Safari bug\n",
- " targ = targ.parentNode;\n",
- "\n",
- " // jQuery normalizes the pageX and pageY\n",
- " // pageX,Y are the mouse positions relative to the document\n",
- " // offset() returns the position of the element relative to the document\n",
- " var x = e.pageX - $(targ).offset().left;\n",
- " var y = e.pageY - $(targ).offset().top;\n",
- "\n",
- " return {\"x\": x, \"y\": y};\n",
- "};\n",
- "\n",
- "/*\n",
- " * return a copy of an object with only non-object keys\n",
- " * we need this to avoid circular references\n",
- " * http://stackoverflow.com/a/24161582/3208463\n",
- " */\n",
- "function simpleKeys (original) {\n",
- " return Object.keys(original).reduce(function (obj, key) {\n",
- " if (typeof original[key] !== 'object')\n",
- " obj[key] = original[key]\n",
- " return obj;\n",
- " }, {});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.mouse_event = function(event, name) {\n",
- " var canvas_pos = mpl.findpos(event)\n",
- "\n",
- " if (name === 'button_press')\n",
- " {\n",
- " this.canvas.focus();\n",
- " this.canvas_div.focus();\n",
- " }\n",
- "\n",
- " var x = canvas_pos.x * mpl.ratio;\n",
- " var y = canvas_pos.y * mpl.ratio;\n",
- "\n",
- " this.send_message(name, {x: x, y: y, button: event.button,\n",
- " step: event.step,\n",
- " guiEvent: simpleKeys(event)});\n",
- "\n",
- " /* This prevents the web browser from automatically changing to\n",
- " * the text insertion cursor when the button is pressed. We want\n",
- " * to control all of the cursor setting manually through the\n",
- " * 'cursor' event from matplotlib */\n",
- " event.preventDefault();\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " // Handle any extra behaviour associated with a key event\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.key_event = function(event, name) {\n",
- "\n",
- " // Prevent repeat events\n",
- " if (name == 'key_press')\n",
- " {\n",
- " if (event.which === this._key)\n",
- " return;\n",
- " else\n",
- " this._key = event.which;\n",
- " }\n",
- " if (name == 'key_release')\n",
- " this._key = null;\n",
- "\n",
- " var value = '';\n",
- " if (event.ctrlKey && event.which != 17)\n",
- " value += \"ctrl+\";\n",
- " if (event.altKey && event.which != 18)\n",
- " value += \"alt+\";\n",
- " if (event.shiftKey && event.which != 16)\n",
- " value += \"shift+\";\n",
- "\n",
- " value += 'k';\n",
- " value += event.which.toString();\n",
- "\n",
- " this._key_event_extra(event, name);\n",
- "\n",
- " this.send_message(name, {key: value,\n",
- " guiEvent: simpleKeys(event)});\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
- " if (name == 'download') {\n",
- " this.handle_save(this, null);\n",
- " } else {\n",
- " this.send_message(\"toolbar_button\", {name: name});\n",
- " }\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
- " this.message.textContent = tooltip;\n",
- "};\n",
- "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
- "\n",
- "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
- "\n",
- "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
- " // Create a \"websocket\"-like object which calls the given IPython comm\n",
- " // object with the appropriate methods. Currently this is a non binary\n",
- " // socket, so there is still some room for performance tuning.\n",
- " var ws = {};\n",
- "\n",
- " ws.close = function() {\n",
- " comm.close()\n",
- " };\n",
- " ws.send = function(m) {\n",
- " //console.log('sending', m);\n",
- " comm.send(m);\n",
- " };\n",
- " // Register the callback with on_msg.\n",
- " comm.on_msg(function(msg) {\n",
- " //console.log('receiving', msg['content']['data'], msg);\n",
- " // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
- " ws.onmessage(msg['content']['data'])\n",
- " });\n",
- " return ws;\n",
- "}\n",
- "\n",
- "mpl.mpl_figure_comm = function(comm, msg) {\n",
- " // This is the function which gets called when the mpl process\n",
- " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
- "\n",
- " var id = msg.content.data.id;\n",
- " // Get hold of the div created by the display call when the Comm\n",
- " // socket was opened in Python.\n",
- " var element = $(\"#\" + id);\n",
- " var ws_proxy = comm_websocket_adapter(comm)\n",
- "\n",
- " function ondownload(figure, format) {\n",
- " window.open(figure.imageObj.src);\n",
- " }\n",
- "\n",
- " var fig = new mpl.figure(id, ws_proxy,\n",
- " ondownload,\n",
- " element.get(0));\n",
- "\n",
- " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
- " // web socket which is closed, not our websocket->open comm proxy.\n",
- " ws_proxy.onopen();\n",
- "\n",
- " fig.parent_element = element.get(0);\n",
- " fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
- " if (!fig.cell_info) {\n",
- " console.error(\"Failed to find cell for figure\", id, fig);\n",
- " return;\n",
- " }\n",
- "\n",
- " var output_index = fig.cell_info[2]\n",
- " var cell = fig.cell_info[0];\n",
- "\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
- " var width = fig.canvas.width/mpl.ratio\n",
- " fig.root.unbind('remove')\n",
- "\n",
- " // Update the output cell to use the data from the current canvas.\n",
- " fig.push_to_output();\n",
- " var dataURL = fig.canvas.toDataURL();\n",
- " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
- " // the notebook keyboard shortcuts fail.\n",
- " IPython.keyboard_manager.enable()\n",
- " $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
- " fig.close_ws(fig, msg);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.close_ws = function(fig, msg){\n",
- " fig.send_message('closing', msg);\n",
- " // fig.ws.close()\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
- " // Turn the data on the canvas into data in the output cell.\n",
- " var width = this.canvas.width/mpl.ratio\n",
- " var dataURL = this.canvas.toDataURL();\n",
- " this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Tell IPython that the notebook contents must change.\n",
- " IPython.notebook.set_dirty(true);\n",
- " this.send_message(\"ack\", {});\n",
- " var fig = this;\n",
- " // Wait a second, then push the new image to the DOM so\n",
- " // that it is saved nicely (might be nice to debounce this).\n",
- " setTimeout(function () { fig.push_to_output() }, 1000);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('<div/>');\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items){\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) { continue; };\n",
- "\n",
- " var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " // Add the status bar.\n",
- " var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "\n",
- " // Add the close button to the window.\n",
- " var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
- " var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
- " button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
- " button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
- " buttongrp.append(button);\n",
- " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
- " titlebar.prepend(buttongrp);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._root_extra_style = function(el){\n",
- " var fig = this\n",
- " el.on(\"remove\", function(){\n",
- "\tfig.close_ws(fig, {});\n",
- " });\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._canvas_extra_style = function(el){\n",
- " // this is important to make the div 'focusable\n",
- " el.attr('tabindex', 0)\n",
- " // reach out to IPython and tell the keyboard manager to turn it's self\n",
- " // off when our div gets focus\n",
- "\n",
- " // location in version 3\n",
- " if (IPython.notebook.keyboard_manager) {\n",
- " IPython.notebook.keyboard_manager.register_events(el);\n",
- " }\n",
- " else {\n",
- " // location in version 2\n",
- " IPython.keyboard_manager.register_events(el);\n",
- " }\n",
- "\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " var manager = IPython.notebook.keyboard_manager;\n",
- " if (!manager)\n",
- " manager = IPython.keyboard_manager;\n",
- "\n",
- " // Check for shift+enter\n",
- " if (event.shiftKey && event.which == 13) {\n",
- " this.canvas_div.blur();\n",
- " // select the cell after this one\n",
- " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
- " IPython.notebook.select(index + 1);\n",
- " }\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " fig.ondownload(fig, null);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.find_output_cell = function(html_output) {\n",
- " // Return the cell and output element which can be found *uniquely* in the notebook.\n",
- " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
- " // IPython event is triggered only after the cells have been serialised, which for\n",
- " // our purposes (turning an active figure into a static one), is too late.\n",
- " var cells = IPython.notebook.get_cells();\n",
- " var ncells = cells.length;\n",
- " for (var i=0; i<ncells; i++) {\n",
- " var cell = cells[i];\n",
- " if (cell.cell_type === 'code'){\n",
- " for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
- " var data = cell.output_area.outputs[j];\n",
- " if (data.data) {\n",
- " // IPython >= 3 moved mimebundle to data attribute of output\n",
- " data = data.data;\n",
- " }\n",
- " if (data['text/html'] == html_output) {\n",
- " return [cell, data, j];\n",
- " }\n",
- " }\n",
- " }\n",
- " }\n",
- "}\n",
- "\n",
- "// Register the function which deals with the matplotlib target/channel.\n",
- "// The kernel may be null if the page has been refreshed.\n",
- "if (IPython.notebook.kernel != null) {\n",
- " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
- "}\n"
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width=\"999.7333333333333\">"
- ],
- "text/plain": [
- "<IPython.core.display.HTML object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "fig, (ax_eps, ax_sig, ax_tau) = plt.subplots(1,3, figsize=(10,3), tight_layout=True)\n",
- "poui.plot_filled_var(ax_eps, x_range, get_eps_f_x(x_range,1 ), \n",
- " color='green',xlabel='x [mm]', ylabel=r'$\\varepsilon$ [-]')\n",
- "poui.plot_filled_var(ax_eps, x_range, get_eps_m_x(x_range,1 ), \n",
- " color='green',alpha=0.8)\n",
- "poui.plot_filled_var(ax_sig, x_range, get_sig_f_x(x_range,1),\n",
- " color='blue', xlabel='x [mm]', ylabel=r'$\\sigma$ [MPa]')\n",
- "poui.plot_filled_var(ax_sig, x_range, get_sig_m_x(x_range,1),\n",
- " color='blue', alpha=0.8)\n",
- "poui.plot_filled_var(ax_tau, x_range, get_tau_x(x_range,1),\n",
- " color='red', xlabel='x [mm]', ylabel=r'$\\tau$ [MPa]');"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "## Pull-out curve"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "### Quick summary - direct derivation\n",
- "\\begin{align}\n",
- " \\varepsilon_\\mathrm{f}(0) &= \\frac{P}{E_\\mathrm{f} A_\\mathrm{f}}, \\;\\;\n",
- " \\varepsilon_\\mathrm{m}(0) = \\frac{-P}{E_\\mathrm{m} A_\\mathrm{m}} \\\\\n",
- " a &= - \\frac{P}{p\\tau}.\n",
- "\\end{align}\n",
- "Thus, the crack opening can be expressed as the area of the triangle\n",
- "\\begin{align}\n",
- " w &= \\frac{1}{2}\\left[\\varepsilon_\\mathrm{f}(0) - \\varepsilon_\\mathrm{m}(0)\\right]a \\nonumber \\\\\n",
- " &= \\frac{1}{2}\\frac{P^2}{p\\tau} \\left[\\frac{1}{E_\\mathrm{f} A_\\mathrm{f}} + \\frac{1}{E_\\mathrm{m} A_\\mathrm{m}}\\right].\n",
- "\\end{align}\n",
- "By solving this equation for $P$ we obtain the pullout curve in the form\n",
- "\\begin{align}\n",
- " P(w) = \\sqrt{2wp\\tau \\frac{E_\\mathrm{f}A_\\mathrm{f}E_\\mathrm{m}A_\\mathrm{m}}{E_\\mathrm{f}A_\\mathrm{f}+E_\\mathrm{m}A_\\mathrm{m}}}.\n",
- "\\end{align}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/latex": [
- "$\\displaystyle \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}$"
- ],
- "text/plain": [
- " \n",
- " ______________ ______________ ______________ ______________ _____\n",
- "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\bar\n",
- " \n",
- "\n",
- " _______________________________________________________\n",
- "_______ ╱ w \n",
- "{\\tau} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── \n",
- " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} "
- ]
- },
- "execution_count": 31,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "eps_f_0 = P / E_f / A_f\n",
- "eps_m_0 = -P / E_m / A_m\n",
- "a_subs = sp.solve({P - p * tau * a}, a)\n",
- "w_el = sp.Rational(1,2) * ( eps_f_0 - eps_m_0) * a\n",
- "Pw_pull_elastic = sp.solve(w_el.subs(a_subs) - w, P)[1]\n",
- "Pw_pull_elastic "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Pull-out curve derived from the displacement field solution "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "**`sympy` explanation:** In parallel let us use again the `subs` and `solve` provided in `sympy` to define the `P_push` and `P_pull` variables in the running `jupyter` kernel. As `solve` searches for zero point of the supplied equation we must transform the above equation into"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": "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\n",
- "text/latex": [
- "$\\displaystyle - w + \\frac{P^{2}}{2 A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p} + \\frac{P^{2}}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p}$"
- ],
- "text/plain": [
- " 2 2 \n",
- " P P \n",
- "-w + ──────────────────────────────────────── + ──────────────────────────────\n",
- " 2â‹…A_\\mathrm{m}â‹…E_\\mathrm{m}â‹…\\bar{\\tau}â‹…p 2â‹…A_\\mathrm{f}â‹…E_\\mathrm{f}â‹…\\b\n",
- "\n",
- " \n",
- " \n",
- "──────────\n",
- "ar{\\tau}â‹…p"
- ]
- },
- "execution_count": 32,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "u_f_x.subs(x,0) - w"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "and then send it to `sp.solve`"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/latex": [
- "$\\displaystyle \\left( - \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}, \\ \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}\\right)$"
- ],
- "text/plain": [
- "⎛ \n",
- "⎜ ______________ ______________ ______________ ______________ ___\n",
- "⎜-√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\b\n",
- "⎠\n",
- "\n",
- " _______________________________________________________ \n",
- "_________ ╱ w \n",
- "ar{\\tau} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── , √2⋅╲\n",
- " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
- "\n",
- " \n",
- " ______________ ______________ ______________ ______________ _________\n",
- "╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\bar{\\ta\n",
- " \n",
- "\n",
- " _______________________________________________________⎞\n",
- "___ ╱ w ⎟\n",
- "u} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── ⎟\n",
- " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} ⎠"
- ]
- },
- "execution_count": 33,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "Pw_push_elastic, Pw_pull_elastic = sp.solve(u_f_x.subs({x:0})-w, P)\n",
- "Pw_push_elastic, Pw_pull_elastic"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "Note that the obtained $P(w)$ covers both the pull-out and push-in case. If we supply the parameters defined above with unit stiffness, area and perimeter we obtain"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": "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\n",
- "text/latex": [
- "$\\displaystyle \\left( - \\sqrt{w}, \\ \\sqrt{w}\\right)$"
- ],
- "text/plain": [
- "(-√w, √w)"
- ]
- },
- "execution_count": 34,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "Pw_push_elastic.subs(data_f), Pw_pull_elastic.subs({A_f:1, E_f:1, L_b:1, p:1, tau:1, A_m:1, E_m:1})"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "### Plot the pull-out curve\n",
- "The symbolic expression must be transformed into a quantifiable form using `sp.lambdify`"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 35,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": "iVBORw0KGgoAAAANSUhEUgAAAa4AAAAyCAYAAAAEJj8WAAAACXBIWXMAAA7EAAAOxAGVKw4bAAASaUlEQVR4Ae2d25UdtRKGt2dNAGaI4EAGYEfgIQMwEWAyOCy/+c0LMjCOwEAGQAQ2ZAAZ4OMMfP5PVjV9UV+kvu2eXVqrp9VSqS5/Syrdes+99+/fnzw4Ao6AI3AOCDx79ux76fHfc9DFdThfBK7PVzXXzBFwBC4QgS/lvO5doN1ucgYCVxm0TuoIOAKOwGoIyGF9IuZ/rybAGd8ZBNxx3ZlX6YY4AodH4DNZ8OvhrXADVkfAHdfqELsAR8ARmIjAF6L7bSKtk10wAu64Lvjlu+mOwJkhcKvlwj/PTCdX5wwR8MMZZ/hSXCVH4NIQkMO6L5vfXZrdZm+0/4meP9X1l55/qOV9qfhTpX1Omu48v9T1H8UvEjOfcVETPDgCjsDeCNxKgUteJsQx4azY43vaehnf6rl+aAVnhaN/0KK7mEd3XBfzqt1QR+CsEXgo7S7yYIYc1iey/XV8O+zz1Z0UyTj1ChvR4+C52nRKuoxw6KVCvcDVvp4W70W/JRG/F6pSLAXsEpa0Z21bltQVsNfWd+iFLm3LkKyD59E5Pz+4DaXqv1U9+SUWflzHQemctCS0Z6N/K88d1wds8v4KOEYKf00tJfrFnEGU/ZvujFDOOkRdP1nS/r0MPpotR9N3r/d6DnL1ri5yv8bs1h3nzRKgOTFeC2nvlNd2UheJFYAQ5s64+HmWLwRqezQQmK/8B9lcRwhH0nUMz6PZcjR9G/irbWUNDimsMosNEBvKrPQgfemc36zE/khsv5KyfwqPupPqfCKgfOpEtXR4JAOX0rXYcUXwmEVs7rT2lJ0L/JF0HbPtaLYcTd8e/HG8ew0Oe1RaPNk/PP4AKQ6p7rRIJa0+AyONn8WqTh2ScGnhaobB36nsXmvSyOY6QjiSrmN4Hs2Wo+nbwP+OON6GTT0PnVlFD91dT2YWhaMKQe+fmeiNLtvnOimN+MV/63av5NfhBR7rsH/ozjcHm4Yo+3fdwzcNmwrPFHYkXcdMO5otR9M3hb9s4EDPr7q3R9wp8sOmyT6+W9q8LzlHwOI7RzU7O/Cj4i91cerwY9JFQ9pFh9KlQr4z2GvGg+y9Znq5leVIuo7ZdjRbjqZvA391TgwOb3XnG57NguQx4ucDV5YoJwWVKd5TU1mfQdRQ7nnf7H15qCGQ7bgELA2KNdaG44rpVtltuvud0heb1kYZNOaG7Jo9yajoaRwvdd9sllaqKwbsoW8SuJg4xRbR8D+UWPJheYNQ/87k5kNSWPKgbrABvdq7OJq+EZv2DcebVc/bDAqfacMvhGGxM8qUy0e0F33QIBMvJxcC2Y5LZWhQ5qACiLGjwDFUIwPFoWE5ccmNZWS/CELz/jDVxnltGUp1Rcc99B3CZtQWvWc2i3/QnW/rcEzJzxSUzrdsVT0ZEjoj72j6NkwVRsnBYYNohQfJZVCx9YEr6skeDnoFBJ3lVghkOa5ag2qvR+OkvqkrLVpmW3RSP+v6qJ43I85Mry17kF3UIdAofl/Xu8ECy2Vm64roHfUdsnySLdLdZluvBpj9pLzVZltR7tH0bcOF420MDiEQvizhJQcEMX/usiIOZOtl+M9kV/skHeZ4cAR6EchyXOKCI+o0KKXxtTedVtupsFxEJ8IoblblVHmWolKylZwOKsPI9a0uvhFhxsWS1eqOq0RX6XXaS19k94VMW6xTHftEwjae+8QWpx9N37ahsQ4kHa/yOKSxykGNKPdW97nOr21S77NkMcOb1S/0MveMO43AlVmnSkSltRGzJbfv34omdaKFyodzwlGkQl96irYvrU92Hz3pj6UTDd06ShrKFqFEV/TaS98hTHJsCfVHmDf2NfVcDTgUZ+CwSucbjTiavm3s+waHbbqln5nlbb1kR33x/a2l3+QF8LvGRnUmzGaouDig5DJOpHmh/E5QXrKMCG1fqXdUpbKjy3dDsjvKxASVoVGwLEUw+bMc11q6ouAa+sK3L6xkC++7MduSHDpiGzgEdZRm76NPvU760fTtGKAE2WCOvYFRixbH2165CCRKt3baNxBkeT77w1SVgR+zvIbj0jP6MovmvTITgy7YoPtDXd+IhoFIaaDfSPYppQy93GUgcK2KR2dus6jvqay6Ug2rt0GloIKP0uHNhn2nciuNPEZbjL4bDUbP7ZArmwZ2qsm1jjKkt5mLjoaJ42ZZkQMlhkcg1fNquiJA/LP0DUoV/lnLFvG1Du1GcTqjG12kYVtfRzyIu8qdzklf9CkNssOcDnUxOdCLNMmOXHk2a32k8u908cx+FPEQRGP13JKm3qn7xr9ehoNVOEP2qWmrlWOM+pBuy8P1clPj9DWbLU1OVcrpzh+Ba1WcUNl1p7Om8uJEGo5LeYyakw1K6X0B+l9UtuOUlGZODdnw7tAY0yg7d2npgcrVbbDGnexAJYsGSGfC0Vw60ypsoCuycvWt9MuJrGyLdWCMwqulQsUZCPR1qL24Y5fKrVlPSvTNgbuilR0MfGwwlD04VHnq5Gvdq3agOCsVFc6VsMwIfFSks6emdHR+HdkR56RoJV/PzKJxxkUhyrV2WcTDC10uAtdmuioSv0BM43qie/swBY4lOUq08vW7yuO0+OX25GhK6cGp6E6Hxi8DINMadp0V8VzZNHJmaPUj1zeRKQ2wEURHw8VeGhF61R3eSemr6Yoi4p+lL2VKw8q24GSwp92ZtvHkFBmd4CDukdea2GfpW4p5tGPW4DBiWuGqZ+rMUp1+357aW8kxR4U8Znf1EAaBvEddJbqAf6Nu1JkTF9/V/m1RW5Y/nz8Cqg/Vt4WV44pqM+OyGVBwOiLmmZnTpMopujAK0z3ptOrwiAbnRqPGOXUcl/I4/jtZduTNUlXdaYVkpf1PEXNgkbS6jdqm8mvoigIl+laKl0RWsoXOLdURVR2e5N4XDR2WdcKjuGPfGemLOsVBdiw1OPxaSoweapA8c86p92J2JJfh0RUC46Fom0dwnkZnzPTM4HDKbJA9skEbxKvqqIy/3x0BEGg4LlUU/jkZoyxmQKxnU3knz3hEj6P5VPfKaSkeZjm69y0XMTvrWz55qjzW9CcF5OuyUWK7zFslNGZcoqXxoSsNDaf9j+5Dm9uL6SpZJ8nK1Rf9WV7jDi6hY9I9bJTr/lgXAccNpu3OJmTGP4vZIjmmR6cjUl7dOfE+nystF3dU3lPfJXGfPTgUFrSzzuAMkCwI41l7asZHd5ZU6Req96j4faXxzjuDTaVRP1/pssGJoslwKz70LR4cgWwErhIlbIT8VBWLBsJMo6q0CfqQJBo6o4e6V04r0sJjKFjlb5SLst9MkQ1z0dG5DAVsoMFVQWVoXKHxKF5tPFcE3cgiusK2UF+cPx0WdrC8ycEXHG3oWBX/kUvPdPJcQ2ExWyTE9ot6HaX0on6EJVnFc3HHjj31XQx32Q4vGxxafaQOWrvD1t6g8rxrcOx1DJEGvODJ0qwNLNp8mW0NDdSgp2z7vTJAoj01HI940dZDP6C7B0dgNQQ6jkuVjwbBxRIhI+RG5dRzJ6hM6DjJUJyRPhe/d8boi8bRN9s6KY8GQCNj9gEfC8hmdDoaYrmxX9F+C6OWjFHedQKVna1rTYdSfYMd4lPvTMCXd2aB5xt7SN2XsiXyDoMT8azrUIlVOp3f77omdc5VwVrkDPRdBPdokuGQNTiMZcG6tz1BI6xshmTOvtOGRUP7HhvcwC4MOIgQVI5n2uUjxWkPISh+XxHqHLr1OUqjJf9NePA/jkABAtc9ZWhYOJ2pMx5bvgr7Wy2eg40s0tryybd6ZuZDxabxDZaNjQXZoaHo+Q/F2w2Khg7fQKM7DqP34Ijyx0KRrjBdUl/xqjqNqPA/Y4on8ufa8lI8wwwA3tKJd2EdPJ0YnZnlcyAj6dhEMzXsru8SuINDxALnQb2cvBwuWg5FTHE4J3TVhfN6ojuztHp7wpkNHrgSvbUZBqLWtpH/eYuXkk63SmPGD0/ksfzerqPQEXB+nWXlkON/HIEJCFynaFThOBDBiJ6OYjSIdrABjDFQeZwU8mjINCgunM1gUBkahi1TJWlFw7JM375XssxQYqmu8NxD35VtGdxnGZJdkrcA9pvqO2Jj7uAwsBMGo+2iJdecfdWmxIN2NuXQk+1v0TbrM/yWiFC3rY0xeCTg9CwtJNT+wHexdyF7cIQvdS/uh1QWx4xe5qyx1xw9gzACchiIMfAolgWjrcIS2AzpuhduSceFolJo0CEMGVOYRwNjNsSonZGiVZpCdqsW21NXa0RjBjLbmRL2tGWKfm2avfRdFHfV76zBYRuEqc+0I2SJnllQ7oErOvFBh5XQw+gfKq/PcYW9zkTZ0iRm/jiV4iBs2Os7l/9uUGxHouBsbBI8q6S9cLuqNNg5IgBshMPSHqPR1YNk0rnzYk+K/6xrUuUX3ea6Rh3RNywToW9Ms+Um9hJtn5DO/aTn0SUl0Wxui2QW4R5t2kvfRXGPtvDLFFsM0Kw9Td5Ti++I9pC1pFezx2YumFoF5cNz7pJxnR/1P4Sosz1m31XedH41UPgn5S32ziSTNmvLsANi87PEdzFshqTvgVvvjGtI0RXz6BxozItV7CFdJeed8kuXLDbVFTuivo2ZsNLYw7BNeMgIDZoPSYN/N7VlJu4Ysoe+DUwXwn3wpSyVKV2z9tREz+AxDH50x9kxQxo7fVhXl8GFOYF6OnHSs5xhm4E9SycGQOypvtGFQ7zRRZsuDfaO0X8oNH57c4hwr7wVsBkyZXPczmbGBSo0Dl0GwhBQu+cdSdcxsI5my9H0HcN/o3xmXXT0oweuhC/LmHyPeU8XBzFynBbmhIGnyuFM2oElxDHH0C7T97z0f1MIzlZ6NwbOejYnflIcx9i3BNqn5x7pS2MzZMPmuJ2V4xpCxvMcAUegHAF1uHS2OIyqEy7nNlrydaR4kKDku7LZS23iQWfJsh3B+HFwYk7A0TacquSw3NaYYS2h/xwlx8quhM2Q2M1xux7SxvMcAUfg7iCgDm2r1Qzr/JFXLWNLPo7FnEwxsOLDzPGkuy0LGs+Q3mYsOjrWp7pYVuz89wfoRRNmDYryE2wsRd/oIg2efALQCVP4dgqtnCCdsrCZq04JbnNlUt4d1xIoOg9HwBGoEFBnxqlgnAoOox5wBEvsbz0Qf3OO8EcWIelglM5BJo6vMwNs66SkEMypL/bfDYzxxvdcbOaqV4LbXJnuuGYj6AwcAUcghQCOhRNz9Q+RcR7MZoqD+OF4OEFbP1TF7IjQWSpEPum649zQqe7w9FiFMOMSXWN/S7kNeuWz1Mlhl6l8gwDRs0QbZFQSP0Tgwyzv61Y6j3zKULczQfJvkmizsPm35KxYFm6zJNUKX9fiHnUEHAFHYCkE2OfidCKzHOv8b9W55n5A3daHTr7TmStt1n9/kBA6fdOzLtM+JThJBk6GjtqcG85wUlBZPgDvBKWDUe6pzQ6fmFCCTR+vqekluE3l3UvnjqsXGs9wBByBGQiYEwgdW+z0bS+qiC2dvK6+E33sXzVmXKINMxClM+tjxpP87w/KC7MG5XeWMZVXd07skz2fyle0mwXplIsNWLGEyv2RLsOAU5/f6Hqsi8AgIfmfJgpwmy0zaKQ/7rgMCb87Ao7AYgioU2M5DX7sgXCcno7RZiqK5gXxajilRGkcTIMm6sBM54niyRlP5GP7NOZsO+xVHidoS47YNoVvh88aCdKlYXdCRgobW4bkxGQ14xMvfrKLH2MImOjOgIDl3dT+YS5u7H3iCOfIVPHT6Sr89T+OgCPgCCyPAI6KpUICI/nOjCbkjPxRZ0fHXPrfFEa4h2yW606Sk3SsSsfp/q6rWjaE/hzCTGxwSoS6w2ZWXMeB5xuIEqEEt7kygxo+40q8DU9yBByBRRAIv2gRO1f2t4ZmPR2Bor+vRJazcBwnPS/23x8i75dii1MMMxalIcs6Vjpr5Fu+/fqIkvYPUf9FsBEvZmT10PufJpbCLUdmXTGLu+MyJPzuCDgCSyNQ/6X4bN6xc7PlqGR50bDn1bfvlSxDYuTNstUhw5rYDAFyLri54xp6S57nCDgCcxCwJShmWhafw+8ult0Tl74lwDbOzDyXCovIvPf+/fulFHI+joAj4Ag0ENAI3TqYrxTPnhk1mGU+SB4dLsuB7MUgmxOB9f0bJeWHtfjma1JeItpgS438NiXvh5+34vQly6UMNsCKgxks1fJPQmd9yrCkTHdceiMeHAFHYB0E1FlxIIOO7yPF23sp6wh1rncegas7b6Eb6Ag4AnsiwKido9futPZ8C3dMtu9x3bEX6uY4AmeGQNER+DOzwdU5MwT+D/q8oWBFUWGOAAAAAElFTkSuQmCC\n",
- "text/latex": [
- "$\\displaystyle \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}$"
- ],
- "text/plain": [
- " \n",
- " ______________ ______________ ______________ ______________ _____\n",
- "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\bar\n",
- " \n",
- "\n",
- " _______________________________________________________\n",
- "_______ ╱ w \n",
- "{\\tau} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── \n",
- " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} "
- ]
- },
- "execution_count": 35,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "py_vars = ('w', 'tau', 'p', 'L_b', 'A_f', 'A_m', 'E_f', 'E_m')\n",
- "map_py2sp = {py_var : globals()[py_var] for py_var in py_vars}\n",
- "sp_vars = tuple(map_py2sp[py_var] for py_var in py_vars)\n",
- "sp_vars\n",
- "Pw_pull_elastic"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "For plotting, let us also evaluate the for the displacement at the unloaded end\n",
- "\\begin{align}\n",
- "w = u_\\mathrm{f}(x = -L_\\mathrm{b})\n",
- "\\end{align}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 36,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/latex": [
- "$\\displaystyle \\begin{cases} \\frac{A_\\mathrm{f} E_\\mathrm{f} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} & \\text{for}\\: L_{b} \\geq \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}} \\\\\\frac{A_\\mathrm{f} E_\\mathrm{f} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} + \\frac{A_\\mathrm{m} E_\\mathrm{m} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} + \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{m}} L_{b} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}}{\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}}} & \\text{otherwise} \\end{cases}$"
- ],
- "text/plain": [
- "⎧ \n",
- "⎪ \n",
- "⎪ \n",
- "⎪ \n",
- "⎪ \n",
- "⎪ \n",
- "⎪ \n",
- "⎨ \n",
- "⎪ \n",
- "⎪ \n",
- "⎪ \n",
- "⎪ A_\\mathrm{f}⋅E_\\mathrm{f}⋅w A_\\mathr\n",
- "⎪───────────────────────────────────────────────────── + ─────────────────────\n",
- "⎪A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} A_\\mathrm{f}⋅E_\\mathr\n",
- "⎩ \n",
- "\n",
- " \n",
- " \n",
- " \n",
- " A_\\mathrm{f}â‹…E_\\mathrm{f}â‹…w \n",
- " ────────────────────────────────────────────────────\n",
- " A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m\n",
- " \n",
- " \n",
- " \n",
- " ________\n",
- " 2 √2⋅╲╱ A_\\math\n",
- "m{m}â‹…E_\\mathrm{m}â‹…w L_b â‹…\\bar{\\tau}â‹…p \n",
- "──────────────────────────────── + ─────────────────────────── - ─────────────\n",
- "m{f} + A_\\mathrm{m}â‹…E_\\mathrm{m} 2â‹…A_\\mathrm{f}â‹…E_\\mathrm{f} \n",
- " \n",
- "\n",
- " \n",
- " \n",
- " \n",
- " \n",
- "─ \n",
- "} \n",
- " \n",
- " \n",
- " ____________________________\n",
- "______ ______________ ____________ ╱ w\n",
- "rm{m} ⋅╲╱ E_\\mathrm{m} ⋅L_b⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ───────────────────────────\n",
- " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} +\n",
- "──────────────────────────────────────────────────────────────────────────────\n",
- " ______________ ______________ \n",
- " ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} \n",
- "\n",
- " \n",
- " ______________ ______________ \n",
- " √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱\n",
- " \n",
- " for L_b ≥ ───────────────────────────────────────\n",
- " \n",
- " \n",
- " \n",
- "___________________________ \n",
- " \n",
- "────────────────────────── \n",
- " A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
- "─────────────────────────── \n",
- " \n",
- " \n",
- "\n",
- " __________________________________________\n",
- "______________ ______________ ╱ w \n",
- " E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅ ╱ ─────────────────────────────────────────\n",
- " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅\n",
- "──────────────────────────────────────────────────────────────────────────────\n",
- " ____________ \n",
- " ╲╱ \\bar{\\tau} ⋅√p \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " otherwise \n",
- " \n",
- " \n",
- "\n",
- "_____________\n",
- " \n",
- "──────────── \n",
- "E_\\mathrm{m} \n",
- "─────────────\n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " "
- ]
- },
- "execution_count": 36,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "w_L_b_elastic = u_fa_x.subs(x, -L_b).subs(P, Pw_pull_elastic)\n",
- "w_L_b_elastic"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "and also the expression for the debonded length as a function of the control displacement $w$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 37,
- "metadata": {
- "slideshow": {
- "slide_type": "fragment"
- }
- },
- "outputs": [
- {
- "data": {
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\n",
- "text/latex": [
- "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}}$"
- ],
- "text/plain": [
- " ___\n",
- " ______________ ______________ ______________ ______________ ╱ \n",
- "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅ ╱ ──\n",
- " ╲╱ A_\n",
- "──────────────────────────────────────────────────────────────────────────────\n",
- " ____________ \n",
- " ╲╱ \\bar{\\tau} ⋅√p \n",
- "\n",
- "____________________________________________________\n",
- " w \n",
- "─────────────────────────────────────────────────── \n",
- "\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
- "────────────────────────────────────────────────────\n",
- " \n",
- " "
- ]
- },
- "execution_count": 37,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "aw_pull_elastic = a_subs[a].subs(P, Pw_pull_elastic)\n",
- "aw_pull_elastic"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 38,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "outputs": [],
- "source": [
- "import traits.api as tr\n",
- "\n",
- "class PO_LF_LM_EL(tr.HasTraits):\n",
- "\n",
- " get_Pw_pull = sp.lambdify(sp_vars, Pw_pull_elastic)\n",
- " get_aw_pull = sp.lambdify(sp_vars, aw_pull_elastic)\n",
- " get_w_L_b = sp.lambdify(sp_vars, w_L_b_elastic)\n",
- " get_u_fa_x = sp.lambdify((x,) + sp_vars, u_fa_x.subs(P, Pw_pull_elastic))\n",
- " get_u_ma_x = sp.lambdify((x,) + sp_vars, u_ma_x.subs(P, Pw_pull_elastic))\n",
- " get_eps_f_x = sp.lambdify((x,) + sp_vars, eps_f_x.subs(P, Pw_pull_elastic))\n",
- " get_eps_m_x = sp.lambdify((x,) + sp_vars, eps_m_x.subs(P, Pw_pull_elastic))\n",
- " get_sig_f_x = sp.lambdify((x,) + sp_vars, sig_f_x.subs(P, Pw_pull_elastic))\n",
- " get_sig_m_x = sp.lambdify((x,) + sp_vars, sig_m_x.subs(P, Pw_pull_elastic))\n",
- " get_tau_x = sp.lambdify((x,) + sp_vars, tau_x.subs(P, Pw_pull_elastic))\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "### Interactive exploration\n",
- "Now that we have finished the construction of the model we can track the process and explore the correspondence between the internal state and externally observed response"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 39,
- "metadata": {},
- "outputs": [],
- "source": [
- "po = poui.ModelInteract(\n",
- " models=[PO_LF_LM_EL],\n",
- " py_vars=list(py_vars),\n",
- " map_py2sp=map_py2sp,\n",
- " E_f=1, A_f=1, p=1, tau=1,L_b=10, E_m=1, A_m=1\n",
- ")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 40,
- "metadata": {
- "hide_input": false,
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "outputs": [
- {
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- " } else {\n",
- " alert('Your browser does not have WebSocket support. ' +\n",
- " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
- " 'Firefox 4 and 5 are also supported but you ' +\n",
- " 'have to enable WebSockets in about:config.');\n",
- " };\n",
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- " if (warnings) {\n",
- " warnings.style.display = 'block';\n",
- " warnings.textContent = (\n",
- " \"This browser does not support binary websocket messages. \" +\n",
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- " }\n",
- " }\n",
- "\n",
- " this.imageObj = new Image();\n",
- "\n",
- " this.context = undefined;\n",
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- "mpl.figure.prototype._init_header = function() {\n",
- " var titlebar = $(\n",
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- "\n",
- " function canvas_keyboard_event(event) {\n",
- " return fig.key_event(event, event['data']);\n",
- " }\n",
- "\n",
- " canvas_div.keydown('key_press', canvas_keyboard_event);\n",
- " canvas_div.keyup('key_release', canvas_keyboard_event);\n",
- " this.canvas_div = canvas_div\n",
- " this._canvas_extra_style(canvas_div)\n",
- " this.root.append(canvas_div);\n",
- "\n",
- " var canvas = $('<canvas/>');\n",
- " canvas.addClass('mpl-canvas');\n",
- " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
- "\n",
- " this.canvas = canvas[0];\n",
- " this.context = canvas[0].getContext(\"2d\");\n",
- "\n",
- " var backingStore = this.context.backingStorePixelRatio ||\n",
- "\tthis.context.webkitBackingStorePixelRatio ||\n",
- "\tthis.context.mozBackingStorePixelRatio ||\n",
- "\tthis.context.msBackingStorePixelRatio ||\n",
- "\tthis.context.oBackingStorePixelRatio ||\n",
- "\tthis.context.backingStorePixelRatio || 1;\n",
- "\n",
- " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
- "\n",
- " var rubberband = $('<canvas/>');\n",
- " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
- "\n",
- " var pass_mouse_events = true;\n",
- "\n",
- " canvas_div.resizable({\n",
- " start: function(event, ui) {\n",
- " pass_mouse_events = false;\n",
- " },\n",
- " resize: function(event, ui) {\n",
- " fig.request_resize(ui.size.width, ui.size.height);\n",
- " },\n",
- " stop: function(event, ui) {\n",
- " pass_mouse_events = true;\n",
- " fig.request_resize(ui.size.width, ui.size.height);\n",
- " },\n",
- " });\n",
- "\n",
- " function mouse_event_fn(event) {\n",
- " if (pass_mouse_events)\n",
- " return fig.mouse_event(event, event['data']);\n",
- " }\n",
- "\n",
- " rubberband.mousedown('button_press', mouse_event_fn);\n",
- " rubberband.mouseup('button_release', mouse_event_fn);\n",
- " // Throttle sequential mouse events to 1 every 20ms.\n",
- " rubberband.mousemove('motion_notify', mouse_event_fn);\n",
- "\n",
- " rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
- " rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
- "\n",
- " canvas_div.on(\"wheel\", function (event) {\n",
- " event = event.originalEvent;\n",
- " event['data'] = 'scroll'\n",
- " if (event.deltaY < 0) {\n",
- " event.step = 1;\n",
- " } else {\n",
- " event.step = -1;\n",
- " }\n",
- " mouse_event_fn(event);\n",
- " });\n",
- "\n",
- " canvas_div.append(canvas);\n",
- " canvas_div.append(rubberband);\n",
- "\n",
- " this.rubberband = rubberband;\n",
- " this.rubberband_canvas = rubberband[0];\n",
- " this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
- " this.rubberband_context.strokeStyle = \"#000000\";\n",
- "\n",
- " this._resize_canvas = function(width, height) {\n",
- " // Keep the size of the canvas, canvas container, and rubber band\n",
- " // canvas in synch.\n",
- " canvas_div.css('width', width)\n",
- " canvas_div.css('height', height)\n",
- "\n",
- " canvas.attr('width', width * mpl.ratio);\n",
- " canvas.attr('height', height * mpl.ratio);\n",
- " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
- "\n",
- " rubberband.attr('width', width);\n",
- " rubberband.attr('height', height);\n",
- " }\n",
- "\n",
- " // Set the figure to an initial 600x600px, this will subsequently be updated\n",
- " // upon first draw.\n",
- " this._resize_canvas(600, 600);\n",
- "\n",
- " // Disable right mouse context menu.\n",
- " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
- " return false;\n",
- " });\n",
- "\n",
- " function set_focus () {\n",
- " canvas.focus();\n",
- " canvas_div.focus();\n",
- " }\n",
- "\n",
- " window.setTimeout(set_focus, 100);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('<div/>');\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items) {\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) {\n",
- " // put a spacer in here.\n",
- " continue;\n",
- " }\n",
- " var button = $('<button/>');\n",
- " button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
- " 'ui-button-icon-only');\n",
- " button.attr('role', 'button');\n",
- " button.attr('aria-disabled', 'false');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- "\n",
- " var icon_img = $('<span/>');\n",
- " icon_img.addClass('ui-button-icon-primary ui-icon');\n",
- " icon_img.addClass(image);\n",
- " icon_img.addClass('ui-corner-all');\n",
- "\n",
- " var tooltip_span = $('<span/>');\n",
- " tooltip_span.addClass('ui-button-text');\n",
- " tooltip_span.html(tooltip);\n",
- "\n",
- " button.append(icon_img);\n",
- " button.append(tooltip_span);\n",
- "\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " var fmt_picker_span = $('<span/>');\n",
- "\n",
- " var fmt_picker = $('<select/>');\n",
- " fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
- " fmt_picker_span.append(fmt_picker);\n",
- " nav_element.append(fmt_picker_span);\n",
- " this.format_dropdown = fmt_picker[0];\n",
- "\n",
- " for (var ind in mpl.extensions) {\n",
- " var fmt = mpl.extensions[ind];\n",
- " var option = $(\n",
- " '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
- " fmt_picker.append(option);\n",
- " }\n",
- "\n",
- " // Add hover states to the ui-buttons\n",
- " $( \".ui-button\" ).hover(\n",
- " function() { $(this).addClass(\"ui-state-hover\");},\n",
- " function() { $(this).removeClass(\"ui-state-hover\");}\n",
- " );\n",
- "\n",
- " var status_bar = $('<span class=\"mpl-message\"/>');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
- " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
- " // which will in turn request a refresh of the image.\n",
- " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_message = function(type, properties) {\n",
- " properties['type'] = type;\n",
- " properties['figure_id'] = this.id;\n",
- " this.ws.send(JSON.stringify(properties));\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.send_draw_message = function() {\n",
- " if (!this.waiting) {\n",
- " this.waiting = true;\n",
- " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
- " }\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " var format_dropdown = fig.format_dropdown;\n",
- " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
- " fig.ondownload(fig, format);\n",
- "}\n",
- "\n",
- "\n",
- "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
- " var size = msg['size'];\n",
- " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
- " fig._resize_canvas(size[0], size[1]);\n",
- " fig.send_message(\"refresh\", {});\n",
- " };\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
- " var x0 = msg['x0'] / mpl.ratio;\n",
- " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
- " var x1 = msg['x1'] / mpl.ratio;\n",
- " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
- " x0 = Math.floor(x0) + 0.5;\n",
- " y0 = Math.floor(y0) + 0.5;\n",
- " x1 = Math.floor(x1) + 0.5;\n",
- " y1 = Math.floor(y1) + 0.5;\n",
- " var min_x = Math.min(x0, x1);\n",
- " var min_y = Math.min(y0, y1);\n",
- " var width = Math.abs(x1 - x0);\n",
- " var height = Math.abs(y1 - y0);\n",
- "\n",
- " fig.rubberband_context.clearRect(\n",
- " 0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
- "\n",
- " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
- " // Updates the figure title.\n",
- " fig.header.textContent = msg['label'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
- " var cursor = msg['cursor'];\n",
- " switch(cursor)\n",
- " {\n",
- " case 0:\n",
- " cursor = 'pointer';\n",
- " break;\n",
- " case 1:\n",
- " cursor = 'default';\n",
- " break;\n",
- " case 2:\n",
- " cursor = 'crosshair';\n",
- " break;\n",
- " case 3:\n",
- " cursor = 'move';\n",
- " break;\n",
- " }\n",
- " fig.rubberband_canvas.style.cursor = cursor;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
- " fig.message.textContent = msg['message'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
- " // Request the server to send over a new figure.\n",
- " fig.send_draw_message();\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
- " fig.image_mode = msg['mode'];\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Called whenever the canvas gets updated.\n",
- " this.send_message(\"ack\", {});\n",
- "}\n",
- "\n",
- "// A function to construct a web socket function for onmessage handling.\n",
- "// Called in the figure constructor.\n",
- "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
- " return function socket_on_message(evt) {\n",
- " if (evt.data instanceof Blob) {\n",
- " /* FIXME: We get \"Resource interpreted as Image but\n",
- " * transferred with MIME type text/plain:\" errors on\n",
- " * Chrome. But how to set the MIME type? It doesn't seem\n",
- " * to be part of the websocket stream */\n",
- " evt.data.type = \"image/png\";\n",
- "\n",
- " /* Free the memory for the previous frames */\n",
- " if (fig.imageObj.src) {\n",
- " (window.URL || window.webkitURL).revokeObjectURL(\n",
- " fig.imageObj.src);\n",
- " }\n",
- "\n",
- " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
- " evt.data);\n",
- " fig.updated_canvas_event();\n",
- " fig.waiting = false;\n",
- " return;\n",
- " }\n",
- " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
- " fig.imageObj.src = evt.data;\n",
- " fig.updated_canvas_event();\n",
- " fig.waiting = false;\n",
- " return;\n",
- " }\n",
- "\n",
- " var msg = JSON.parse(evt.data);\n",
- " var msg_type = msg['type'];\n",
- "\n",
- " // Call the \"handle_{type}\" callback, which takes\n",
- " // the figure and JSON message as its only arguments.\n",
- " try {\n",
- " var callback = fig[\"handle_\" + msg_type];\n",
- " } catch (e) {\n",
- " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
- " return;\n",
- " }\n",
- "\n",
- " if (callback) {\n",
- " try {\n",
- " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
- " callback(fig, msg);\n",
- " } catch (e) {\n",
- " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
- " }\n",
- " }\n",
- " };\n",
- "}\n",
- "\n",
- "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
- "mpl.findpos = function(e) {\n",
- " //this section is from http://www.quirksmode.org/js/events_properties.html\n",
- " var targ;\n",
- " if (!e)\n",
- " e = window.event;\n",
- " if (e.target)\n",
- " targ = e.target;\n",
- " else if (e.srcElement)\n",
- " targ = e.srcElement;\n",
- " if (targ.nodeType == 3) // defeat Safari bug\n",
- " targ = targ.parentNode;\n",
- "\n",
- " // jQuery normalizes the pageX and pageY\n",
- " // pageX,Y are the mouse positions relative to the document\n",
- " // offset() returns the position of the element relative to the document\n",
- " var x = e.pageX - $(targ).offset().left;\n",
- " var y = e.pageY - $(targ).offset().top;\n",
- "\n",
- " return {\"x\": x, \"y\": y};\n",
- "};\n",
- "\n",
- "/*\n",
- " * return a copy of an object with only non-object keys\n",
- " * we need this to avoid circular references\n",
- " * http://stackoverflow.com/a/24161582/3208463\n",
- " */\n",
- "function simpleKeys (original) {\n",
- " return Object.keys(original).reduce(function (obj, key) {\n",
- " if (typeof original[key] !== 'object')\n",
- " obj[key] = original[key]\n",
- " return obj;\n",
- " }, {});\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.mouse_event = function(event, name) {\n",
- " var canvas_pos = mpl.findpos(event)\n",
- "\n",
- " if (name === 'button_press')\n",
- " {\n",
- " this.canvas.focus();\n",
- " this.canvas_div.focus();\n",
- " }\n",
- "\n",
- " var x = canvas_pos.x * mpl.ratio;\n",
- " var y = canvas_pos.y * mpl.ratio;\n",
- "\n",
- " this.send_message(name, {x: x, y: y, button: event.button,\n",
- " step: event.step,\n",
- " guiEvent: simpleKeys(event)});\n",
- "\n",
- " /* This prevents the web browser from automatically changing to\n",
- " * the text insertion cursor when the button is pressed. We want\n",
- " * to control all of the cursor setting manually through the\n",
- " * 'cursor' event from matplotlib */\n",
- " event.preventDefault();\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " // Handle any extra behaviour associated with a key event\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.key_event = function(event, name) {\n",
- "\n",
- " // Prevent repeat events\n",
- " if (name == 'key_press')\n",
- " {\n",
- " if (event.which === this._key)\n",
- " return;\n",
- " else\n",
- " this._key = event.which;\n",
- " }\n",
- " if (name == 'key_release')\n",
- " this._key = null;\n",
- "\n",
- " var value = '';\n",
- " if (event.ctrlKey && event.which != 17)\n",
- " value += \"ctrl+\";\n",
- " if (event.altKey && event.which != 18)\n",
- " value += \"alt+\";\n",
- " if (event.shiftKey && event.which != 16)\n",
- " value += \"shift+\";\n",
- "\n",
- " value += 'k';\n",
- " value += event.which.toString();\n",
- "\n",
- " this._key_event_extra(event, name);\n",
- "\n",
- " this.send_message(name, {key: value,\n",
- " guiEvent: simpleKeys(event)});\n",
- " return false;\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
- " if (name == 'download') {\n",
- " this.handle_save(this, null);\n",
- " } else {\n",
- " this.send_message(\"toolbar_button\", {name: name});\n",
- " }\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
- " this.message.textContent = tooltip;\n",
- "};\n",
- "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
- "\n",
- "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
- "\n",
- "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
- " // Create a \"websocket\"-like object which calls the given IPython comm\n",
- " // object with the appropriate methods. Currently this is a non binary\n",
- " // socket, so there is still some room for performance tuning.\n",
- " var ws = {};\n",
- "\n",
- " ws.close = function() {\n",
- " comm.close()\n",
- " };\n",
- " ws.send = function(m) {\n",
- " //console.log('sending', m);\n",
- " comm.send(m);\n",
- " };\n",
- " // Register the callback with on_msg.\n",
- " comm.on_msg(function(msg) {\n",
- " //console.log('receiving', msg['content']['data'], msg);\n",
- " // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
- " ws.onmessage(msg['content']['data'])\n",
- " });\n",
- " return ws;\n",
- "}\n",
- "\n",
- "mpl.mpl_figure_comm = function(comm, msg) {\n",
- " // This is the function which gets called when the mpl process\n",
- " // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
- "\n",
- " var id = msg.content.data.id;\n",
- " // Get hold of the div created by the display call when the Comm\n",
- " // socket was opened in Python.\n",
- " var element = $(\"#\" + id);\n",
- " var ws_proxy = comm_websocket_adapter(comm)\n",
- "\n",
- " function ondownload(figure, format) {\n",
- " window.open(figure.imageObj.src);\n",
- " }\n",
- "\n",
- " var fig = new mpl.figure(id, ws_proxy,\n",
- " ondownload,\n",
- " element.get(0));\n",
- "\n",
- " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
- " // web socket which is closed, not our websocket->open comm proxy.\n",
- " ws_proxy.onopen();\n",
- "\n",
- " fig.parent_element = element.get(0);\n",
- " fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
- " if (!fig.cell_info) {\n",
- " console.error(\"Failed to find cell for figure\", id, fig);\n",
- " return;\n",
- " }\n",
- "\n",
- " var output_index = fig.cell_info[2]\n",
- " var cell = fig.cell_info[0];\n",
- "\n",
- "};\n",
- "\n",
- "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
- " var width = fig.canvas.width/mpl.ratio\n",
- " fig.root.unbind('remove')\n",
- "\n",
- " // Update the output cell to use the data from the current canvas.\n",
- " fig.push_to_output();\n",
- " var dataURL = fig.canvas.toDataURL();\n",
- " // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
- " // the notebook keyboard shortcuts fail.\n",
- " IPython.keyboard_manager.enable()\n",
- " $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
- " fig.close_ws(fig, msg);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.close_ws = function(fig, msg){\n",
- " fig.send_message('closing', msg);\n",
- " // fig.ws.close()\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
- " // Turn the data on the canvas into data in the output cell.\n",
- " var width = this.canvas.width/mpl.ratio\n",
- " var dataURL = this.canvas.toDataURL();\n",
- " this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
- "}\n",
- "\n",
- "mpl.figure.prototype.updated_canvas_event = function() {\n",
- " // Tell IPython that the notebook contents must change.\n",
- " IPython.notebook.set_dirty(true);\n",
- " this.send_message(\"ack\", {});\n",
- " var fig = this;\n",
- " // Wait a second, then push the new image to the DOM so\n",
- " // that it is saved nicely (might be nice to debounce this).\n",
- " setTimeout(function () { fig.push_to_output() }, 1000);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._init_toolbar = function() {\n",
- " var fig = this;\n",
- "\n",
- " var nav_element = $('<div/>');\n",
- " nav_element.attr('style', 'width: 100%');\n",
- " this.root.append(nav_element);\n",
- "\n",
- " // Define a callback function for later on.\n",
- " function toolbar_event(event) {\n",
- " return fig.toolbar_button_onclick(event['data']);\n",
- " }\n",
- " function toolbar_mouse_event(event) {\n",
- " return fig.toolbar_button_onmouseover(event['data']);\n",
- " }\n",
- "\n",
- " for(var toolbar_ind in mpl.toolbar_items){\n",
- " var name = mpl.toolbar_items[toolbar_ind][0];\n",
- " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
- " var image = mpl.toolbar_items[toolbar_ind][2];\n",
- " var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
- "\n",
- " if (!name) { continue; };\n",
- "\n",
- " var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
- " button.click(method_name, toolbar_event);\n",
- " button.mouseover(tooltip, toolbar_mouse_event);\n",
- " nav_element.append(button);\n",
- " }\n",
- "\n",
- " // Add the status bar.\n",
- " var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
- " nav_element.append(status_bar);\n",
- " this.message = status_bar[0];\n",
- "\n",
- " // Add the close button to the window.\n",
- " var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
- " var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
- " button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
- " button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
- " buttongrp.append(button);\n",
- " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
- " titlebar.prepend(buttongrp);\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._root_extra_style = function(el){\n",
- " var fig = this\n",
- " el.on(\"remove\", function(){\n",
- "\tfig.close_ws(fig, {});\n",
- " });\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._canvas_extra_style = function(el){\n",
- " // this is important to make the div 'focusable\n",
- " el.attr('tabindex', 0)\n",
- " // reach out to IPython and tell the keyboard manager to turn it's self\n",
- " // off when our div gets focus\n",
- "\n",
- " // location in version 3\n",
- " if (IPython.notebook.keyboard_manager) {\n",
- " IPython.notebook.keyboard_manager.register_events(el);\n",
- " }\n",
- " else {\n",
- " // location in version 2\n",
- " IPython.keyboard_manager.register_events(el);\n",
- " }\n",
- "\n",
- "}\n",
- "\n",
- "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
- " var manager = IPython.notebook.keyboard_manager;\n",
- " if (!manager)\n",
- " manager = IPython.keyboard_manager;\n",
- "\n",
- " // Check for shift+enter\n",
- " if (event.shiftKey && event.which == 13) {\n",
- " this.canvas_div.blur();\n",
- " // select the cell after this one\n",
- " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
- " IPython.notebook.select(index + 1);\n",
- " }\n",
- "}\n",
+ " -P ⎞⎞\n",
+ " for x ≤ ────────────⎟⎟\n",
+ " \\bar{\\tau}⋅p⎟⎟\n",
+ " ⎟⎟\n",
+ "p⋅x ⎟⎟\n",
+ "──────── otherwise ⎟⎟\n",
+ "athrm{m} ⎠⎠"
+ ]
+ },
+ "execution_count": 44,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sig_f_x = E_f * eps_f_x\n",
+ "sig_m_x = E_m * eps_m_x\n",
+ "sig_f_x, sig_m_x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "The profile of shear stress along the bond zone is obtained as\n",
+ "\\begin{align}\n",
+ " \\tau = \\frac{\\mathrm{d} \\sigma}{\\mathrm{d} x}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 45,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJkAAAA/CAYAAADzGWpJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAALzElEQVR4Ae2d63UUOwzHl5wUkBsquNABhAoIHQCpgNABnHzjWw50AFQA3A6ACnh0AB0A6YD7/2ktH8+M57E7s4/sWuc4HsuyrJE1suzxbG78/ft31gcvXry4JZoPSj91/aiPvtQXDaQaOEgLuWsZ1bnwP5R+Kz3J0RRc0UCXBg67KmVgz1T/UumNrp920Za6ooE2Ddxomy5lVKdq9FHpu67vtjEo+P3SQLCL57pr7OON0pXSkdKxEvBcND/nl/O/XZ7sdSAsU2SqsT2/lgF9UiJGv6W8MrupzKyHY7qdqikbk4n4DkyU8GLf0wblumhAGnig9CmjiV/CYTcVyBqZKM4C1bsKdSkUDcw14KFUXR94tv/qyLbp0q2xMrfWG29bWV6XlTDxAR4496Rtm8jXTh7pFdtAx1G/AcdUyVRamUK5wTYjo24hEHM6AXCZzMkvhVubkaqvb+rzUumr0jeVHyhFRQhXYBoN4MUI9s+lX+fIOD9RGXwDJjEyMbcBVm6uUjmW7gO9ckNTf+bB6F+JJw05MLadAd3XQ93MhdIjXa9cpx2Ks3hMMrzqoKlUjTYydRYH2DkLd6XEQLNCRahVA33YAkX9MgA781Yi6JctA7zyfXSrfJOAJ0OewTDayNQTA5pbgX4R/pmUcrQmxfBGYmdAOmMj3APpu2vSYaf+JEMjHutsECqnMDIsm025OrhLp96m0TpBKVc1oEEkzGBKZGp8rXJlv6lKvd6SZMHofVZ6qvKl0iCvOsrI1AlK6QPfCe6jW7he/bOfx6BgyDOVrS/lNl0qRz4WJLx7BRi0D8LbgkA57ajnCWXRwINxTwl8Z+wTeBMqALR5ogQf3/75IppBD1fghRwmj8pbY1ySyUAyEYMNjsNCM8sO08IS125AXRY9xBCX6NqMimkaY+CEyEy5GVe4xgDBs8p0rwrNR6U7Sq+UMDamoj/KGVjoiCN5ahnwnIcW2oDVsy3XlUP/VgnD4rUKPDCaTiMTHbqhnRm5ysZP5Z2CgzXczc019JHrAgNjtRkNLBARtGIgGKED8dypcE7/j65bDUx1eDCMyIGHjCnO2/DwpfVOV8nFp+vhrNBe58JYT9YVbLuXY99sraDBw4DwDiw+KqA6NmrBMa3hCQEGOxrjgMH/KppIr7YcIICvGY3y6FGF7wRolZAVD4hh8gC4sXa2batU+yPVfVYiHwrI4fqwNir3HzYcwH2UkUkItiroJnczjksHY4BIk5AwaMDVPMv+TT0ZBF0PTIVBfTBU+ViJmG4pED90RDCNzi6UE0MS+C8VA6kd9z365Iz43BCf0TDKyELvxDU+qKlA7sksyE4r1nDthu2GnuvSabyuyyCdppFrIE6FpJ8Yfwln/YbBbrRpQwR6pnO8Gts/GBt8B6/k2nhvEn8wQefEPicZPpUpJFO/MpQGB7eP0fiSO/alOowCQO6FQe3Z92Px4HwI1vHoqdHijZYyWhdI7VmYsBjB0Hh7gmcz43Wa65KPNjLdOPHDb+UEvgZBGUwhLOvXASi/PgD3hXssWerTInGPryxdtlx7r6vnGBeJe6ZdZZoVjrpGLCjcUiB+nErG2Din9VnX9ftZiu8ijdTnuRKxYiUN5ZE9GStmPOUYDcFgnAbamIoGZTN4V0oE+uwb4eIrgaRwk4L4o3DfJ0MGZGUbwWIZ5UzjTD/IBVDGI6T7ZHgi7hUa8O9U33rPqqMf7hUPM1MZg6U9XpN3uBhfa3vV7x1MYmR7p7U9umE9MDyYOJ2cB7WTLqJhS4fwiIfMgYfOHM2hY2o5T2uBPdeAjAc7YCawF/MqMwtUNowDDZrCEO3otXB8Ovk14G63GdkxrQQrne7mXezv3zBA6dM/RBmN/awhjZalkYypUbldpOzAvVfCm/lmNvWEH3jBWZuR4RrrKyboC0yoAQ0gA0FQv5UQ5DPZdM2CJl1BO95wqmd6xJM5mA1ROHCM54EZxU3sb7kYJd8+DfAWo2vVfKL61GZ4o4KHaxqZcKycgHVtP8x7K3+3XQN4smz4JMfEtEj8hmeehTKejHiuOl2qknmVyqe6tgYQFSgaQAOyicZ0GTTjBvhQNKAIAeJBy7iFoUr2elgh8EpjqXdmaltgDzUge+FoEzG8ea66CiwmUyVTJOeaWLkUA6trqZT7NIAna43XPPBnmnwvAys71X3qLPUVDQQHRUzGxixxWQNsugyVn0Mt3qxt7m0wKIiigT4NxJgMQhkXG4NY5b+6LoE/SikwWgM+XTojTi7g8tyrOb7kRQNLa6BiZMF7EfjzoQWrzQJFA6M1UDGywI3lKOCbsvNS+Vs0sKQGKjGZ85AX4xMxpk2+2imxmSum5EtpIOfJYMQxDYD3UQWKBkZp4LCltXsvvNnOg7w1r9LYjL6lxH5herxlK+9fMiIruwG8oRn1Cd2qb7DNk626343x14A0Yk3h+GaSk52c1z/emHCLdYyR4QRGf/q2WLeLU7d5soU4aYB4Y8B5ohxw5n0rPIPk8IHJyQnu2mxC6174VcNrETNPZWS466122cGqdmpbRkbmYU24ve3M9ma61IAQdzWmyu0clt2SaipPxuAxZbYtFDiftjJPJ970iwz2mZpyzjOlPxGFB+OkJnAqeo40AdnP31TPtOpej8/74md2NHIIdBxvod+bSnz4a6GB8lOVkQlel0pMxfACzylTctpSTx3XxIO054EAh96YFpEXefBc0HECFRxtqYefga5pC29ofTzOhI+xm65pl5Vb+MmhbZ/Mb6r3u0sJbGeJJBnnuwmcUSw3EEE02ROVkWDEhXijVORt/ESUcHzpHY8u6RpjyP5Cs/Az1fsZdQzUHgrl8GcVd1vXMWYLeF6/cTjP8Mr5Can6gLLn+F4J3ugBGeyhEz1GQH08w5fg7HMz1RkIT3vapTIgV/ynaqEtslfiY5V/KNm3BMq5n165rdOJ/hyM4RMEZiBREoNnxkSepjF9DGiLgaVfyXgTDJ0vnlHqInCiNtHrch+hMd4hBfpluyMd9Nwrud+iw3u6jPFnqYTD23C86kzJIODAR+8UqtBp7Cvg4J3CiQrI7x7M6/wtDuWhcnvb0flYI+PG4xk0XTOgKGgtEPrD9X+pd6g6N444gHWalrJvRNer48Al/eJJ6kC/TIsO6MNlmaltXT/vVM+7Yu6DeqZFjJzww0A4DNy9bMA2M9ExjWJ4f3TNw8+PtvDvacybK2d86GeI3CKbBg6nYRO5MKC9yojU4y9sYMSmPnAp50U9Wdq27dr7ZaqMxhCI8Rp1Q2Xgs6D2eDjkJxbD+95TmZnhXIkz8zzETJ3UDQFirwsljJXQBW/u/+VvUbnVfDxMbWTcWN3Nj5eynYNPH0ftJDOnaZBI+QzA0MFL2ztPvEX05ClB7brrIYCUmA2DYoHwC4QAHIY3hD/0M7XHiNiX5J7svnTNQ8CX3xj/onKryXg4GM9iziHcIK45Tg1T8W7jE/piACuBLvSq8xiKGMShb7CdrjNP+j3LESZ956pzOAwAA3mr5EYFjliOxQTXQwCvXfGsas/UC09iNcYGHUwlt1j1w2RGpq7wYv6k9Pc8HQUHLYf+RBQxy0lH18cddfUq+sUI3JitXmWmqFQPRyqTWiEMPm14SK1tgmO1mvKr86nzvhB9HUfZP7wdKne9n6XLo7cwvGfdGB4ju5/kNKvK1TdegOnhKvRBOf5EVMBZFuTkmoG7VJlPufAAF0o8KPBgQJi64MOUhSEZXrQxHNC196vquFdGv2wr0Ia2Kc/svhyNRY/Hop17MnDmlZTH1W6gdXndwJGXj7F5gPDqPuXq0vbvmNbdyODbKjcNpobJjGxqwQq/3dHAwe7cSrmTbdVAm5H5knuRGGVb77HItWENtBmZb9Y1Vm0blrd0fw01kDWyJNAkaC1QNDBKA1kjCxz9VQSrngJFA0trILu6dG7yaEybLJd5fbK2TVbvv+S7oYEuT8YdsnHHfhL/rMD3ZMAXKBoYrIFOT+ZcZGBstBKf2Tkox5e8aGCIBvo8mfGQkbHLzdv9rtcbQ/orNHuogf8B7ZR8fpkD0tgAAAAASUVORK5CYII=\n",
+ "text/latex": [
+ "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: x \\leq - \\frac{P}{\\bar{\\tau} p} \\\\\\bar{\\tau} & \\text{otherwise} \\end{cases}$"
+ ],
+ "text/plain": [
+ "⎧ -P \n",
+ "⎪ 0 for x ≤ ────────────\n",
+ "⎨ \\bar{\\tau}⋅p\n",
+ "⎪ \n",
+ "⎩\\bar{\\tau} otherwise "
+ ]
+ },
+ "execution_count": 45,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "tau_x = sig_f_x.diff(x) * A_f / p\n",
+ "sp.simplify(tau_x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Plot the strains and stresses\n",
+ "Similarly to the callable function `get_u_fa_x` let us define the functions for the strains and stresses using the `sp.lambdify` generator "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "get_eps_f_x = sp.lambdify((x, P), eps_f_x.subs(data_f))\n",
+ "get_eps_m_x = sp.lambdify((x, P), eps_m_x.subs(data_f))\n",
+ "get_sig_f_x = sp.lambdify((x, P), sig_f_x.subs(data_f))\n",
+ "get_sig_m_x = sp.lambdify((x, P), sig_m_x.subs(data_f))\n",
+ "get_tau_x = sp.lambdify((x, P), tau_x.subs(data_f))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "To make the code for plotting shorter let us define a general procedure plotting and filling the curves and attaching the labels to a specified subplot in one call "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Pull-out curve"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Quick summary - direct derivation\n",
+ "\\begin{align}\n",
+ " \\varepsilon_\\mathrm{f}(0) &= \\frac{P}{E_\\mathrm{f} A_\\mathrm{f}}, \\;\\;\n",
+ " \\varepsilon_\\mathrm{m}(0) = \\frac{-P}{E_\\mathrm{m} A_\\mathrm{m}} \\\\\n",
+ " a &= - \\frac{P}{p\\tau}.\n",
+ "\\end{align}\n",
+ "Thus, the crack opening can be expressed as the area of the triangle\n",
+ "\\begin{align}\n",
+ " w &= \\frac{1}{2}\\left[\\varepsilon_\\mathrm{f}(0) - \\varepsilon_\\mathrm{m}(0)\\right]a \\nonumber \\\\\n",
+ " &= \\frac{1}{2}\\frac{P^2}{p\\tau} \\left[\\frac{1}{E_\\mathrm{f} A_\\mathrm{f}} + \\frac{1}{E_\\mathrm{m} A_\\mathrm{m}}\\right].\n",
+ "\\end{align}\n",
+ "By solving this equation for $P$ we obtain the pullout curve in the form\n",
+ "\\begin{align}\n",
+ " P(w) = \\sqrt{2wp\\tau \\frac{E_\\mathrm{f}A_\\mathrm{f}E_\\mathrm{m}A_\\mathrm{m}}{E_\\mathrm{f}A_\\mathrm{f}+E_\\mathrm{m}A_\\mathrm{m}}}.\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/latex": [
+ "$\\displaystyle \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}$"
+ ],
+ "text/plain": [
+ " \n",
+ " ______________ ______________ ______________ ______________ _____\n",
+ "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\bar\n",
+ " \n",
"\n",
- "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
- " fig.ondownload(fig, null);\n",
- "}\n",
+ " _______________________________________________________\n",
+ "_______ ╱ w \n",
+ "{\\tau} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── \n",
+ " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} "
+ ]
+ },
+ "execution_count": 48,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "eps_f_0 = P / E_f / A_f\n",
+ "eps_m_0 = -P / E_m / A_m\n",
+ "a_subs = sp.solve({P - p * tau * a}, a)\n",
+ "w_el = sp.Rational(1,2) * ( eps_f_0 - eps_m_0) * a\n",
+ "Pw_pull_elastic = sp.solve(w_el.subs(a_subs) - w, P)[1]\n",
+ "Pw_pull_elastic "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Pull-out curve derived from the displacement field solution "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "**`sympy` explanation:** In parallel let us use again the `subs` and `solve` provided in `sympy` to define the `P_push` and `P_pull` variables in the running `jupyter` kernel. As `solve` searches for zero point of the supplied equation we must transform the above equation into"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$\\displaystyle - w + \\frac{\\frac{A_\\mathrm{f} E_\\mathrm{f} P^{2}}{\\bar{\\tau} p} + \\frac{A_\\mathrm{m} E_\\mathrm{m} P^{2}}{\\bar{\\tau} p}}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}}$"
+ ],
+ "text/plain": [
+ " 2 2\n",
+ " A_\\mathrm{f}â‹…E_\\mathrm{f}â‹…P A_\\mathrm{m}â‹…E_\\mathrm{m}â‹…P \n",
+ " ──────────────────────────── + ────────────────────────────\n",
+ " \\bar{\\tau}â‹…p \\bar{\\tau}â‹…p \n",
+ "-w + ───────────────────────────────────────────────────────────\n",
+ " 2â‹…A_\\mathrm{f}â‹…A_\\mathrm{m}â‹…E_\\mathrm{f}â‹…E_\\mathrm{m} "
+ ]
+ },
+ "execution_count": 49,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "u_f_x.subs(x,0) - w"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "and then send it to `sp.solve`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$\\displaystyle \\left( - \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}, \\ \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}\\right)$"
+ ],
+ "text/plain": [
+ "⎛ \n",
+ "⎜ ______________ ______________ ______________ ______________ ___\n",
+ "⎜-√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\b\n",
+ "⎠\n",
"\n",
+ " _______________________________________________________ \n",
+ "_________ ╱ w \n",
+ "ar{\\tau} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── , √2⋅╲\n",
+ " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
"\n",
- "mpl.find_output_cell = function(html_output) {\n",
- " // Return the cell and output element which can be found *uniquely* in the notebook.\n",
- " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
- " // IPython event is triggered only after the cells have been serialised, which for\n",
- " // our purposes (turning an active figure into a static one), is too late.\n",
- " var cells = IPython.notebook.get_cells();\n",
- " var ncells = cells.length;\n",
- " for (var i=0; i<ncells; i++) {\n",
- " var cell = cells[i];\n",
- " if (cell.cell_type === 'code'){\n",
- " for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
- " var data = cell.output_area.outputs[j];\n",
- " if (data.data) {\n",
- " // IPython >= 3 moved mimebundle to data attribute of output\n",
- " data = data.data;\n",
- " }\n",
- " if (data['text/html'] == html_output) {\n",
- " return [cell, data, j];\n",
- " }\n",
- " }\n",
- " }\n",
- " }\n",
- "}\n",
+ " \n",
+ " ______________ ______________ ______________ ______________ _________\n",
+ "╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\bar{\\ta\n",
+ " \n",
"\n",
- "// Register the function which deals with the matplotlib target/channel.\n",
- "// The kernel may be null if the page has been refreshed.\n",
- "if (IPython.notebook.kernel != null) {\n",
- " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
- "}\n"
+ " _______________________________________________________⎞\n",
+ "___ ╱ w ⎟\n",
+ "u} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── ⎟\n",
+ " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} ⎠"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Pw_push_elastic, Pw_pull_elastic = sp.solve(u_f_x.subs({x:0})-w, P)\n",
+ "Pw_push_elastic, Pw_pull_elastic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Note that the obtained $P(w)$ covers both the pull-out and push-in case. If we supply the parameters defined above with unit stiffness, area and perimeter we obtain"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAAZCAYAAAA/vnC8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEBElEQVRoBe2a7W3bMBCGbaMDuO4G7gb5mKDOBnG7gbNBivyy/xXtBk42aLJBkwmadoNkgzrewH0fgkdQqhoYFinJgA84kzqRvC/e8SS5t9lsejHO5/OZcBLTDv2ijZq2h/yxrOLZh2iwWCzO1T9Te2G0NlvJcST+v+rIoDX6debXnZtCB8nwXrjUWmexPG/sQjeG6l+pPTZaB9qvkuFYMv3ugCy7ipBEB9ngVngp/GaCDKyj9la4jK5b7UpIoq6ndm8dl1IHrXUtc1yoJcgcOOeJMNbViR/gb7XeXEkCdu0+Q2odCK4bM4hF3mcR8GwnwG+msdr7Tgi0gxCZdMBH51rbRZ85bybijx1kzDWFzQTuMyTXQU5byyAcIx8xzEAEd7ao/wihbfC7ihS+z1FHZOTSAT9N8RORNxE+e69Caxs45760LURN/jl1eJJsJ8jHo8KpkHBsHXzUTdQWnjM9ndT+Tvik63A+q0/moApzc9TyrGrleeN6iT9Rl1MH0uYQPkQezFbCLsD/qjOeP3m++SksV6DMGUfC4zCu3e6M6E11c+tgvhrjvJEw+w4lIoSk6NeAMSGqGKhrIgunAbxhMOEdQT+sGYotjeesZHc+C5OC1u6CDuarEWnz1ciTwNx/8OO2NcZU8zCgA/Uv1WFHYtDKNzh+zNJNKP5wHttaVFnhPBQdxyJfubh51L2kzvPydUGHsHlxHp4k+ipBQnO/0uCVE0pEb2CiifOK1ztHQnNGPJpzi3d4BRAN/j21nGU4Ko5Mom6te+X1ONSTgdZnk3RFB/PVirSZFTCsEAdYxLB7C6D7FCNVURePI2XaWkaHVog6b+iyM238Tm3HdGADA2ucR3oxAsQs4B3I7uXcoKCIYZs3PMwpp8Iq2ietX3ZoEv3a1CEyViHyKAaaqsysUgxvT2QQ0uGdN0wk4z9doik4QeNJmSgSNoKnheKFFURjzovaWp+WWMtD4zoYY9+iL0fFus+HV12g8FsIfkC2RjzgBU/Hzxv1wza8NcZSK3L+ERLJN8KVEFrhGVDXDjTPzkA+L9XWUWs0rkOkCzYYSYap+xirzosIVIiFdGMTUrbiYZuF6CMNNvLxV3yJ8Hu1KZzXig74QfKTQfgwez2AIPguLHylddQMP2LKBiEFUriAlobUzQqn4l3bcUjYlg7iOxR7Kl/85d5t0hKKVHxNAZUngvAMVy5CksvglSbNpoRGdfCC85wb6gMXeVKOSCClkFqyg/jciQk8Q+GSmelMPMPfB1LwakEHxMZewWbhD0gShkh4ULvzAzmrHyCPBeQXMiMvpMMmDM6DpW4QeZwNwbvQD9CuBeQPHg8oUgp1iRUsTjrdJJ1RblNNHaA7FiCY3AfYWKS/QLc7aNvlV10AAAAASUVORK5CYII=\n",
+ "text/latex": [
+ "$\\displaystyle \\left( - \\sqrt{w}, \\ \\sqrt{w}\\right)$"
],
"text/plain": [
- "<IPython.core.display.Javascript object>"
+ "(-√w, √w)"
]
},
+ "execution_count": 51,
"metadata": {},
- "output_type": "display_data"
- },
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Pw_push_elastic.subs(data_f), Pw_pull_elastic.subs({A_f:1, E_f:1, L_b:1, p:1, tau:1, A_m:1, E_m:1})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Plot the pull-out curve\n",
+ "The symbolic expression must be transformed into a quantifiable form using `sp.lambdify`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {},
+ "outputs": [
{
"data": {
- "text/html": [
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o/XNN9/UeE11qb8AAFTLJ594Q6W+fQmVEFkYzgAATvLSey9ZodKzbz9LqFSBrKws69vbM2bMUGZmphITE9WsWTMdPny4yvs/9thjMsYoLS1NWVlZmj59um6//XYZY9S5c+car6uu9BcAgGr78ENvqDRwIKESIgvDGQDASaZtm2aFShO3TCRUKsexY8cUHx9f4XkmBw8eXOn9T506JY/Ho5SUlDI/55eknj17yhij3bt312htdaG/AAD45b33vKHSPfcQKiGyMJwBAJxk3KZxVqiUnZtNqFSOOXPmVHpF3ISEhEqviPvNN9/IGKNf/vKXPvvuv/9+GWN08ODBGq2tLvQXAAC//Otf3lDpgQcIlRBZGM4AAE4yYsMIK1R6+YOXCZXKMWTIEBljtGfPHp99Tz75pIwx2rFjR6XH6NChg9xut8aOHatPP/1UeXl5mjlzpjwej+6+++4ar60u9BcAAL+88443VPr97wmVEFkYzgAATvL42setUOkvO/9CqFSOHj16yBijkydP+uybNm2ajDFasWJFpcc4ePCgunbtWuaiIm63WyNHjqz2OvLz87Vp06YylZ2dbfv+AgDgl/XrvaHSH/5AqITIUheGXwAAquv3K39vhUqvffwaoVI50tLSZIzxOR+S5P1p3NKlSys9RkFBgYYMGaL+/ftr8eLFWrJkifr06SNjjNLT06u1jvT09Aqvemvn/gIA4Jc1a7yh0uOPEyohstSF4RcAgOq6+x93W6HS2n1rCZXKUdk3laZOnVrlN5VOnDihVq1aqU+fPj77BgwYIJfLpffff7/KdfBNJQAAJK1Y4Q2VnnqKUAmRpS4MvwAAVNddf7vLCpXePvA2oVI5Aj2n0ssvvyxjjP72t7/57FuxYoWMMZo0aVKN1lYX+gsAgF9efdUbKqWnEyohsjCcAQCc5PYlt1uh0vbD2wmVyjF79uxKr/4WHx9f6dXfxowZI2OMlixZ4rNv+fLlMsZo/PjxNVpbXegvAAB+WbrUGyplZhIqIbIwnAEAnKT7gu5WqLTzPzsJlcpRUFCg2NhYpaSkqKioyNqem5srl8ulQYMGWduOHDmi3bt368T3BtxXX31VxhjdfPPNPse+9dZbZYzRW2+9VaO11YX+AgDgl8WLvaHSc88RKiGyMJwBAJyk00udZDKMPKM82l2wm1CpApMmTZIxRh07dlR2drZGjRqlxMRENW3aVIcOHbJuN2DAABljtH79emvbmTNnlJqaKmOMrrvuOk2cOFGTJk1Sly5dZIxRjx49aryuutJfAACq7eWXvaHS+PGESogsDGcAACe5eubVMhlGjZ5tpI8LPiZUqsTChQvVtm1beTweNW7cWL1799b+/fvL3Ka8UEkqOVn32LFj1aZNGzVq1EgNGjTQT3/6U40ePbrSn85VpS71FwCAapk92xsqTZpEqITIwnAGAHCSK6ZdIZNhdMG4CwiVbIj+AgAcZ/p0b6g0dSqhEiILwxkAwEkumXSJTIZR0sQkQiUbor8AAMeZPNkbKr34IqESIgvDGQDASc4fd75MhtGPsn5EqGRD9BcA4Djjx3tDpZdeIlRCZGE4AwA4ScKYBJkMo6tmXEWoZEP0FwDgOM8+6w2V5s8nVEJkYTgDADhFcXGxokZEyWQYXTvrWkIlG6K/AADHGTnSGyotXkyohMjCcAYAcIpTZ07JZBiZDKOuc7sSKtkQ/QUAOM6f/+wNlZYuJVRCZGE4AwA4ReF3hVao1H1Bd0IlG6K/AADHeeIJb6i0fDmhEiILwxkAwCmOfH3ECpVue+U2QiUbor8AAMf54x+9odI//0mohMjCcAYAcIq9/91rhUp9lvUhVLIh+gsAcJzf/94bKq1aRaiEyMJwBgBwig//86EVKg1cPpBQyYboLwDAce6/3xsqvfEGoRIiC8MZAMAp/nXoX1aodP/r9xMq2RD9BQA4zt13e0OlDRsIlRBZGM4AAE6xPm+9FSr9YfUfCJVsiP4CABxnwABvqPTOO4RKiCwMZwAAp1ixZ4UVKv1p3Z8IlWyI/gIAHOc3v/GGSlu3EiohsjCcAQCcYtmuZVaolLkxk1DJhugvAMBxevXyhkrvvUeohMjCcAYAcIr5H8y3QqXxm8cTKtkQ/QUAOE7Pnt5Q6d//JlRCZGE4AwA4RXZuthUqTd823Tah0ogRIwKqvLy8oK0l3JhbAACO88tfekOljz4iVEJkYTgDADjFxC0TrVBpzntzbBMquVwuud1uuVwuv8vtdmvdunVBW0u4MbcAABynWzdvqPTJJ84KlfhkLfIxnAEAnGL0W6OtUOmVD1+xVag0efJkHThwwK9677335HK5CJUAALCzrl1LAqV69aQ9e5wVKvHJWuRjOAMAOMVT656yQqVXd79qq1Bp0aJFft/v2LFjhEoAANhdx44loZLH48xQiU/WIhvDGQDAKf6w+g9WqJSzN8c2odI777yjgoICv+935swZvfPOO/r666+DtpZwY24BADhOampJqBQf78xQiU/WIhvDGQDAKe77531WqPT2gbdtEyrBi/4CABynbduSUOmcc5wXKvHJWuRjOAMAOEX/5f2tUGn74e2ESjZEfwEAjpOcXBIqnXee80IlRD6GMwCAU/T6ay8rVPro6Ee2D5Vyc3M1depUZWZm+lzsZOTIkSF//HBgbgEAOE7r1iWhUtOmhEqIPAxnAACn+H+L/p8VKuV9lWfbUOnkyZP6xS9+YV0M5fsXRfn+trqIuQUA4DiXXloSKrVoQagkSQsWLFCHDh3UpEkTud1un4qKiqqNZeD/MJwBAJzi+nnXy2QY1RtZT4eOH7JtqPTEE0/I7Xbrz3/+szZs2CCXy6X58+dr9erV6tKli1JTU/Xxxx+H7PHDibkFAOA4LVqUhEqXXEKoNGLECLndbl144YXq2bOnBg4cWG6h9jCcAQCc4tpZ18pkGMWPidfhrw/bNlS6/PLL1bt3b0m+FzcpKipSmzZt9MQTT4Ts8cOJuQUA4DgXXFASKrVqRajUtGlTpaWl6fTp06F+KFQTwxkAwCmunHGlTIbRec+fZ+tQqUGDBpo+fbok6auvvpLL5dKqVaus/WPHjtUll1wSsscPJ+YWAIDjNG5cEir95CeESnFxccrOzg71w8APDGcAAKe4fMrlMhlGLV5oYetQ6bzzzlNWVpakkivmRkVFac6cOdb+7OxseTyekD1+ODG3AAAcJyGhJFT62c8IlTp16qSnnnoq1A8DPzCcAQCcotmEZjIZRpdPudzWodK1116rhx56yPrvV155pW6++WZJUnFxsW666Sa1atUqZI8fTswtAADH8XhKQqW2bQmVNmzYoMTERL377ruhfihUE8MZAMApzn3uXJkMo59O+6mtQ6WnnnpKzZo109mzZyVJ06ZNk8vl0qWXXqrLLrtMbrdbzz33XMgeP5yYWwAAjhMVVRIqXXMNoZIkLV++XPXr11fnzp3Vv39//e53vytTgwYNqo1l4P8wnAEAnKJBZgOZDKOrX7za1qHSN998o48//lhFRUXWtvHjx6tt27a6+uqr9dxzz6m4uDjgx1m8eLFSUlLk8XiUmJioPn366MCBA9W+/5kzZzRjxgylpqYqPj5ecXFxSk5O1ujRo2u8JuYWAICjFBeXBErGSB06ECpt2bJFjRo1ksvlqrDcbneol4HvYTgDADjBmbNnZDKMTIbRdS9dZ+tQqTZkZWXJGKOOHTtqxowZyszMVGJiopo1a6bDhw9Xef/Tp0+rR48eqlevnvr27asZM2boxRdf1BNPPKF77723xuuqK/0FAKBaTp3yhkqdOhEqXXvttTr//PP1+uuv63eSn9MAACAASURBVKuvvgr1w6EaGM4AAE7wzalvrFCp2/xutg2Vjh49qq1bt2rv3r0hOb4kHTt2TPHx8UpJSSnzbajc3Fy5XC4NHjy4ymM888wzcrvdWr16dVDXxtwCAHCUb7/1hkrXX0+oFBMTo+effz7UDwM/MJwBAJzg6LdHrVCpx+IetguVzp49qyFDhigqKkput1tut1vt27fX559/HtTHkaQ5c+bIGKN58+b57OvSpYsSEhJ06tSpCu//7bffqmHDhurZs6ekkpOHf/3110FZG3MLAMBRvvrKGyp160aodMkll2jixImhfhj4geEMAOAEB746YIVKv/7rr20XKk2ePFkul0vNmzdXr169dNVVV8nlcqlHjx5BfRxJGjJkiIwx2rNnj8++J598UsYY7dixo8L7r169WsYYjR49WsOHD1ejRo1kjNG5556roUOH6kQAwzBzCwDAUY4e9YZKN99MqJSZmal27dqV+So1wovhDADgBB8d/cgKlfr/vb/tQqV27drpiiuuKPONn7vvvltRUVH68ssvg/pYPXr0kDFGJ0+e9Nk3bdo0GWO0YsWKCu8/adIkGWPUpEkTNW3aVFOmTNGyZcvUt29fGWN0ww03VOtE4vn5+dq0aVOZys7OZm4BADjH4cPeUOmWWwiV1q1bp2uuuUbt2rXTnDlz9Oabb2rjxo0+hdpDqAQAcIJ3j7xrhUr3vnav7UKl+Ph4n1MI7NixQy6XS1u3bg3qY6WlpckYo7Nnz/rsK/1p3NKlSyu8f2ZmpowxioqK0q5du8rsKw2WqnOupfT0dBljyi3mFgCAI+TleUOl228nVCrvSm/fL67+VvsIlQAATvD2wbetUOmhVQ/ZLlRyuVxauHBhmW0FBQVyuVx68803g/pYlX1TaerUqVV+U2n8+PEyxujnP/+5z74333xTxhg9/vjjVa6DbyoBABxvzx5vqHTnnYRK8+bNq1ah9hAqAQCcIGdvjhUqPbH2CVuGSosWLSqz7dixY3K5XFq3bl1QHyvQcyotWbJExhjdcccdPvt2794tY4zuueeeGq2NuQUA4Ci7dnlDpbvuIlRC5GE4AwA4wfLdy61QacSGEbYMlX7zm99o7NixVqWnp8vtduuee+4ps33s2LEBXW139uzZlV79LT4+vtKrv+Xl5ckYo9TUVJ99OTk5Msbo6aefrtHamFsAAI7ywQfeUKl/f0IlRB6GMwCAEyz+92IrVBr7zlhbhkr+VCCnEygoKFBsbKxSUlLKXFwlNzdXLpdLgwYNsrYdOXJEu3fv9rmiW+fOneVyubRlyxZrW3FxsW699VYZY7R58+YarY25BQDgKLm53lBp0CBCJUQehjMAgBPMfne2FSpN2TrFdqHShg0b/K5AlF7BrWPHjsrOztaoUaOUmJiopk2b6tChQ9btBgwYIGOM1q9fX+b+O3bsUEJCgho2bKinnnpKU6dO1U033SRjTJlQyl/MLQAAR9m82Rsq3XsvoZIkLViwQB06dFCTJk18TtTtdrsVFRVVG8vA/2E4AwA4wZStU6xQadb2WbYLlcJh4cKFatu2rTwejxo3bqzevXtr//79ZW5TUagkSTt37tTtt9+uc889V9HR0briiis0ceLEcq8qV111qb8AAFRp40ZvqPTAA4RKI0aMkNvt1oUXXqiePXtq4MCB5RZqD8MZAMAJxr4z1gqVFuxYQKhkU/QXAOAob7zhDZV+/3tCpaZNmyotLU2nT58O9UOhmhjOAABOkL4+3QqVlu1aRqhkU/QXAOAoq1Z5Q6U//pFQKS4uTtnZ2aF+GPiB4QwA4ATD1wy3QqUVe1bYLlT6yU9+4lddccUVQX38SMHcAgBwlNde84ZKjz9OqNSpUyc99dRToX4Y+IHhDADgBENXDLVCpTf3v2m7UMnlcik2NlaXXHJJtasuYm4BADjK3/7mDZWefppQacOGDUpMTNS7774b6oeqscWLFyslJUUej0eJiYnq06ePDhw4UO37b9++Xd27d1fDhg0VHx+vLl26aOPGjeXe9tSpUxoxYoQuvfRSRUdH6+KLL9Zjjz3mc1nemhy7uhjOAABOMOjVQVaotPWzrbYLlRISEuRyuXTdddfppZdeqnBWqOuYWwAAjrJkiTdUysggVJKk5cuXq379+urcubP69++v3/3ud2UqkMvMBiorK8u6fO6MGTOUmZmpxMRENWvWTIcPH67y/tu2bVNMTIySkpI0btw4TZkyRcnJyapXr57Wrl3rc/s77rhDxhj169dPs2bN0tChQxUVFaW0tDSfK6P4e+zqYjgDADhBn2V9rFDp31/823ah0okTJzR37lx16tRJLpdLCQkJuvvuu7V58+agPk6kY24BADjK/PneUGnUKEKlLVu2qFGjRnK5XBWW2+0O9TLKdezYMcXHxyslJUVFRUXW9tzcXLlcLg0ePLjKY7Rv315xcXE6ePCgta2wsFDNmzdXq1atVFxcbG1fvXq1jDEaNmxYmWOMHz9exhgtWLCgxsf2B8MZAMAJbn3lVitU+vTYp7YLlb7vk08+0eOPP65mzZrJ7Xbrxz/+sZ5//nl98cUXIXvMSMHcAgBwlDlzvKHS2LGEStdee63OP/98vf766/rqq69C/XB+mTNnjowxmjdvns++Ll26KCEhQadOnarw/vv27ZMxRgMHDvTZl56eLmOMtmzZYm3r16+fjDE+P607efKkYmJi1L179xof2x8MZwAAJ+g2v5tMhpErw6X8wnxbh0qlzp49q9dee0233Xab6tevr/r162vWrFkhf9xwYm4BADhKdrY3VHrhBUKlmJgYPf/886F+mBoZMmSIjDHas2ePz74nn3xSxhjt2LGjwvu/8sorMsZo5syZPvtycnJkjNHkyZOtba1bt1azZs3KPVaHDh107rnn1vjY/gj2k+j4d8f1aM6jFEVRFBVR1WxCM5kMI0+mR4eOH6oToVKp1atXKy0tTS6XSyNGjKi1xw0HQiUAgKNkZXlDpSlTCJUuueQSTZw4MdQPUyM9evSQMUYnT5702Tdt2jQZY7RixYoK71/6s7WVK1f67Nu1a5eMMRo+fLi1LT4+XqmpqeUe69e//rWMMdZJOP09dkXy8/O1adOmMpWdnR3UJ9FHRz+yfl5AURRFUZFW9UfW14dffKgPv/hQuYdytes/u2wZKuXl5emZZ55RUlKS3G63WrZsqREjRujIkSMhfdxwI1QCADjKCy94Q6UZMwiVMjMz1a5duzLnLIoUaWlpMsb4nCBb8v40bunSpRXef+TIkTLGaN26dT77Sn++9uCDD1rb3G63OnXqVO6xSn8aV1BQUKNjV6T0p3LlFaESRVEU5YSqN7Kecj7NsWrTwU369tS3QXkNlEIbevzvf//TwoULlZaWpqioKMXExOi3v/1tufNBXUWoBABwlLFjvaHSrFmESuvWrdM111yjdu3aac6cOXrzzTe1ceNGnwqHyr6pNHXq1IC+qbRz506/vqnUq1evan9TqbxjV6Q2vqn03xP/Vf+/99evlvxKtyy+haIoiqIiohqPbSyTYRQzKkY7vtihHV/s0L8O/Us7/7PTFt9Uuv/++3XOOefI7Xbr6quv1vTp01VYWBjUx7ADQiUAgKOMGuUNlebOJVQq70pv369wXv2NcyoxnAEA6q4b598ok2HkHuHWZ4Wf2e6cSi6XS7Gxserbt6/Gjh1bZUXqOSwDxdwCAHCU9HRvqLRgAaHSvHnzqlXhMHv27Eqv/hYfH1/p1d/27t1b5RXaNm/ebG3r27dvpVd/u+mmm2p8bH8wnAEAnODWV261fgK39797bRkq+VPh+pAu1JhbAACO8qc/eUOlJUsIlSJZQUGBYmNjlZKSUuacT7m5uXK5XBo0aJC17ciRI9q9e7f187RSqampiouLU35+vrXt+PHjatGihS677DIVFxdb21euXCljjIYNG1bmGBMmTJAxRvPnz6/xsf3BcAYAcII+y/pYodKH//nQdqHShg0b/K66iLkFAOAow4d7Q6VlywiVIt2kSZNkjFHHjh2VnZ2tUaNGKTExUU2bNtWhQ4es2w0YMEDGGK1fv77M/bdu3SqPx6OkpCRNmDBBWVlZSk5OVlRUlHJycnwe77bbbpMxRv3799fs2bM1bNgwRUVFqWvXrj4nDPf32NXFcAYAcILfvfo7K1Tadmib7UIllKC/AABHefhhb6j0j384L1TauHGjjh496vf9ioqKtHHjxrCcgHLhwoVq27atPB6PGjdurN69e2v//v1lblNRqCRJ27ZtU7du3ZSQkKDY2Fh17ty53NtJJVdxSU9PV8uWLRUdHa2LLrpIw4cP17ffln8VGn+OXV0MZwAAJ3hwxYNWqLTxwEZCJZuivwAAR3nwQW+otHKl80Ilt9utRYsW+X2/Y8eOye12O+oSueHCcAYAcILha4ZbodLKPSttFSrZ8UO6UGFuAQA4yj33eEOltWudFyq5XC5NmTJFBw8e9Kvef/99uVwuQqVawHAGAHCCZ958xgqV/r7777YKlfiQzou5BQDgKAMHekOlDRucGSq53e4aV10agiIVwxkAwAmee/s5K1RatGORrUIlPqTzYm4BADjKb3/rDZU2bXJeqJSRkRFQ5eXlBXtJ+AGGMwCAE0zZOsUKlWa/O9t2oRIf0pVgbgEAOMqdd3pDpX/9y3mhEiIfwxkAwAlmvTvLCpWy/pVlq1CJD+m8mFsAAI5y++3eUOm99wiVEHkYzgAATrDo34usUGncO+NsFSrBi/4CABylRw9vqPThh4RKiDwMZwAAJ1i+e7kVKo3YMIJQyaboLwDAUbp394ZKH39MqITIw3AGAHCCnL05Vqj0xNonCJVsiv4CABwlLa0kUIqKKgmUCJUQaRjOAABO8NaBt6xQ6eHVDxMq2RT9BQA4SqdOJaFSgwaESohMDGcAACfYfni7FSoN+ecQQiWbor8AAEdp374kVIqLI1SSpK+//jrUDwE/MZwBAJzgo6MfWaFS/+X9CZVsiv4CABylXbuSUKlRI+nTTwmVbr75Zv3qV78K9cPADwxnAAAnyPsqzwqV7vzrnbYOlVq1aqWNGzeG7PiRjLkFAOAoV15ZEiolJhIqSdJFF12k9PT0Cvf/6le/0syZM0O9DHwPwxkAwAn+8+1/rFDp1sW32jpUcrlcWrRoUciOH8mYWwAAjvLjH5eESk2b/v/27j06qvpe//hngpBJSAAzojGAQVq1tSgmKGoDgiilKKg93tBVjQdUqAcvVNuKpSuRoFCBAgZIJEFQOBQbBbVQBES0CHIIcsAiVAQCEdSfST1BuRyI4fn9wckMMdcJM8ns7Pdrre/q6t4zO9/5rCzy+MyNUkmSvF6v8vLyJEllZWUaMmSIdu7c6T//xBNPqHfv3uHeBk5BOAMAuMG3x771l0oDXh5AqeRQ5BYAgKv84AcnS6XOnSmVJMnn8yknJ0eS9NVXX8nj8Wj16tX+8zNnzlTHjh3DvQ2cgnAGAHCD7yq+85dKvV/s7fhSaeHChbWeX7Jkifr163faP2fhwoVKTU2V1+uVz+fT0KFDtXfv3kZd6/bbb5eZ6aKLLjqtPZFbAACuct55J0ulrl0plSQpLS3N/5lKGzZskMfj0V/+8hf/+by8PLVu3Trc28ApCGcAALdok9VGlmm6YvYVji+VEhMTNXjwYP3+979XQUFBlVd+P/3002rTps1p/Yzs7GyZmdLS0pSTk6OsrCz5fD4lJSXpwIEDQV1r6dKlioqKUkxMDKUSAADBOPfck6XSD39IqSRJ+fn58ng8Gj58uHr27KnOnTvrnnvu8Z9/5JFH5PP5wr0NnIJwBgBwiw4TO8gyTd1ndXd8qdS1a1fFxcXJ4/EoKirKX9okJyerdevWuuKKKxp9/dLSUsXFxSk1NVXl5eX+44WFhf4c11DffvutzjvvPI0aNUrJycmUSgAABOOss06WSj/6EaVSpZEjR6pVq1Y666yztH79erVr104PPfSQpk6dqri4OA0aNKgptoH/QzgDALhF0pQkWabph8//0PGlUuVnKn366acqKCjQ2LFjdcstt+jKK6/UL37xC23btq3R158zZ47MTPPmzat2rm/fvoqPj9exY8cadK1HH31U5557rg4ePEipBABAsNq3P1kqde9OqXSqQ4cO+cPI4sWL/c+0xcXF6YMPPmiqbUCEMwCAe/xg+g9kmaYuf+rSYkqlcBgxYoTMrMpb6iqNGTNGZqatW7fWe52NGzcqKipKixYtkiRKJQAAghUbe7JUSkmhVKpLWVmZ/v73v+vLL79sri24FuEMAOAWl8y6RJZp6vhcR0qlOgwePFhmpiNHjlQ7N3PmTJmZli1bVuc1ysvL1aNHD/3sZz/zHwu2VCouLta6deuqrNzcXHILAMA9Wrc+WSpdcQWlEiITpRIAwC2uzLtSlmmKezbO0aXSypUr9cknn4Tt+v3795eZqaKiotq5yrfGFRQU1HmNiRMnyuv1ateuXf5jwZZKGRkZMrMaF7kFANDinThxslAyk66+mlIJkYlSCQDgFv3m9ZNlms4Yd4ajS6Vwq+uVSjNmzKj3lUq7du1STEyMxo0bV+U4r1QCACAI5eWBUqlPH0olRKaWEH4BAGiIG/7zBlmmyTJNe/9nL6VSLU73M5VuvvlmJSUl6ZNPPlFRUZF/derUSd26dVNRUVGjP/KgJcwXAIAGOXIkUCpdey2lEiIT4QwA4Ba3/eU2f6m0o2QHpVIt8vPz6/z2t7i4uDq//a1Hjx61vm2tcg0cOLBRe2sJ8wUAoEEOHgyUSgMGUCohMhHOAABuce+Se/2l0ocHPqRUqkVJSYliY2OVmpqq8vJy//HCwkJ5PB4NGzbMf+zzzz/Xjh07dPiUgPvOO+9oyZIl1VbHjh3VqVMnLVmyROvXr2/U3lrCfAEAaJCSkkCpdOONlEqITIQzAIBbjPjrCH+p9P6+9ymV6jBt2jSZmdLS0pSbm6vx48fL5/MpMTFR+/fv998uPT1dZqY1a9bUe81gP1OpJi1lvgAA1OvzzwOl0s03UyohMhHOAABuMfqt0f5SadWuVZRK9ViwYIFSUlLk9XqVkJCgO++8U3v27KlyG0olAADCZN++QKl0662USohMhDMAgFv8fvXv/aXSG/98g1LJgZgvAMA1du0KlEp33kmphMhEOAMAuMX498b7S6VF/1hEqeRAzBcA4Bo7dgRKpV/+klIJkYlwBgBwiz+t/5O/VJr733MplRyI+QIAXOOjjwKl0n33USohMhHOAABukVuY6y+VZm2cRankQMwXAOAaH34YKJUeeIBSCZGJcAYAcIuXt7zsL5WmrJ9CqeRAzBcA4BobNgRKpV/9ilIJkYlwBgBwi4KPC/yl0jN/f4ZSyYGYLwDANdauDZRKjzxCqYTIRDgDALjFsp3L/KXS2NVjKZUciPkCAFzjnXcCpdKvf02phMhEOAMAuMWaojX+UunxFY9TKjkQ8wUAuMaKFYFS6Xe/o1RCZCKcAQDcYsNnG/yl0kNLH6JUciDmCwBwjaVLA6XS739PqYTIRDgDALjFR19+5C+Vhr0+jFLJgZgvAMA1Fi8OlEpPP02phMhEOAMAuMWuf+3yl0p3vXoXpZIDMV8AgGu88kqgVHrmGUolRCbCGQDALQ58c8BfKt2y6BZKJQdivgAA11iwIFAqPfccpRIiE+EMAOAW/3P0f/yl0s8X/JxSyYGYLwDANebODZRKf/oTpRIiE+EMAOAWx7475i+V+s3tR6nkQMwXAOAas2cHSqXsbEolRCbCGQDALU6cOKFWT7eSZZquzLuSUsmBmC8AwDVmzgyUSjk5lEqITIQzAICbxD0bJ8s0XZZzGaWSAzFfAIBrTJsWKJXy8ymVEJkIZwAANzl70tmyTNNF2RdRKjkQ8wUAuMakSYFS6aWXKJUQmQhnAAA36TqtqyzTlDw1mVLJgZgvAMA1nn02UCr9539SKiEyEc4AAG7y4xk/lmWazpl0DqWSAzFfAIBrPP10oFT6y18olRCZCGcAADfp+UJPWaapw4QOlEoOxHwBAK4xdmygVFqyhFIJkYlwBgBwkz4v9pFlmrzjvZRKDsR8AQCu8dvfBkqlpUsplRCZCGcAADcZOH+gLNNkmabtX22nVHIY5gsAcI3RowOl0ooVlEqITIQzAICb3LLoFn+ptPnzzZRKDsN8AQCuMWpUoFR65x1KJUQmwhkAwE3ufu1uf6m0rngdpZLDMF8AgGuMGBEoldaupVRCZCKcAQDc5P437veXSqt2r6JUchjmCwBwjWHDAqXShg2USohMhDMAgJs8/LeH/aXSm/98k1LJYZgvAMA17rknUCpt2kSphMhEOAMAuMnvVv3OXyoVfFxAqeQwzBcA4BpDhwZKpY8+olRCZCKcAQDc5Ol3n/aXSi9veZlSyWGYLwDANW69NVAqbd9OqYTIRDgDALjJc+8/5y+VXtj0AqWSwzBfAIBr3HRToFT69FNKJUQmwhkAwE1m/NcMf6k0/YPplEoOw3wBAK4xaFCgVNq7l1IJkYlwBgBwkxc3v+gvlSaunUipVIeFCxcqNTVVXq9XPp9PQ4cO1d69e+u939dff61p06ZpwIAB6ty5s7xery688EI98MADKi4uPq09taT5AgBQp+uvP1koeTzS/v2USohMhDMAgJss+scif6mUsSaDUqkW2dnZMjOlpaUpJydHWVlZ8vl8SkpK0oEDB+q87/LlyxUVFaXrrrtOzz77rPLy8vTYY48pJiZG7du318cff9zofbWU+QIAUK++fU+WSq1bUyo5xYoVK9S7d2+1bdtW7du314033qiPPvooqGt8+umnuvXWW5WQkKCYmBj16tVLr732Wo23PXHihLKzs3XxxRcrOjpaiYmJevDBB1VaWlrldkePHtXs2bN10003KTk5WV6vV+eff76GDh2q7du3N/rxSoQzAIC7vPHPN/yl0u9W/Y5SqQalpaWKi4tTamqqysvL/ccLCwvl8Xg0fPjwOu9fVFSknTt3Vju+atUqmZluu+22Ru+tJcwXAIAGufrqk6VSbKx04AClUqR74403FBUVpe7du+v555/XpEmTdN555yk+Pr7BxVJRUZHOOuss+Xw+ZWVlKScnR2lpaTIzzZ07t9rtH3/8cZmZBg8erNmzZ2vMmDGKiYlR9+7ddejQIf/tduzYITPTVVddpczMTOXn5+upp57SmWeeqTZt2uidd95p9OMmnAEA3GTV7lX+UunR5Y9SKtVgzpw5MjPNmzev2rm+ffsqPj5ex44da9S1ExISdNFFFzV6by1hvgAANMjll58sldq1o1SKdOXl5erSpYs6d+6sgwcP+o/v27dPbdu21XXXXdeg6wwdOlQej0eFhYX+Y8ePH1dKSorOPPNMffPNN/7j27dvV1RUlG666aYq13j11VdlZsrKyvIfKy0t1Ycffljt53388cdq06aNLr/88gY/1u8jnAEA3GRd8Tp/qTTiryMolWowYsQImVmNrzYaM2aMzExbt24N+rplZWVq3bq1+vTp0+i9tYT5AgDQID16nCyVEhIolSLd6tWrZWbKzMysdi49PV0ej6fezw84dOiQvF6v+vXrV+3c3LlzZWb685//7D/2hz/8QWamd999t9rtu3bt2uBn8VJSUhQdHd2g29aEcAYAcJPNn2/2l0rpS9IplWowePBgmZmOHDlS7dzMmTNlZlq2bFnQ133iiSdkZsrPz2/Q7YuLi7Vu3boqKzc31/HzBQCgQS6++GSpdPbZlEqRbsKECTIzrVy5stq5F154QWamN954o85rfPDBBzIzPfXUU9XOffLJJzIzjR492n9s4MCBioqK0v/+b/Uge9ddd8nMVFZWVufPrKio0LnnnqsuXbrUebu6tITwCwBAQ/2z5J/+Umnoq0MplWrQv39/mZkqKiqqnat8a1xBQUFQ13zllVfk8Xg0YMCAGq9bk4yMDJlZjcvJ8wUAoEEuuOBkqZSURKkU6UaNGiUzq/FDr5ctWyYz08yZM+u8RuXb1mbNmlXt3OHDh2Vmuv322/3HunfvrrPPPrvGa/3mN7+RmdX77SgzZsyQmWns2LF13q4Sz/gBANyuuKzYXyrdsugWSqUa1PVKpcrsEcwrlZYtW6Y2bdooNTW13ifMTkVuAQC4WteuJ0ul886jVGoqhw8fVkZGRoNXUVGRJGnYsGEyM+3evbvaNSvfGjdp0qQ6f/bLL78sM9OcOXOqnauoqJCZ6cYbb/Qf69atW62vMKp8a9ypn830fWvXrlV0dLQuueSSGkNfTXjGDwDgdqWHS/2l0s8X/JxSqQah/Eyl5cuXKzo6Wpdeemm1b7dtjJYwXwAAGqRTp5OlUrdulEpNpaSkpNbSpKa1Zs0aSXW/Umnp0qWn/UqlQ4cOBfVKpcrPHKjtlUqbNm1S+/bt1bVrVxUXF9e5r1PxjB8AwO0OHz/sL5WunXctpVIN8vPz6/z2t7i4uAZ9+9tbb70lr9erSy65RCUlJSHZW0uYLwAADXL22SdLpQsvpFSKdE76TKUPP/xQZ555prp06aI9e/Y05OHViXAGAHCTihMV/lLp6vyrKZVqUFJSotjYWKWmpqq8vNx/vLCwUB6PR8OGDfMf+/zzz7Vjxw4d/l7AXbFiRcgLJallzBcAgAY588yTpdJPfkKpFOnefvvter/9bf/+/XVe49ChQ4qOjq7z298WLlzoPzZ27Ng6v/3twgsvrHZ88+bNSkhIUOfOnbVr166GPLR6Ec4AAG4TMz5GlmlKyU2hVKrFtGnTZGZKS0tTbm6uxo8fL5/Pp8TExCqZKD09vcqrv6WT5ZPX61V0dLSmTp2q+fPnV1uN1VLmCwBAveLiTpZKPXpQKkW68vJyderUSZ07d9bBgwf9x/ft26e2bduqf//+VW5fUlKiHTt2VHsl0R133CGPx6NNmzZVuXZqaqo6dOhQ5drbtm2Tx+PRTTfdVOUajiyXcAAAF9dJREFUr732msxM48aNq3I8HIWSRDgDALhPwh8TZJmmH8/4MaVSHRYsWKCUlBR5vV4lJCTozjvvrPYq6ZpKpcon0+pajdWS5gsAQJ2io0+WSj17Uio5weLFi+XxeNS9e3dlZ2dr8uTJSk5OVlxcXLUPo6z8wOu5c+dWOb579275fD75fD6NHz9eubm5SktLk5kpPz+/2s987LHHZGYaPHiw8vLy9NRTTykmJkY//vGP9e233/pvt3fvXvl8Pnk8HmVmZtb4jN+hQ4ca9bgJZwAAt+n8p86yTFO36d0olRyG+QIAXCMq6mSpdOWVlEpO8dZbb+mnP/2pYmNj1a5dO91www3asmVLtdvVVipJJz8/6d/+7d/UoUMHeb1eXX755SooKKjx51VUVGj69On60Y9+pDZt2uicc87RAw88UO2zB9asWVPvM36V32QXLMIZAMBtLsy+UJZpSpqSRKnkMMwXAOAK3313slAyk3r3plRC5CKcAQDcpkdOD1mmKeGPCZRKDsN8AQCucPRooFTq149SCZGLcAYAcJur86+WZZraPtOWUslhmC8AwBW++SZQKg0YQKmEyEU4AwC4zXUvXSfLNLV6upU+Lf2UUslBmC8AwBX+9a9AqTRoEKUSIhfhDADgNkMWDpFlmizTtP2r7ZRKDsJ8AQCu8OWXgVJpyBBKJUQuwhkAwG3uKLjDXypt/nwzpZKDMF8AgCt89lmgVPrFLyiVELkIZwAAt7nv9fv8pdL64vWUSg7CfAEArrBnT6BUuuMOSiVELsIZAMBtHlr6kL9UWr1nNaWSgzBfAIArfPJJoFS6+25KJUQuwhkAwG0eX/G4v1Ra9skySiUHYb4AAFfYti1QKqWnUyohchHOAABu84d3/uAvlV77+DVKJQdhvgAAV/jv/w6USsOHUyohchHOAABuM2HtBH+ptGDrAkolB2G+AABX2LgxUCqNGEGphMhFOAMAuM30DdP9pVL+h/mUSg7CfAEArrBuXaBUGjWKUgmRi3AGAHCb2Ztm+0ulGf81g1LJQZgvAMAV1qwJlEqjR1MqIXIRzgAAbrNg6wJ/qTRp3SRKJQdhvgAAV1i5MlAq/fa3lEqIXIQzAIDbLN6+2F8qZb2XRankIMwXAOAKy5YFSqWnnqJUQuQinAEA3Gb5p8v9pdJTbz9FqeQgzBcA4Aqvvx4olTIyKJUQuQhnAAC3eW/ve/5S6ddv/ZpSyUGYLwDAFQoKAqVSVhalEiIX4QwA4DaFBwr9pdJDSx+iVHIQ5gsAcIWFCwOl0sSJlEqIXIQzAIDbbPt/2/yl0r+//u+USg7CfAEArvDSS4FSafJkSiVELsIZAMBt9ny9x18q3f3q3ZRKDsJ8AQCukJ8fKJWmT6dUQuQinAEA3ObLb7/0l0q/WPQLSiUHYb4AAFfIyQmUSrNmUSohchHOAABu883/fuMvlX6+4OeUSg7CfAEArvD884FSafZsSiVELsIZAMBtyivK/aVSv7n9KJUchPkCAFxhypRAqfTii5RKiFyEMwCAG7Ue11qWaboq/ypKJQdhvgAAV5g4MVAqzZ9PqYTIRTgDALhR+wntZZmmHjk9KJUchPkCAFxh3LhAqfTKK5RKiFyEMwCAGyVOTpRlmi7KvohSyUGYLwDAFf7wh0CptHgxpRIiF+EMAOBG3aZ3k2WakqcmUyo5CPMFALjCk08GSqU336RUQuQinAEA3Kj7rO6yTNM5k86hVHIQ5gsAcIXHHw+USsuXUyohchHOAABu1CuvlyzT1G5CO0olB2G+AABXeOSRQKn09tuUSohchDMAgBv1ndtXlmlqM64NpZKDMF8AgCv86leBUum99yiVELkIZwAANxq0YJAs02SZpsPHIjecNaeFCxcqNTVVXq9XPp9PQ4cO1d69ext8/02bNmngwIFq166d4uLi1LdvX7333nuntaeWNF8AAGp1//2BUmn9ekolRC7CGQDAjW595VZ/qVR6uDRk120pf1ezs7NlZkpLS1NOTo6ysrLk8/mUlJSkAwcO1Hv/jRs3KiYmRsnJyZo0aZKef/55de/eXWeccYZWrVrV6H21lPkCAFCn9PRAqbRxI6USIhfhDADgRr9c/Et/qVRcVhyy67aEv6ulpaWKi4tTamqqysvL/ccLCwvl8Xg0fPjweq9x1VVXqW3bttq3b5//WFlZmTp16qQLLrhAJ06caNTeWsJ8AQCo1913B0qlLVsolRC5CGcAADd68M0H/aXSJ6WfhOy6LeHv6pw5c2RmmjdvXrVzffv2VXx8vI4dO1br/Xfv3i0z03333VftXEZGhsxMH3zwQaP21hLmCwBAvW6/PVAqbdtGqYTIRTgDALjRY8sf85dKW77YErLrtoS/qyNGjJCZaefOndXOjRkzRmamrVu31nr/P//5zzIzzZ49u9q5FStWyMw0ffr0Ru0tLPOdN0+aM4fFYrFYrMhZKSmBUmnnTkolRK6VK1fKzJSbm6t169axWCwWi+WKde/0e2XDTDbM9MLiF0J23dzcXJmZVq5c2dx/4htt8ODBMjMdOXKk2rmZM2fKzLRs2bJa7z958mSZmf72t79VO/fxxx/LzPSb3/ym3n0UFxdXm+/UqVNDn1tat9Y6MxaLxWKxInPNn691r7xy8n8XLdK61asjNrdQKrlQ5S8Ri8VisVis0K3c3Nzm/hPfaP3795eZqaKiotq5yrfGFRQU1Hr/cePGycy0evXqaucq3xr3H//xH/Xuo/KtciwWi8ViscK7QpVbKJVc6LPPPlNubq5WrlwZ8raTVz+FdjFXZuqUxVyZqVNWOOa6cuVK5ebm6rPPPmvuP/GNVtcrlWbMmCGzxr9Sadu2bTJr/CuVlixZomeffZbc4oDFXJmpUxZzZaZOWU7ILZRKCIl165z/eRKRiLmGHjMND+Yaesw0PJhrzSL5M5XCgd+D8GCuocdMw4O5hh4zDQ8nzJVSCSHhhF92J2KuocdMw4O5hh4zDQ/mWrP8/HyZ1f7tb3FxcXV++9uuXbtkVve3v61fvz6kez4d/B6EB3MNPWYaHsw19JhpeDhhrpRKCAkn/LI7EXMNPWYaHsw19JhpeDDXmpWUlCg2NlapqakqLy/3Hy8sLJTH49GwYcP8xz7//HPt2LFDh7/3TTS9evVS27ZtVVxc7D928OBBde7cWT/4wQ904sSJ8D+QBuL3IDyYa+gx0/BgrqHHTMPDCXOlVEJIOOGX3YmYa+gx0/BgrqHHTMODudZu2rRpMjOlpaUpNzdX48ePl8/nU2Jiovbv3++/XXp6usxMa9asqXL/DRs2yOv1Kjk5WVOmTFF2dra6d++uVq1aacWKFU38aOrG70F4MNfQY6bhwVxDj5mGhxPmSqmEkCguLlZGRkaVZydx+phr6DHT8GCuocdMw4O51m3BggVKSUmR1+tVQkKC7rzzTu3Zs6fKbWorlSRp48aNGjBggOLj4xUbG6trrrmmxts1N34PwoO5hh4zDQ/mGnrMNDycMFdKJQAAAAAAAASNUgkAAAAAAABBo1QCAAAAAABA0CiVAAAAAAAAEDRKJQAAAAAAAASNUgkAAAAAAABBo1QCAAAAAABA0CiVcNpyc3N1991366KLLpLH45FZ3b9W33zzjUaPHq3OnTurTZs2uuCCCzRhwgSVl5c30Y6d69ixY3r++ed12WWXqV27durQoYN69uyp7OxsHT9+vLm352hHjx7VhAkTdOmllyomJkbt2rVTamqq8vLymntrjldRUaGrrrpKZqaBAwc293Yca//+/Xr22Wd1zTXXKDExUbGxsbr44ov1xBNPqLS0tLm3F/EWLlyo1NRUeb1e+Xw+DR06VHv37m3ubaEZkFuaFtklPMgt4UV2OX3kltPjpNxCqYTTlpycrPj4eF1zzTXq1KlTneHs+PHjuuqqq9SqVSs9/PDDysvL0z333CMz03333deEu3amO+64Q2amW2+9VbNmzVJ2drauvfZamZnuueee5t6eY5WVlemKK65QbGysRo4cqby8PM2cOVOjR4/W2LFjm3t7jpedna22bdsSzE5TTk6OWrdurSFDhmjy5MmaPXu27r//fp1xxhnq0qWLvvjii+beYsTKzs6WmSktLU05OTnKysqSz+dTUlKSDhw40NzbQxMjtzQtskvokVvCj+xy+sgtjee03EKphNNWVFSkiooKSdLAgQPrDGe5ubkyM02ZMqXK8VGjRsnMtHbt2rDu1cmKi4tlZrrllluqHK+oqFBKSoqioqJ0+PDhZtqds917772KjY3Vli1bmnsrLc7+/fvVrl07TZ48mWB2mrZt21ZjkMjLy5OZ6YknnmiGXUW+0tJSxcXFKTU1tcorSwoLC+XxeDR8+PBm3B2aA7ml6ZBdwoPcEl5kl9AgtzSOE3MLpRJCqr5w1qdPH8XExOjIkSNVjhcVFcnMNGLEiHBv0bH+8Y9/yMz00EMPVTs3aNAgtWnThpeRN8LevXsVFRWlRx99VNLJoPvtt982865ajptvvlmXXnqpysvLCWZhcvDgQWZbhzlz5sjMNG/evGrn+vbtq/j4eB07dqwZdoZIQG4JL7JL6JFbwo/sEl7klro5MbdQKiGk6gpnFRUVio2N1U9/+tMaz5977rlKSUkJ5/Yc7fjx40pOTlZMTIzy8vJUVFSkTz/9VBMmTFBUVJSysrKae4uOVPks9Jw5czR8+HDFxMTIzHTOOecoIyODz8w4Da+++qo8Ho/Wr18vSQSIMNm+fTtvI6nDiBEjZGbauXNntXNjxoyRmWnr1q3NsDNEAnJLeJFdQo/cEl5kl/Ajt9TNibmFUgkhVVc4Ky0tlZnpjjvuqPH8FVdcoY4dO4Zze463detWXXbZZTIz/4qOjlZ+fn5zb82xHnvsMZmZOnbsqAsuuEB5eXlatGiRbrjhBpmZhg0b1txbdKSysjIlJSXpwQcf9B8jmIXHbbfdJjPT22+/3dxbiUiDBw+WmVV7pYkkzZw5U2amZcuWNcPOEAnILeFHdgktckv4kF2aBrmlbk7MLZRKkCQdPnxYGRkZDV5FRUU1XqeucFb5vvraWuk+ffqobdu2oXpIEet0Zl1UVKR77rlHI0eOVEFBgV5++WX97Gc/U1RUlOvDWWPnOnz4cJmZ2rVrp6+++sp/vRMnTqhPnz4yM+3YsaOZHlXzOp3f1ZEjR+rss8/W119/7T9GMDspVP/eStJzzz0nM9P999/fdA/AYfr37y8z83+GzqkqX2JeUFDQ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+ "image/png": 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\n",
+ "text/latex": [
+ "$\\displaystyle \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}$"
],
"text/plain": [
- "<IPython.core.display.HTML object>"
+ " \n",
+ " ______________ ______________ ______________ ______________ _____\n",
+ "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅╲╱ \\bar\n",
+ " \n",
+ "\n",
+ " _______________________________________________________\n",
+ "_______ ╱ w \n",
+ "{\\tau} ⋅√p⋅ ╱ ───────────────────────────────────────────────────── \n",
+ " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} "
]
},
+ "execution_count": 52,
"metadata": {},
- "output_type": "display_data"
- },
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "py_vars = ('w', 'tau', 'p', 'L_b', 'A_f', 'A_m', 'E_f', 'E_m')\n",
+ "map_py2sp = {py_var : globals()[py_var] for py_var in py_vars}\n",
+ "sp_vars = tuple(map_py2sp[py_var] for py_var in py_vars)\n",
+ "sp_vars\n",
+ "Pw_pull_elastic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "For plotting, let us also evaluate the for the displacement at the unloaded end\n",
+ "\\begin{align}\n",
+ "w = u_\\mathrm{f}(x = -L_\\mathrm{b})\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
{
"data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "5c51964df7934170b3808eb6ab042c7a",
- "version_major": 2,
- "version_minor": 0
- },
+ "image/png": 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\n",
+ "text/latex": [
+ "$\\displaystyle \\begin{cases} - \\frac{A_\\mathrm{m} E_\\mathrm{m} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} + \\frac{\\frac{2 A_\\mathrm{f}^{2} A_\\mathrm{m} E_\\mathrm{f}^{2} E_\\mathrm{m} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} + \\frac{2 A_\\mathrm{f} A_\\mathrm{m}^{2} E_\\mathrm{f} E_\\mathrm{m}^{2} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}} & \\text{for}\\: L_{b} \\geq \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}} \\\\\\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} + \\frac{\\frac{2 A_\\mathrm{f}^{2} A_\\mathrm{m} E_\\mathrm{f}^{2} E_\\mathrm{m} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} + \\frac{2 A_\\mathrm{f} A_\\mathrm{m}^{2} E_\\mathrm{f} E_\\mathrm{m}^{2} w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}} - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{m}} L_{b} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}}{\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}}} & \\text{otherwise} \\end{cases}$"
+ ],
"text/plain": [
- "VBox(children=(HBox(children=(FloatSlider(value=1e-05, description='\\\\(t\\\\)', max=1.0, min=1e-05, step=0.05), …"
+ "⎧ \n",
+ "⎪ \n",
+ "⎪ \n",
+ "⎪ A_\\mathrm{m}⋅E_\\\n",
+ "⎪ - ─────────────────────────────\n",
+ "⎪ A_\\mathrm{f}⋅E_\\mathrm{f} + A\n",
+ "⎪ \n",
+ "⎨ \n",
+ "⎪ 2 2 \n",
+ "⎪ 2⋅A_\\mathrm{f} ⋅A_\\mathrm{m}⋅E_\\mathrm{f} ⋅E_\\m\n",
+ "⎪ 2 ───────────────────────────────────────────────\n",
+ "⎪ L_b ⋅\\bar{\\tau}⋅p A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\m\n",
+ "⎪─────────────────────────── + ───────────────────────────────────────────────\n",
+ "⎪2⋅A_\\mathrm{f}⋅E_\\mathrm{f} 2⋅A_\\mathrm{f}⋅\n",
+ "⎩ \n",
+ "\n",
+ " 2 2 \n",
+ " 2â‹…A_\\mathrm{f} â‹…A_\\mathrm{m}â‹…E_\\mathrm{f} â‹…E_\\mathr\n",
+ " ───────────────────────────────────────────────────\n",
+ "mathrm{m}â‹…w A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathr\n",
+ "──────────────────────── + ───────────────────────────────────────────────────\n",
+ "_\\mathrm{m}â‹…E_\\mathrm{m} 2â‹…A_\\mathrm{f}â‹…A_\\m\n",
+ " \n",
+ " \n",
+ " 2 2 \n",
+ "athrm{m}â‹…w 2â‹…A_\\mathrm{f}â‹…A_\\mathrm{m} â‹…E_\\mathrm{f}â‹…E_\\mathrm{m} â‹…w \n",
+ "────────── + ───────────────────────────────────────────────────────── √2⋅╲╱\n",
+ "athrm{m} A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
+ "────────────────────────────────────────────────────────────────────── - ─────\n",
+ "A_\\mathrm{m}â‹…E_\\mathrm{f}â‹…E_\\mathrm{m} \n",
+ " \n",
+ "\n",
+ " 2 2 \n",
+ "m{m}â‹…w 2â‹…A_\\mathrm{f}â‹…A_\\mathrm{m} â‹…E_\\mathrm{f}â‹…E_\\mathrm{m} â‹…w \n",
+ "────── + ───────────────────────────────────────────────────────── \n",
+ "m{m} A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
+ "────────────────────────────────────────────────────────────────── \n",
+ "athrm{m}â‹…E_\\mathrm{f}â‹…E_\\mathrm{m} \n",
+ " \n",
+ " \n",
+ " ____________________\n",
+ "______________ ______________ ____________ ╱ \n",
+ " A_\\mathrm{m} ⋅╲╱ E_\\mathrm{m} ⋅L_b⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ───────────────────\n",
+ " ╲╱ A_\\mathrm{f}⋅E_\\mat\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " ______________ ______________ \n",
+ " ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} \n",
+ "\n",
+ " \n",
+ " ______________ _________\n",
+ " √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathr\n",
+ " \n",
+ " for L_b ≥ ───────────────────────────────\n",
+ " \n",
+ " \n",
+ " \n",
+ "___________________________________ \n",
+ " w \n",
+ "────────────────────────────────── \n",
+ "hrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
+ "─────────────────────────────────── \n",
+ " \n",
+ " \n",
+ "\n",
+ " __________________________________\n",
+ "_____ ______________ ______________ ╱ w \n",
+ "m{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅ ╱ ─────────────────────────────────\n",
+ " ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\ma\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " ____________ \n",
+ " ╲╱ \\bar{\\tau} ⋅√p \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " otherwise \n",
+ " \n",
+ " \n",
+ "\n",
+ "_____________________\n",
+ " \n",
+ "──────────────────── \n",
+ "thrm{m}â‹…E_\\mathrm{m} \n",
+ "─────────────────────\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " "
]
},
+ "execution_count": 53,
"metadata": {},
- "output_type": "display_data"
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "w_L_b_elastic = u_fa_x.subs(x, -L_b).subs(P, Pw_pull_elastic)\n",
+ "w_L_b_elastic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "and also the expression for the debonded length as a function of the control displacement $w$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "fragment"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{A_\\mathrm{m}} \\sqrt{E_\\mathrm{f}} \\sqrt{E_\\mathrm{m}} \\sqrt{\\frac{w}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}}$"
+ ],
+ "text/plain": [
+ " ___\n",
+ " ______________ ______________ ______________ ______________ ╱ \n",
+ "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ A_\\mathrm{m} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ E_\\mathrm{m} ⋅ ╱ ──\n",
+ " ╲╱ A_\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " ____________ \n",
+ " ╲╱ \\bar{\\tau} ⋅√p \n",
+ "\n",
+ "____________________________________________________\n",
+ " w \n",
+ "─────────────────────────────────────────────────── \n",
+ "\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m} \n",
+ "────────────────────────────────────────────────────\n",
+ " \n",
+ " "
+ ]
+ },
+ "execution_count": 54,
+ "metadata": {},
+ "output_type": "execute_result"
}
],
"source": [
- "po.interact_fields()"
+ "aw_pull_elastic = a_subs[a].subs(P, Pw_pull_elastic)\n",
+ "aw_pull_elastic"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Interactive exploration\n",
+ "Now that we have finished the construction of the model we can track the process and explore the correspondence between the internal state and externally observed response"
]
},
{
diff --git a/pull_out/2_2_3_PO_ESF_RM.ipynb b/pull_out/2_2_3_PO_ESF_RM.ipynb
index b29ac62075c6cdeb946e3beed8003d9a49a59f2a..718a4197c024f81208a0db9fea92051025edac39 100644
--- a/pull_out/2_2_3_PO_ESF_RM.ipynb
+++ b/pull_out/2_2_3_PO_ESF_RM.ipynb
@@ -12,33 +12,6 @@
"Pull-out of a short fiber from short matrix "
]
},
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "ca3da96b6fe144d79d69b0c1be56b25c",
- "version_major": 2,
- "version_minor": 0
- },
- "text/plain": [
- "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "%matplotlib widget\n",
- "from pull_out import PullOutAModel, PO_ESF_RLM_Symb\n",
- "po = PullOutAModel(symb_class=PO_ESF_RLM_Symb)\n",
- "po.interact()"
- ]
- },
{
"attachments": {
"image.png": {
@@ -331,7 +304,13 @@
},
"source": [
"\n",
- "The strain at $x = b$ must be zero and the displacement must be equal to $L_\\mathrm{b} - b$. Thus following the same arguments as above we can directly write\n",
+ "\n",
+ "The strain at $x = b$ must be zero and the displacement must be equal to $L_\\mathrm{b} - b$. The strain profile of the pulled out fiber with the instantaneous length $b$ is linear with $\\varepsilon(b) = 0$. Thus the elongation of of the fibuer equals\n",
+ "\\begin{align}\n",
+ "\\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b\n",
+ "\\end{align}\n",
+ "The current pull-out displacement is thus a sum of the slip \n",
+ "at the free end and the fiber elongation of the zone $b$\n",
"\\begin{align}\n",
" w = u_\\mathrm{f}(-L_\\mathrm{b}) - \\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b \n",
"\\end{align}\n",
@@ -368,9 +347,9 @@
}
],
"source": [
- "sig_down = P_down / A_f\n",
- "eps_down = 1 / E_f * sig_down\n",
- "eps_down"
+ "sig_0_down = P_down / A_f\n",
+ "eps_0_down = 1 / E_f * sig_0_down\n",
+ "eps_0_down"
]
},
{
@@ -400,7 +379,7 @@
}
],
"source": [
- "w_down = (L_b + b) - sp.Rational(1,2) * eps_down * b\n",
+ "w_down = (L_b + b) - sp.Rational(1,2) * eps_0_down * b\n",
"w_down"
]
},
@@ -448,9 +427,9 @@
"outputs": [
{
"data": {
- "image/png": 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DGDzEMW5bE63THthfdwizeJX8YU6k7wfdiw5tXxoBI7CPQMiC7hzjIYc3GWMOUpP5+khpaT1X2D0XSJnGKb9cX1ab76LLA3jTzhlGeKCKdZPzG7MfllQH/FsPmkP9XKxwqEFuFpojpmfOE6Bt1gQPJujJT+Mqi3KCYGm0XF0np7RVFZxMD+tBqRA9yM2hpe45lUXoMDjJx+TeKEWZHoJsLQWMtnai2+CqeFfokn9fPilKCjfjT7Tho+SFMRAKGqwe7OiDKjeLRSZEX6M92mqEfc6nzo668g0fih+qlJbtPS7bE03ap73u5OT7J93FUMXsjIARWIJAnnM8aMRDR0NOeXwmgOsn8rFGsAY0c1H5zZpAwYrbbL6rbR4S4R3hzoPNnxQOWVoq7G2TJD5Yw7rr2DaNZapXS6mL6XSTFSIEQhFoKQnKY2+sFOaDzebyvB8cT/ZNeaWx4K+m4IgewmPX0xbfvWCw1BzbL7yq+0A+0aCQ6KzKHzTloFkbGA2mahcewDkUn2Pyx2SnvTUcilrX4pAWDPUxKV7K72LBOOFpIpWDCcVjLM5W+oKOQhQWcC0XCHigrVjcdJlc7CvHtUMjYATWQSDW4GZ+V8iyRpbuurwYim8930WfNYgHbtYStm5YKzisGWv1EHvVPNVFNl2cW6xwRI8FAIswC/NThVgLGg1TaZhcqlstUT9C1WOR53vsjdICPfIVNpqo4mspOGicyfQWPBQhfUChaDmVZ+CEgGtNAuWtqoCJXgjZPYGuvBJjlI0kGI/JXwaGe9bcr5y2F4ivQy0OQQvFgjHQwlxpYNQoBcpfS+mjPZ6gyvZIayk8ub2uAqJidkbACKyAQKxzrLt9LspEfjlnI20s3HS+53UEWZi2MnSN4sHWMOfRZvGr8gd/UXkMhC3z761MPJ5MATU5AYOQ4RzGKKAqg6B4X2FT/4bKDhotjTXTQ8hwEDU04Fw8KTiNAIrEbqh6CKqhz2bD8/2ynurAI/28rzjKCoJ+zymduov4y0SZBLiWkLtJuvlVW/Qf3FCCjspfbhsFc1DgKh+Lw5fyMUZumC9+c5nGalNkRZT71cJBdcAfrJsxAy/ypMXWC1aTlsv1htqiPLh2F7Ja2hPRa/HVaswXRsAIHIwA81mVmc+xFja0lBcPZJzxWOpqc7uWtni+i28OuXLEAKWDMyhYPO4v7cDU+sdsq+TpqrxYGlcnePpk4X2qEC2OQcJi/8EYbZXlxjJoOPzTFQSPlFYzPyG8EDgIm2SlULlJCk60p3DoC6ZJyaGsfBI8ChFmtJf6qHDIHcxfQZT+7Gi3SGuiSmfCgVuyMFBO/tj8dYVywx8R8bPY4iAaTEbopHuS6TJm6Gv1C32qs9TqBua0mZzogfUDedpNLqftWZ8i36ERMAKzEagJXmTI95pvCOZyLWSNjTdUoiHq12hEfl949PmuvvBQyncwWOfpH6/3l/3r43WncvQxHqZiTRr9PECu918KWTcntVUyoTqsg6y7D+W/kn8tH471knTeFtqTC2+9edPeClIhOsFrRTgOvJRvA9ykDvxmZliAYYgGeV2mb8uioaQyaHoBWpOeIwjR6paM0mkLANJJZF1jsagKIGgpn/4hoKmDA/BWeZXh5sNzWQZFiD4FjV91PWrWUplZ/BX0v1QcPELgde8D/eDGErbwUZvpHm7Fn9prnNoAy1cKawphU46IyiS+FMXi1dqC0TWKI1ajKh2lc09oi3EQ94WDyixAewNb6ckpDwwZW0zqUimtWdJuKhW/qhPK72sl8zE4FgjuzbU8aa1vdOjazggYgQMQ0FxjrUOAMr9ZK1jzmrUlz2XWYOYdjrnN/E/WRYXUY46zVlCGdN6+6K6dSq47lb2Y+Q6v8o1szbw/Ujj4cobyUdKwOM+W74GaaKQzcgr3HtiVxjpdVXxqCgc3PbYZ0FIO0YCoz2BAENCpXoGg/EVOtBlkCPVZCs6SRtUmk2GqwmH+CrCFHRMa5eLdclwojlLQ++GsXI9vc1QVz6KJvajqzFb69og4wQgYASNwRghoXcNawAN9KFzxcNUrt1UWecTD0vfyzbeMFJ/l8pqKBbn14AgRpXHUID2cd4ne6ybomqfm5FRptrKRqz5XiFBmi2UzZYO2RB+w4RPNGI/2djbO/O3dirg/zYAURjyRjJ3zYaKkibVHcTwh2nya2+IV1nhKGq/tEkbACBiB80MA68YPM9mKz1Ygl9+fWbcsznr8MhK0nvJJDGQ+DvlfdVeV1DiYM9kM1aWhhhEeKAGNUOmWWfmaDmLG2VzBOZBv85eB07iYfc4nD2S091eH4K/68VEgFNJkdTuEjusYASNgBKYikNet2C2YWo0dgUkP+irXfTECBYT1tVpf6c3/bqkcikpjXAjmKJPjWKCht+eUHtv8WFdQWlA0sD6n7XCFzcOc4i16LYVDmVTkaROH6ftgJ1qzTd+HNqa2jqbgZIzYw98pDkaYjwatOMo3f+2bi8UBDRmLA9j1WhyUz3hEUcA90zXfZ+lOtJvc4d9zV/qGuXeuETACF4WA1ikE7+B5irU6pLZQAlgrq3JX+ay3pYWYLezH8o3LNDjbhtJD+T5HHtspSSHJ9RolIyrl9Ba91hkOFUAQoJEgIPf2ZoKQQyOwFAGNr6Od8wlec5tMpkEFMco7NAJGwAicOwJaz7D+8vDL2rYn+OFf6eSXedRBQWk++64yKBJYLQZ3JpTPmbjm/Iau7+s6fRohxx8pRIfYo3elgskpEwZQNmDqk5ToHyOwHQJHtzhojFe1/+26aMpGwAgYge0QyHKbT1CkoxD5eqeweahSnK2U1vaIrkPhIOQtR0KMDGyNlFsvNeZRJBp6Ko/OENs4WKM5jFqldw9qykRDSVqLwt43BShrZwTWQEBjjjNCxzznswbbpmEEjIAROAsEslDHcsHrsRwGZVsF68R1MKg0lAMUgpZTeigkKAa7fM05SLa3q58myOXi/Ea5PUMWNGgLSwfWD+jv0btSBsoG5m0KWNkQCHbHQUBjzxaH40DtVoyAEbh9CCC3Q343vdO6GmcrUEY4p4Fy0Jx7yzI/3tzjXBwKwp4C0RDMEZVhB+RJvuS/YXI08YDigsIxuKZfqQAMJfMHDStuZwSMgBEwAkbACJwxApLXex/dKtlVPopHs/UReVnOV/OiTC1UPSwfvdaPWp1u2j/85S9/+VH+H5Xx7wr/9/e///3c13i6NH1tBIyAETACRsAIXAgCUiawlPyb/L9ID/gf6QH/uYT1PnrNWyoqgPmFL0BiKmnML0sadV0jYASMgBEwAkbACIBAo3BwIUWDd3PZXmk+l0q6nREwAkbACBgBI2AEliBwr1M59ns4XWpnBIyAETACRsAIGIFVEGgpHLJwcFKVg6P3FWd7xc4IGAEjYASMgBEwAosR4C2VrvtKCeksh8KzPsshpYh3gnlNh9d1NnFqY/Qv6IcazjxudhD33PkbwsZ5RuDcEVg6v869f+bPCBwTgZrCwXYKCgcfEsHScc6vyvIuMV9ZG/wU6zEBrbQFj71/F1wpf+ykc+fv2Hi4PSNgBIyAEdgAgZrC0XylTO09lB/9IMgGfI2SlJKRvnimMD6pOqUOB2K/Vp3Bj5OMEppY4BAeJ5Jepdhc/lT+qPit0kkTMQK3BIG7Nv/UXx58eV2TT2+fpRy6JUPraN2oKRzxyVOYQMCcq+Ob7fG1tKk8Yr2JT7NOrbOkXJVHTR62gPj2PQodjr8KLi1JTDKwf0Ceyqfv5Cu+tqvyN9DIYvzOqO8D3dzPEt/cj7Ckcd9QzLGuVRXe3E/+upk/SMJRjrn1rfLOeqsSZtd2c/Fbu/1bQu/OzD+NF7ahn8uzNv6o66O9Oam2WJ89dwXC2q71WmwQF+Bvcvwsv8kh/mY/aasOCz8Tdqf4onMZGZvBYAqPKgPOaO9Vi4vSk2KicHWFQzRnYajyq+Ineifr++CNq2RmrPi/guY+KI6yG/en9+kr9/NnhUf5m+oK+ydPUt8Zawfhd3Lmz4QBYXhn5p/6imUDZf7dPHaYa58oXj6UbX5n1B5r1CZzV7R5qPxennlxZx5AahaOzW/kCg3wpBlPm1PJISz4w7CPdIP5g5nSkjOVxpxygzyq/UeZWK+wUj4DcStBNchfpaOr4XcGfa90bzCJBS9eGU8F1QcWRBZGlNjqJ4aVH9Y0xt1il9trlJ4OwWvlt3js5C+6FG3GK/PmkMVxFn6n7OcSkBZiNNb0XZp/9DVZDoUp6zT/YnpUp3ZXnbtd5kWf/y/5QOn8lwnfv0LxWPTZ8G4b53h9cQqHbgqaIX+hO3lxVVkWvHLRg8ZmbiKPITj4l94hx2Bc1U3kr2lzA/xO1vemU/MiCNufhMPb8uVTFsrikAIbSuXYPZ7EjdpG2B8i8CfRHynEnDl03szC78T9HIFhMHsJRr2Ehcfa69clzD+2LE/pVp27tY7ktSQ9+CnOX8Kz1vNwwt+7l+tMrfpFpt27QK6ZfOztTXK6cZhzf1GIpvxLrkTalm4Kj2lAi6+WhUPXmOmTU5xB18rPWUuDKfwFD1vgd8q+H4Id9wDTat8igKCpuSckqt4W97DW3rmmHYrfufbnaHxp7Hj+HQ3tVkNHnbu6z5/LY81G6eDMyp/k+9aVFqOXdHF1SczmG/BI4WTrhvqH6TvKxzYKhzE3cTN4xGTXEkSqiyBuCTWlVQ8lHsr8DP6iiS3wO0nfo0NzQ2HWZ9JNZteBe0T+avdP7aAoxsn9WjfSmSuVo13GEgffPpFHaHH9mxw/6n74HPym9lH92E3tp8qxcIMb/cdS1ViJMg1wS2uEQs5KgDOvsrfmotJO4e7M/Mv3goPsjNWdrh/kMM0/XXMfuTdh9UVA89ZhWkcVUo98xjsPpaz3zAHSP1Z+rP+6HHWrzt3R1nIB8ZismAoZh98r5NAsysck3lXurMf61VQgzqTcrLcqBD4DrTRnx03b6lwEMI3ymPmiLHvi6SCr4gwU+N2SN5Ef549CuC3wO3Hfbzq2wq/6wYLEwoZJdM8V/WwplXsFJyaI3gsVRQCy+GJuZmFtta0yodw8URxBxdj6Xh4TbdofVkg90sOsrujxnfjYw09pc/oI01P7yT45eLCIfynfKByKM1+Ze+HAmPv6UH6VexeE54bid/X1K9OElVOsPYMQiDfGL4pBWhMVJkWDSoozXtK4VTzWcdJ564tvRmEh4H6hKP6qkHWUcowprMZgWd53Xdad6lMWd7L7Lx7YWvkm84JSRV+mPCic9Vi/AtVzcAKUxYCDNEM3mf3yOQKZwRvWDbrJYoJjQdlzKstAYyFmAeJJqHWIR9dr8RiLPfwlIaEQnpg8zWTSdeOUPsgbBVVmLf6i3VXxy0Q36XswfMSQxY8FoTVGivajn6XCW2T/PSoaLKYIQg5+Rr2mQM5nbDSHTxXfyYeC0S37KicwptgKaurpmqfDZtsulztF0MJPPILBpD7CbC4/2s9OObC9pn7hmFc8DSen8t/Jg2t1HuZixwo8//6OdIyX7n1B6WYLIu4bNbjHj5QWVqvu2SvKDLmYg4vn7lAjM/NKpbhaVf1lDsWcOMuxflXlfEaiOgkQPEWNAlKQbQQtaaLBAsiTBoNp6BVRtNVJLtNEiy/rPMiV+3hlgPHGAeVaZVbmkUVuJ5qNwFC8KxjIL7/02stbprUqhmobeqvhB4/Zrd73IEwIZgoWjceSXi2uNhhT3K/mCaxSLvrZq0DDqzxKNq9GM/a7i2kiS74i5VhhYXmdMvd/4CvKUq4RprloGtcqU46thorS6VvivUm8iaS5o/xSgY8i8D+ERZRLYW6jhZ/S5vQROpP6qXIocYHHY103eCgdfMCje4/49k31XqjsTnnHwOgi5x/4rO3yfUJ5DmHaNKE8xh7XnLmI+8zcaO6f8vvmCvVqbrW5WyM+JU088/D4TJ5+IC+b/gzUL+fEKmN9oK2Dsq5Gav12JH+Xb2ZVSRirS77qM+kxdbG/ykldzGMxcJTUOPZZJ1k3VC4W1dBUGyLK491qBjdDKRAAAA27SURBVG/L5Tos/gzO1gBV2to8Qq+7yMEPC1lymR/2nTEV0p8qbxRem7/cHnRXwQ8eC7dq3wu6KSqeuXcHj8cuve616HNPHtSw6ZSln7VxnIplOoyBGGssch+kzPEfFtfq01fu/05hWjRVrjvOuKcxlvZaUr2aQgE9FkAU0D6Lzh6tWoLqT8Wvt4/QFZ2Em8Kxfv53Lg//zKPSrE5dsOjeJ6xAvU7lt8YIPndq5+LmXy9oyzJivY65UqPGfCvddXkxM77l3B1kRfec+YHVhnn7ga6H+tyiFWUVrjbWWw2scHE1QuNvI/mLswVOmuwKefJAq0eraz0tKY+b0Ahjxccch2yqi4Iqoik+KAmoLAOM8vcVT4eSFDYLk+Kr8ShasUDuCQzllVosff5CaYO80Q+VWY0/6Mmtit8NycTn6n0P2scIhTMTmY8RNeNT8bQYKmzuneLRz5cDfPHlxDTGFHKPETKPct33FR/ar4WPhgfFaw5hxRNPd8GCt2Zs1ypulSZeJuGX25/SR4pO7SfleBou8SCtpZApn3uR5pPCUznPvzbyMbeYI30uykR+eZ8jbTTU/d967lZ5ULvIPmQQ259LDyyf7Vi/V+39CRLzQsBCmL5r0GEBjW/SIpkHzNC/szIQWwNXdVhgaGOnOIfLqm0pnbpLeWQw4FoL3U3Sza/aQYi9T3vyk3ijJuUVLOJPNJhwm+Anupv1XbQ3dcIFQcQ9SeOkaAzBeF1cEx3sp2iwuJQKJ5izYKJgYkHAdIziu+eUz9jA0jAmFKHZGmOqgxLLGOn2QUnbOrU9Gb8ZfYTpqf0Et65QqqVxELWF27bItKmrbc+/NiQ7YcJYZ9zGvGpKZLy45ozHGi7aqI4BtXfw3O0yJ1rpAVdhsqgp5GEG+UNfl7jauK6lHX2sXy3p1QZ1WWTDpJQsFAKfBZ3DeaM3QWUAlRO91S8/Zn6TcKCsfHcBykUGg0U8ijL92antqsBQOgsOk2fsCRYyNXcwf2p7a/y27nsNj8VpgYsIcTCta2nDKtHdZujtp8pyf1i0yjHKIsdTbYxxwofyNQftwXErOvdVBgGfxjpElMa9RdGYZaal7lKX22ZMz8FvsI/wJLpz+sl8A5PkVJd59kAeXJLLaaUiGFlHCdW+598N0tzXrmO7kddE+SJnuXYyn+INlahD/RqNyB8Kt5y7TbvqA/xx1oz+TDoq0FQej5ztWD8rhUPAYwJGs3yqMDQ9tlgG97ZVlpvHgsYistM1T+ithVVpDCSUmFRGYXp/W+mznvZUfjaPqgN/X8qzoKQFTmldjZwyCBlCTL9VDVt5g24Bf5vgd8y+DwKzLBMhxH1DGe66tPhN6Cf1Q+B1FWjuezkOOYPSJ3DZbukqPUpquRjjzCGUGxxnpNjG6aObCm30M4pfp90pfaTK5H6q32DB4g52r+X5COA/y39ZpLW+0aG8ozi1z5y/8/NPODA/WO/TOqhrMHmlEIWCNZF5EXJB0TQnuU5rpULGA2s8c+2xrlEoXyos39JSUtspH/yH1ue15m7TsNpkDG5y1ky0z3asXzUInE8EjZWB81TAsThyYpyb0+tyfpjCquVUhkE3OPCqFeuJs3jM/B1qsahzMJx6CH+b4HeCvg8jc0Cu+jD6BLKwn5hWy6e2x2LzkxqrKjdlHHEvWaChWdKtkdw8TXyM4lcyMbGPVJnVT9FNVtOyLcWn4Nmpsu6l+GJ9u/PzTzgwVnvvh/KRB7V7mG6I8lE8Zj+oZfx7203E+38mz91+EuvnqE81nA7t42oM3huhNPqWykj92dl50DDw0HTxCM+zcufO47nzd1Y38zyYwWrGU9ZOIVYUlOwlyjEK++yFl/YHHEJxUPEfqLtV1hb9XMLrOWK0pD+uO47A2nN3vMULLjFm4dj8LZUe7J4rHXMaN3NzE7DaYLHHpLZTHJMr++lj7R6FxwN5oytH4Y+GFvBI9V63Fd3eBk+XwZMHYy4Ojw0+7Q6xmTHDBPxqqNzcPNFdW4GZy0Kr/Fb9bDUy8+JUGGUs5q5fo73biu5ow5dV4KC5m7EdOpxfQ6H1/apagXNPe+vNGz5L0XYCIxLTfzO0c49zJR64GVM/eHIcpjqtnDuP585fB05fLkRA95tzSlgF2QvHSsiZheobV8q7WHdX+nmxN8iMG4EeBM5W4ejh18lGwAgYASNgBIzABSIwdobjArtklo2AETACRsAIGIFzQ8AKx7ndEfNjBIyAETACRuAWIjCmcBz9LZVbiLG7ZASMgBEwAkbgziMwpnCc6i2VO39jDIARMAJGwAgYgduEwJjCcZv66r4YASNgBIyAETACJ0LACseJgHezRsAIGAEjYATuEgJWOO7S3XZfjYARMAJGwAicCAErHCcC3s0aASNgBIyAEbhLCFjhuEt32301AkbACBgBI3AiBPr+S+XPmZ8fTsSXmzUCRsAIGAEjYARuEQJ9Cse/5j7+h8KT/731LcLbXTECRsAIGAEjcCcR6FM4ZoOhP1SKv5H/RZXflZ/yj6uz23EFI2AEjIARMAJ9CEgW8eeF/HvuO/Jf6frTvrLnki4e4ZU/LP2D4rfuDxcD51XOcAgggHqlELA+BzT5bxUHRDsjYASMgBEwAqsjIBkTD7oNbaX9Vf49JVzLP2gyzjuCrLwvD9+31i1WOHRjnwqd+wq/CZQUf6041y8izaERMAJGwAgYgbUQkJwJId1H8ue+jHNLV1++E09vKzx7a8wS7BYrHGr8Y/naOY9XSn8kANHa7IyAETACRsAIrInAR2sSOzUtyUoe1G+1G1M4pvx52yMhhOmq60K7JN/OCBgBI2AEjMAqCEg4c05jbztlFeImshkCY4dGB/+8baL14lL20DYD2YSNgBEwAkZgGgJZrqBM/JRr8BLC10pn22GnEMvGE+JyWNG/vonuXirebO3nNMq/o3hYQ95XnPOGnDVsuVyO84e0+xt5jgqkLQ6FPDjDE7Sey/NADS3SsfITUpd88ogj+6iPckTap6LznTz8wg8WDcrRL9KoSz70klOcutCmbOwWPFF6c9ZDcepV+Vb6WbmrhdyEMjFkCgqQFjbl6kbACBgBI3CbEcgCFuH7oeJhJd8pzksIv5P/XB6l4huFKAYI6KFzD8gflJKkYChEgP+okPolfdK/l38v0hV+Jk9Z0lAKCH9ViAJEXc4ofiYP/S/kv1Kc/BeKJ8WnSEvKhvJ2SvtY/ltFSQseoM3LF43TNbzztueHTaIium76q/gg32W9c4jfOwITaIp2RsAIGAEjYATGEEDZaCkDuQJP8AhfBOwc91B1mtdMFY/zhlgNSke7vEIbCsBOcZQUlJywjlCe4wMoGMEjBz0TfYU8eKNoPJFPLqeR3lgtchZv0jRt5bTu0YSHSod/FI/SlS9jTOW7rH+y+FKFowtQ2ZEH+YLvctgZASNgBIyAEehFQIIVZeId+VfdQsoLRaER5t0yPdc/9KQ3Qrxot2VhyPVol62TcCgPwctOdbku3UtdoKTQD/JRVlBIeJszOaWh7GDhGHQqh1UFGfur4lh4sLi8I19aa2hnCt+DbR0rc9GWijr+Wh5em5tXMB5pXS2uKOKoETACRsAIGIGEQBLSinWFeAnPXAtHWbcvHu2yrdEoBrkw1oSu0oISUHWqj+UD/tn2wCrzvq75PtVT+Y/ksYCwXUTeFMdZjWfyKC6cIcHKw/YN9OfyrSqndYsUjsw6Wlh0vOxNWDjItzMCRsAIGAEjMIRAPJzGw2qtbJTZy5MQRhhPFeRl/aCJFQGFYMwNKUTU5SwHysVzhWHhJw0lYQp9FUvWEeTqde5T6pfiKEScEUERmsu3qpzW3VuhefaQ2GvqOjQz9qnGbk63nq+NgBEwAkbgjiEgWcFWBfKidUgSGJTHNgQOeRNuFdlStPskCJdh0XaZPBRHGUBZ4PPqoWCQxtkPDpkSn+Kw5rQsLqrP9gw0OdsReK3F9xSeFpVZrHBkANDCMPkkp/h9RR7Lf3KT4l8jYASMgBEwAqMIfKASjyVDulsnbCfwhkppMSdee9iNRsLKHtdDIe2iEIRik8rqmnbDkkAasg3f61QHRYA6nLdIdYs0Xmkt6XXpdGk/U/luGteBw1S+u+2c5PqtN2/e7DWsDkYir+00J3z3CuaEDAg35rU8JiQO2TxXOsDbGQEjYASMgBGYhIDkBtYBthCQJziu2UYIIZsS+VFaWDwQ4sgczhWirDyT5yEYGtRjewM6bGugVKR0lW3eHlE82lV28y0O2v1ZnjrULWm+VHpYMKjTOKVjyaBek694slYobMlUXQe/oezALw/rKFNYe2JbRtH0fRC2fhosFO/lmwrn5MYUjvgztnPi2bwYASNgBIyAETACF4bAvR5+w+TDB07sjIARMAJGwAgYASOwCIE+hSO2Qob2xxY17MpGwAgYASNgBIzA3UGgT+GIU7R8wOT+3YHDPTUCRsAIGAEjYAS2QKCqcOQDKbGt0notZwsmTNMIGAEjYASMgBG43QhUFY7cZU7k4mqv5dzk+NcIGAEjYASMgBEwAhMQ6FU4spWDb7azpcIHTOyMgBEwAkbACBgBI3AQAtXXYktKUjx4z5l3j+P77WW240bACBgBI2AEjIARGEWg18IRNaVw8GEUPsLyNCsfkeXQCBgBI2AEjIARMAKTEBhVOKAiRYOtFb7J8ZJrOyNgBIyAETACRsAIzEHg/wFsAvo1fvuCbAAAAABJRU5ErkJggg==\n",
+ "image/png": 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\n",
"text/latex": [
- "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: w \\leq 0 \\\\\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f} & \\text{for}\\: L_{b} \\geq w \\\\0 & \\text{otherwise} \\end{cases}$"
+ "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: w \\leq 0 \\\\\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f} & \\text{for}\\: L_{b} > w \\\\0 & \\text{otherwise} \\end{cases}$"
],
"text/plain": [
"⎧ 0 \n",
@@ -485,7 +464,7 @@
"f}â‹…E_\\mathrm{f}\n",
" \n",
" \n",
- "≥ w \n",
+ "> w \n",
" \n",
"se "
]
@@ -498,7 +477,7 @@
"source": [
"Pw_short = sp.Piecewise((0, w <= 0),\n",
" (Pw_up_pull, w <= w_argmax),\n",
- " (Pw_down_pull, w <= L_b),\n",
+ " (Pw_down_pull, w < L_b),\n",
" (0, True)\n",
" )\n",
"Pw_short"
@@ -507,6 +486,33 @@
{
"cell_type": "code",
"execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$\\displaystyle A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + \\frac{L_{b}^{2} \\bar{\\tau}^{2} p^{2}}{A_\\mathrm{f} E_\\mathrm{f}}$"
+ ],
+ "text/plain": [
+ " 2 2 2 \n",
+ " L_b â‹…\\bar{\\tau} â‹…p \n",
+ "A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\bar{\\tau}⋅p + ─────────────────────────\n",
+ " A_\\mathrm{f}â‹…E_\\mathrm{f}"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sp.simplify(Pw_down_pull.args[1].args[3].args[0].subs(w,w_argmax))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -519,7 +525,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 14,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -529,7 +535,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "74df2b6e7399463fa0aa57a1e9ca25d7",
+ "model_id": "daaf80a467424a8c9b6103dd43387dd4",
"version_major": 2,
"version_minor": 0
},
@@ -539,13 +545,24 @@
},
"metadata": {},
"output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x7f154c095340>]"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
}
],
"source": [
- "w_range = np.linspace(0,2,50)\n",
- "params = {w: w_range, A_f:1, E_f:1, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
+ "w_range = np.linspace(0,2,5000)\n",
+ "params = {w: w_range, A_f:1.8, E_f:2, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
"param_vals = tuple(params[map_py2sp[py_var]] for py_var in py_vars)\n",
- "fix, ax = plt.subplots(1,1, figsize=(8,2))"
+ "fix, ax = plt.subplots(1,1, figsize=(8,2))\n",
+ "ax.plot(w_range, get_Pw_short(*param_vals))"
]
},
{
@@ -561,7 +578,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 15,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -612,7 +629,7 @@
"therwise "
]
},
- "execution_count": 14,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -627,7 +644,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 16,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -636,9 +653,9 @@
"outputs": [
{
"data": {
- "image/png": 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N8zhX3pT5Kp9Td5YNq/J1zpMcbXCqoc0e3dSN8uD/upExHWUpH9Oy1H/29Wjk71MTMIE6gRgPmvcYD1W8VRv3IKm4Xx/JL/Xnspt7OYlTGYWX/cti97vy5WG/KmdnDh7cos9kv83khzKlgX3toXZuHXep3KiCNAw0Yqbv2QOCFt020DGNP2qmQfFQghjAKs1d55WR/6LKVM6PmZFS+bqfC0T7PjKKywDHjUA4yxaVEpbzY+BcQtmjnIPyrJjK3RzcCb+nIylksjtly3nN5qe8kaOUhesfiiDZn2SohzKoOqacGfWNMimvUixyOGkOpNURDE5RfsvyPi/LU/6UT3nNzoBvDDU7XkWzMQETOIVAvud4qIkHnCo7hfF5DM4f64g+gj6guhcVnvoEInWY1e53lc1DKbKjTPAg9bXsvhmkDhGX9ZYM9F/NPmzZQibkdndC3M2iClJqULIZcGLQrCklCmMts1QcOuXLcXn/PmYsanHlz+CymDKl/BioDm3lyY9vy9Aw2wxLWLyifl9HyoNISrOofMqS/NoaYcVTZVI+jEPBapVN4WvIR6dCeUsZlMLabIrqlzon2UnRU3iTB22Fp6SIF+1wlnJZ5IOCBNuyM0IGyoqOVKfJxD6AOLdtAiawDIHog9P93ZEl/WRpXpcnfe6173flTz/Ewz19Cctf9BVs5o3+uk+81jClZWy6OCO5Wz+yukvlJuhKaDp8BoGnspkFqTRn+TF11bpcFemxlYbBhP+nqJQjuVPDlp3yk72oMqXy0KTT9CUyNAxlorzUjOLTSGMwrd1wS8qnvGIwP1IeFFbyRbFJA3CfbFRC4Uvz45pV14syuozKPmU2hWxRYnjKqjGXH5yi/ksql5THk2FZHn415UrhlNlUduRlYwImsACB6Ovod7tMxInw8p4NvyF71fs99yOMhWlJSOcoOSyvs39wkryK36okDFVwr+F39ipYIVc8cXMBk9FFYEBj70zvxVM4A8RD2VXamxwOpD/SwnN+DGhsUg7NPidJylQa7MKjzVY6BsW+T/sj870yrdIgJ/W8JzeKEYrFkZE/aU+ST+m52TC1wfTG6+ZX5VB3uKFsjZKNlMSXdZJ8yoOyUWQHB3bFYTblOx3RRuSsmxynmpGqh6YzrleNhdLAn7qkdoMsOjiPpStmgmomp+krJ+JTv2an2eb3WHnW5IoMbJuACZxGgHtaOXBPR39YZaiweABkT86ppu3ebvM7+X6X3GyAZpsGCg57hpjJuXdqBcam37KsMTLdHRPpnHEEjKdqOvmnstFOaZAMLh/3yaV4NCAaJ5vCmoPOI/l1Td8xUDK4MbCl2RfFHatMpTIVv+/rx0mpUpxqJkpuBk/KS3WU3Wdmy5czpS4HymwrRP7c2HBLMyfE0zFWNrJcQr7m4E++NSOZULpQpGbvy1Ie3Pjkk66J7IP8uIbU9+jLngo7eSZR+cKdMpNRnvC+r4Nyk8l+RzNrEW7bBExgMoG2QZ4x5KXuN5SAsj+kD4s3paIg0rflEeFd9ub3u+pCv8i3ZujrqR+ftCjr1yXrQfGoYzy8RZ80+EmMnO7/yqbfHFVWCKH49IH0uQ90/KDjjY4w9JX488ba4LgQibDfeft2/WU2CQUwXqXDsBmqfCvlxrfnN1eezh4AVJDXxLqWfVJOCkd7jYuT/IofBuzOJS2FURbA0454nTMTczTYRX4Kp34oBKTBcHFr8RWHhobMZRwUL+p0yHn8JXtwalBx5sj3nYqBRwyszWtAHWhE2DU+U2RT2sNU+UgTRmnh+Ep2l/IZUZOteNG2mMmrLWXpHCWV2bDWvOTPNaE82kJcF5QlOrvWG0n+MKRt0XmUym/bDKGiHRulC2X7jUL5sCOdEdfntQ78at/A0bmNCZjADAK61+jvGKy5v+kr6Peq/iXfz/TB3HcY7m/u/zRrKpt03Of0FcTBnzeBmv2nvNuN4l7M/Y6sOqqxNcv+SHbvizsKRyFkJn3y+A41pU97GmUfTQzIjz56UMEin9JspdzQwGKpBg1skmaHwEpDehoegw4AWwcfhZ1slDcNGgVitDJ1aqEqkxtvrHKzqXxTZIPD1vxUHp0HiswHclftQm6UkM6P4OV0fPumU9FV+iOj+JOUy6MM7GECJmACOySgvo3ZDiYPQrmLh7nOcVtxGY94MHupo/pWmNyjTe5TmRmvPaCSgfzYqpEmAUZnqIh3pkQ+IS4zAslIyMmKTU76XDYKAMtU1QCWwxa1lD8XFjnR+DnQSndjLN/RpYjrU90AYsST1tC+LG7KdBMf5djvEeU9zeXwynY8+fWndKgJmIAJ7JcAsza/ThQvPtXCuPxwYtqITl/8fZyoP+UTMIz3GMb+yebu5BTzEsSmrdFTec1iVFEGKhSOagBrxln4HKBMh62uTM2U2/JlcGoXk/dl5RuHp5JXU/krbXzcC8WXG/roaWNqno5vAiZgAkMEcr8VqyBD0SOclY5RkwqKxxJ5aVB26F9b08u/+i9CxUMpqiYyIhPiZDcz6+RXM/KLrRLMGKEcodQwo562E8iuHhzl7s2rzHh15UbCIChP0RiWD2Yb5TVp+WB2QUqosjZTpjIj9lxQLoyYhuudnVL4JvKpHK7fJNlyPTaRj7KyYTYF7Z/ZFNj9Kru6KXKcZMmf9ohignmmc76B1Lypb0K7f/euXHZL7hATMIGLJJD7tN79L0tVTGWhdNBXto67Cqe/LWe+2QbwuY7K5DzYj4iCRfw2gz9LUknxyWmO+u7sP5RXlf/qe24kEIMO2haDnZ9wK/R2LE1A7WuzfVnInsvjpu1VRJeup/MzARMwgTUJqE9jVpsHbfq3I0WDsuVPeBlGGpSh6q8pFAfFhRmZzhUXhbGHsdpvo/N7Ok+fA8nuR7LRHwbzUrrK3K1cKzgkDJVFsQHAkxWKcJYmUBLYdDZF7bv1iaYUyG4TMAETuCQCedzmsytpO0k+P8iuHuLkZjmqtsSk81BusHnjFpsJDZaYyuWrJg6UliovxUVfiGUwZtjZpDw2ryrvO5VrYYeEQftKGpnszjdWFi7W2d1iAmpz7Onacl/WLabtqpuACVwbgaxEMCPDK+FsFGZpilmX11FX+aGMoIDUjPxD+UEROeRz9q2yRaDrcxyx36Zc3kr5Kg3lMIPDrA559+aVEhU/q8zcSBAUG5YIEMiKTQHcznUJqO15NmVdxM7dBEzgegkwbsf4XdVS/Wrsh0HxYV8Nyki1TzGP+fEWKfsYUUiOFJYqQzkUzqrO4+zH/2RlZyofBQnlZnZ/vopyI4GofJpGksBHGp7CbEzABEzABEzABHZEQOP10Uf0SvEUjpJTLSFFWB7nW8MiTtNWGmZzWmd0mnHnnK+yLCWh0egQmv+34ONqNiZgAiZgAiZgAreEgMZ+ZoBQeNgQHG9Mz6r9nLxWfVtKAjGFhXLDlFM1hTWrdk5kAiZgAiZgAiZgAiMIrKrcUL6UGt59Z4mq+qQz/jYmYAImYAImYAImsAaBVZalGoLG+hw7nW1MwARMwARMwARMYFUCqys3mrlhxzSbiu/J7f03q15OZ24CJmACJmACJrDW21JNsj/II+29kb3rvTdSwHjvntfTeE1tFaMy3pmbseWbS87pTGAfBE65//dRA0thAvsnsJVyw5IUyg0fBWIGZ8+vh/OuPl9n7Pxc9Jkvq+U78wVw8SZgAiZgAvsmsJVyU33dUDge6Oj9uM+5kEmhSV9LlB2ffh4URXHZLP2j7NkfGxosJEeYI9/YvJeIN0e+LfktUUfnYQLXROC23X+qLw/ZvKLM3wPschy6pvZ1zrpspdzEZ5mpK8rAXg3/YxFfWRwrI7NS8QnpsWnmxuuUTzcqy2j8FwjKI4a/ny9nyLihYX+fMMVP/xsi95KmU76eQk7mt5O691SxPUhycz1ihpDrxkMAs4atynWu50PFiW9GEI9762eF7Xq5VzIubqbyW1yA68jw1tx/ai98ffe5DvpGvsG22Ru8Kov+2feuIGxlVn8VPCqii/s2u3f5zRvJN3kGRmkYZOgcDnLP3keTufRaY+VTPDjzVNI6kyT/pATJXlS5UX5n5ycZzlL33gvXEZh58f8t1XWQG8U6rk/nU2Wu5x+yP+jI/uq9VXfa2yx+Vw9nZAXFcNH+K7fLzfueMdWVbMzY8ODwgQ7aDvfaE7nLB8AxWZ0UR+XRR61y7ypvHmBf6uC+uHUPO80Ls9XMTbPcPZ7zBB1P0WPlY2Dizxo/VWPiD77KGaqxeYyNNyifyn+UM+scGBVOo19jUByUr6Wii/E7c91bqjboRecan0lIkVUHOl86YRTm1s+gKzxmCWl3J5tcXqVgNTJ8rfCajI3wk06VN+2V+2ZORzya3znreBIgJT6R0VDxt+n+o65pRlRM6af5t+pNjcpd9N5tCq/8+T+nj+XPfzvxfTmUnNX+3qBZ/t7OrdzoiqgBoPHyt+yjO3LFpXMtO1jyWMVMkC8GKf6Nvc/Q8BczE+SrylyB31nqXlVouoOB/XdxeFdH+fSIYtqnLIcCO3SNR0mkslEs5igXo/IfiMQ9M/e+Gc3vzHUcQDAYfAqjzszFZOn+6xLuP5Z9z2kWvXfbKpL7kvSgKfeXOujreRB6nsPakl2l352rrNX0SnGjsxY7yqiRMK35p2yeAP7MifBby4yVL908kqs2c6NzljqSkZuBtBaeg06xxsoXMqzB71x1n8uNa8D0NNejzXQN+o+JrHRLX8M2GfbsN5ffnuu0iWxqO77/NiF9VMim966u8zc6mKVHwWGP0dc6uvqVI2Ev3ePupVfgVPnzxX4ke/Ssjcpk+SDix1IUG3UXNxPlY9qzNugpPYN+bQCVX+uG1TnCT5QviliD3+Z1j8rMscWta1o8TV33XCPCF7l+KgOlNN4eaatGtT9OcSmXtsSmyCc6GCA5fy+7N92/MIXfGvVUngwSsKP+zMBVs19ywwp2qY+Qzd4WWH8kd+1elN85zK25//K14EUH2upB5/ezne4/nXMduTYxm40ywNuvqR+VTTrCae88ANPfcw/g/5nCo//X6aBZ7N4dLKmIIBnT7Kxs2uFL2WyoRtEZJbviXWRbv1swuK3OSW/46ELTqMslgWgga+xj4ZqMki/LRXz2MKRNznLTKJF3LdmU9Tj5iIhZg98Z635TqYV+VQ86PzpRppWPTFHPmgJ7FHGEh/J6oWgMtHTyTNfTgdfKVZxSiXqscwZF2tZLHUxzp/V82aTFP5Ym5NzeSI4jfvJbq57sa4AHA8Z3OirlRm7uWe69MHDmuj7QcfK1i0zn2JJ38f4r54k4W/c9gwgkG20YJST1ibKTUkNCuWkvqd3KHf04/rx9yDfZmPngeqGU/iWbfpR4tClmw2FZXnedthulJy7mbNdfMrA89VOWBQWOuox5KLnItn4X2tdqdPHoeNhk1deg2N8wZfDnRolZG9DRcWHovI6M4tKo6fTp7HjCqzZ4yb2kfDGwIF8alGQjEzdqdePqvDLy75SNSApfUr4odzF+kaHsxete5L2lk46WzqdqI43Co56lct2IcnOqPOi4GXTZFBzpUmAOo11Um5LlPugolZmbjPQrf/J6lT1oUyynVWl1zlNvtfSZ453DqvHLci9ezwYP2L5uVJb7iqf8ZBT/Fx2wbb0Pc7StLN9/f5OO9tK8Lij5LOPEdSMF1/iR/GI2rrlXjjh9Ju7Bk+7dvgJmhJUKeGty1be89y+qrd9trdGZPQUU6DwdDsIvRK0GdfyUB50tT1A03L7XotHCR5mcJ08nZZr7OXGXrDRm3nwhXhVnBfnoUA/Ktxqg5G4OQoSXX4hulS3ns2t+yFiYRete5JucMJPjpPbYzLN5rjJoU1yv6smyGUfnUc9OZT2ur2xeyaXtNzvuA2HyL9sJHdgbHV0GuSI+cauBOydI7VpxyrZV5SV/6pZkrzxvHOneUXj5sBBRkL+PRcRLdi6jxk9+q9RTBaIwBo/PdV7xkD984NG8Rnxb6uhaKF4yCtuCEff0Iv1XFjusaJfB5EBddZZflbcAABGVSURBVJQKMH5l++jseyLTNW3JwnVCUQ+lvSpOYbQ9ztkjE3Xi/qiun8L77hfSNk0waraLKp7yTHxy+a33bhV5hkP58rD6TAd5M15W9enJrrz3F2nrPWUtGnR30dzGZfbvQ9EEnYbTqpAMpSVc6Wm4TBeyHs6OcaYYo5HKqzKsi4+atVE8OqyD7NDAq0zkx7cLuFFqJqd5I5v6VDeDzheXT/mTZ9uNQ6eZTJaHfQJMt1KfI9mIuIZ8uTzyPpkfMjbMYnVv5JtOJTPXbnZ7bMuz9FP+XJP7bWzKeHJTz7Z2nKLlfGgD0dboUD9Ogf0/dOKdT5S5/gfZqYNW3GY745pGWzoqSenalBfyo7NlsO2aqTrKq81D6cfyW6qe/4McWX7uo3JpAkawaF4nZrc6jeKvzQg5kfni7r9OaKcFRH8d90pbbtxvpXldnkx0r3XvDoqha879wWwU9+3HOu+rcy2/iCube3WRtl4rYMWTcyg3/7tifVLWuhCpY5HNE1XMQNSeAhXGBa8G/hEysQGrtQNSWjTg+2UeiktjJv49udOGNdmpE5S9qHzKLwadowFKYaV2Tp2/lV+nbNRB4YvKR54yi/G7ye7mV7IuWvcy7y3ckp9Ogw+LVe1T7tTxyq6undxRz+975OKLq9HGuMZ0Ro9y2odyd62vI0NVvtxdhoGRJ7lm54hs5QDflX5xf8kyil8ueOl6woOn/JIHfjXlT+Fci3RPZTnOYfn+q1OPe4t7pMtEnAgvr3P4Ddq6/mveu53lq1zGPsYgZtBO3cx+SW09MbmTfq/0J3c6dLrpuyGNaqLJjuqQc+Pk091dhkZfu0mUhs6MMg5ys/HwqCz5ke5k+ZQHDQ9T61RvvG5+VRYD5kPK1DEoG6mIK+tk+ZQPN/fi/JBRZpW632S97q+4MOhxTVI7KUpjEH5dnOPsrafyoCMrlVuY0zmjzDIzwvQ7SnbNKIx2wezJmMGXPGttTOlQmGknzTrIa12jskfzW6mesGsOgG1+bMaucVuXTD13le37r47kICa0d9pt3FdVjMyLc/bkLGGijNY2oPJm3bttgimv9DAtO80UyubBifGHup5i2tp1m99Z23pZwbvlyZW66dBjWi7NvOhCM3iwcXPwgisOF5Cd5a1fjM3M0kBEXB3Nzi5H6bROki/nSn0OKrt1gJI/nRs36pinc7IqzUnyqey1+a1Z95LDou7gokzZtNicQWS2pblU01lPxeUa0UGWbZQOlaf1aOPYD3Q0DfkOtlnlc0/xUCZSWycT+XFtUWomTXWT9lSTy6ZNT+G3dD2532CSjGTiPruvAy7JZL9S6YygTezgJLtsG82yT+m/OtslheT6z+17mnKeck77bRqWbHk1mi/5ln0n91O8KRVpSN+WR4T32Z2MVO4p926tTOWFfOwNpD6jtlvUMug/2X1bb4p/9cqNLjLT6GjMT2WHBsumqt69CIpLQ+GmpMM66JyZh1onLj8aLQpTiiM7fR9B/qOfYhX3FPm+U5l0pKkzVV7IWxrq8EAHNtPnrU8OZYKm+0T5VuEnmajP6nVvslj4nAGP64bi3TSpox1RT9LH4NpU1rnuZTtkz1Db4M5yVVO5kteRiTbOPYQihWFPG0thbfmmCCv+DPJrlL14PVVvWDCQwO+NDj7o+R86viv8at/AUdgmRuVzj9z6+08cuD/o71M/qHOYvJKN8kKfyH0R44Kc6Z7kPPWVsmn39PHca5/rHOX1e9m1zdLyqxmFD/VRS9y7zTJpg6vsDVR9dtvWaxCKk7uF+5qdaMc00qe6SHTEvLlAQ+g0OTymE1vjKQ4NvLeRtyY89pwr35yZmOPSh33myrcKv3xttqr7MJ0ZMVSHwSerE+vJ9HT5NPq5xHzSFFVxxnLkWjIYkGeZbzPLTc4lxyC/UpC16ql802xwWZbcY5k2ki13Krno3279/ScOtNXO66FwxoO2a5guhsJRcuY8FMK/s9yUeffPqHu3O/k6IWLRxmluHdcRssj1TuHeyjn4ttTSguQGSiNHg+dgsN6NsXy7uRTXJAgzgveokGxmh1DoT1HEeTiY3MlTfo9hAODYk1mjnqfUb4+MTqmP0w4TWPreHS7xCmOcY+Zm9belOq7Tc/kzJUnDWX0aXWUwsLB0cpCbaWv2P/SVu5l8M2SjGpvJR2EzZSRpr1kr395CzxPIExVtLjYW9j7F94mYmTGN/qov3tQw5bu0sjRVhFr8tepZK2TiybkYZRZT+q9RNVsr31GFX06kWfduZtv34kYbgdr34doiXKrfO2/f8omW9Y3AR0HV/9WsX2q9BMnAhR/78aJ64g3OLN8GkF3EJAJqk+wrY7aTvQvMfrLH5OjNP/lftLkt9bzoi2ThTWACgVul3Ezg4qgmYAImYAImYAIXSuAce24uFJXFNgETMAETMAETuAQCVm4u4SpZRhMwARMwARMwgdEEzqHcbP621GgajmgCJmACJmACJnDxBM6h3JzrbamLv1iugAmYgAmYgAmYwDCBcyg3w1I5hgmYgAmYgAmYgAnMJGDlZiY4JzMBEzABEzABE9gnASs3+7wulsoETMAETMAETGAmASs3M8E5mQmYgAmYgAmYwD4JWLnZ53WxVCZgAiZgAiZgAjMJbPnfUv+VZfx1pqxOZgImYAImYAImYAKDBLZUbv4zS/PfsvmPGhsTMAETMAETMAETWJzAlsrNZOH1Z3Zf50R/yv5Ax9A/a08uwwlMwARMwARMoI+AxiL+OJZ/SX9fxw86/6Iv/h7CJCOy8mfRX8l9dX92O8R4t3tudDG4KK9kc2G+4QLp+FluLpiNCZiACZiACSxOQGNMPFRXecvvXzo+ksdrHfergH07GCvv6UDuW2d2qdyoET3Vlbgn+6e4InK/kZvzF+Fn2wRMwARMwASWIqBxJhSCriz/6ArYm7/q8otkelf27meZ1mC3S+VGFf1MR9u+nFfyf6SLhTZqYwImYAImYAJLEvh0yczOnZfGSiYFbqU5h3Iz5o8zH+lqMP3XNKE1E25jAiZgAiZgAosQkCLAvpqjJalFMncmmxM4x4bi3j/OHDkrcylrnptfUBdoAiZgAiZQJ5DHFRSX33MIL6j8KH+Wbg6ymbF5jFuG1YEfb5yH7+WutkdkP+K/L3fM8jyUm/2h7A2tmRyP/aKU+54OtlukZSLZPKQjE3k918HDO3nhz+oFNmkJJww3Yx/pUcTw+0L5/KIDeZGHmRriUS/8SEs4+SUjN2nJm7ixCvJY/tXeHLlJ1yq3/C/C3N2hlKG49E2nxQXZofgWyQRMwARMYC8E8mDOQP+J3DH7f5CbF1Q+1PGNDhSYn2SjhKAM9O1TYfxBAUrKjGyUhd9kk77MH/+XOj4Kf9lf6iAufigg2H/JRtkiLXtKv9RB/t/q+EFuwl/InZSswi8pNgo7yO8zHT/LiV/IQN68mFMZnSM7bx1/UnnKofOqvnL3yl2m27P7zp6F65ENDdjGBEzABEzABIYIoNjUFI+cgJkJBnoG8ynmgdJUr1bLHftDmQ0pDeXy2ngoGwe5UYhQqGLWh/hswUCZCRnZBJzyl81DPkrNYx3JZD/8q9mYHMQbXVVZ2a+5veOB/JEfJac05Ys6Y+Uu0+/OvUflpnkxSmj38wnfvbExARMwARMwgU4CGsRRXN7X8aoZSWGhlFSKQzNOx/mvHf6VwlCUW5s5yekol+WnMCgqIctBaTkvzfc6QSGiHoSjGKH88FZxMvJDsWLmptcoHrNFjLF/yc3MFTNJ7+soZ6EoZ4zcvWWdO3B3y1KC/EYHXKqGUkAKv6Z2WkSx0wRMwARMwAQSgaQQyNVUGEo8U2duyrRd7iiXpaFKCcmRmSVpKkgoHK1G6ZnRQX6Wjphteqhzvv/2VMenOpjZYcmNsDGGvTXPdKAkseeH2SuWwMh/qtxKsk+zO+UmY0K7DMgluZi5IdzGBEzABEzABPoIxINwPBi3xY04R2Ea8Bn4xyoNZfrIk9kRlI8h06d8kZa9Nygyz2XHygV+KCRj8le0NOvDuPo61ynVS26UL/b0oHRNlVtJ9mnu7FOstMubtcGmQeNkXXGoITTT+dwETMAETOCWEdBYwXIP40VtAy0YFMZSDoY9JmEWGVuKch9HxqVdlF1697lRPFBM+AuIUGbwY68OG5BxjzHMUtVmkpSeJS7yZC9O8FpK7jEyrRJnl8pNho12ybRZMnLfk+NzHU9ufPxrAiZgAiZgAoMEPlaMzzWGNJefWJLhTalyJQB324N1FBKrB3HeZ1MuykcoUSmuzik3ZkjwY2zj6DRKg9JBGvbHpLSFH69xl/k182nm/Uzxm36cB4excjfL2dX5O2/fvt1EIMGMgnhVrdpp3lV4hk8jeKODaTg2YD2XPxfZxgRMwARMwARGEdC4wawHyzCMJxjOWYqJAT158iO/mMlBYWDMYR8oitEzHTxwkwfpWCIiH5aGUGCSv+JWbzHJHeUquPrWDeX+oYM0pC3z/F7+MTNDmsrInxka0lXhcqdZGNm1MVXnIW8oVsjLxACKG7NYsbQlZ/r+DstnFQu5O+UmwSWYcyg38UeYl8DHMpqACZiACZiACVwYgTsbyhvTZnysyMYETMAETMAETMAEViGwpXITy0l965mrVNKZmoAJmIAJmIAJ3B4CWyo3sZubjxHduz2IXVMTMAETMAETMIEtCWym3OTNSrE0VXsVbcsKuywTMAETMAETMIHrJrCZcpMxsjMc0/Yq2k2If03ABEzABEzABEzgBAKbKjd59ob/sGBZio8R2ZiACZiACZiACZjAogQ2exW8lFpKDt8R4N3++D+LMthuEzABEzABEzABE5hNYNOZm5BSyg0fOeKDSk+zohNBtk3ABEzABEzABEzgJAJnUW6QWEoNy1N88+Z7zm1MwARMwARMwARMYAkCZ1mWWkJw52ECJmACJmACJmACbQTONnPTJoz9TMAETMAETMAETOBUAu/84x//4M2llzqmfFjvMy0rxReHkww6jz/GPFUmpzcBEzABEzABEzCB2QS8LDUbnROagAmYgAmYgAnskYCXpfZ4VSyTCZiACZiACZjAbAJWbmajc0ITMAETMAETMIE9ErBys8erYplMwARMwARMwARmE7ByMxudE5qACZiACZiACeyRgJWbPV4Vy2QCJmACJmACJjCbgJWb2eic0ARMwARMwARMYI8E7u5RKMtkAiZwfQT0LaynqtUnHTV7rfAvOsLsbQImYAKTCPg7N5NwObIJmIAJmIAJmMDeCXhZau9XyPKZgAmYgAmYgAlMIuBlqUm4HNkETGAuAS07fa20LE11/dXLF4rzrY4PFeeRjoc6nuh4P5+/l91PFOeN3DYmYAIm0ErAMzetWOxpAiawJAEpIy9yfp/J/kjHL9nGnQ4UG7kxj+X+5saZ/vfufc51fCW/P3T8mMNsmYAJmEArAc/ctGKxpwmYwFIEpJQwE/Oz7J8iT7kPOmp/vkuY/Ij7KsdjxuYP+VXpdP67ji9zuC0TMAETaCVg5aYViz1NwASWIpCVmEqRyQpM17ISykzERdF53pAjLWkpzj0dXXk0kvjUBEzgthHwstRtu+Kurwmcn8BjifBzmxihsMhmzw2G5avS8Cr5m4hXBthtAiZgAkHAyk2QsG0CJrAVgU9V0K8DhaHEMIvTnJ1B6flhIK2DTcAEbjkBKze3vAG4+iawJQEpK+yjYYNwLD11FY8SU5u1URretELZYWOxjQmYgAl0EvCem040DjABE1iBALM2vPHUaaTEsK+G/TavI1JWilBqPpa7OZsT0WybgAmYQCJg5cYNwQRMYEsCfLsmXgvvKpdZG8xXUmTizSi+cfOJznsVo5TKPyZgAreegP9+4dY3AQMwgX0RkAKD8vNANt+/sTEBEzCByQS852YyMicwARNYmcDRfpuVy3P2JmACV0bAys2VXVBXxwQumYBma9hvw6bj+JDfJVfHspuACZyJgJWbM4F3sSZgAnUCUmzYbPwy+z7TOW9H2ZiACZjAZAL/H2Ysc0GZppkWAAAAAElFTkSuQmCC\n",
+ "image/png": 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\n",
"text/latex": [
- "$\\displaystyle - \\frac{\\begin{cases} 0 & \\text{for}\\: w \\leq 0 \\\\\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f} & \\text{for}\\: L_{b} \\geq w \\\\0 & \\text{otherwise} \\end{cases}}{\\bar{\\tau} p}$"
+ "$\\displaystyle - \\frac{\\begin{cases} 0 & \\text{for}\\: w \\leq 0 \\\\\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\- \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} + A_\\mathrm{f} E_\\mathrm{f} & \\text{for}\\: L_{b} > w \\\\0 & \\text{otherwise} \\end{cases}}{\\bar{\\tau} p}$"
],
"text/plain": [
" ⎛⎧ 0 \n",
@@ -677,14 +694,14 @@
"m{f}⋅E_\\mathrm{f}⎟ \n",
" ⎟ \n",
" ⎟ \n",
- "b ≥ w ⎟ \n",
+ "b > w ⎟ \n",
" ⎟ \n",
"wise ⎠\n",
"───────────────────\n",
" "
]
},
- "execution_count": 15,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -696,77 +713,215 @@
},
{
"cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/latex": [
+ "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x \\leq - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{w}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}} \\\\\\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{w} + \\bar{\\tau} p x}{A_\\mathrm{f}} & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x > - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{w}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}} \\\\0 & \\text{for}\\: x \\leq \\frac{\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} - A_\\mathrm{f} E_\\mathrm{f}}{\\bar{\\tau} p} \\wedge w > \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\\\E_\\mathrm{f} + \\frac{\\bar{\\tau} p x}{A_\\mathrm{f}} - \\frac{\\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w}}{\\sqrt{A_\\mathrm{f}}} & \\text{for}\\: w > \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x > \\frac{\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} - 2 L_{b} \\bar{\\tau} p + 2 \\bar{\\tau} p w} - A_\\mathrm{f} E_\\mathrm{f}}{\\bar{\\tau} p} \\end{cases}$"
+ ],
+ "text/plain": [
+ "⎧ \n",
+ "⎪ \n",
+ "⎪ 0 \n",
+ "⎪ \n",
+ "⎪ \n",
+ "⎪ \n",
+ "⎪ ______________ ______________ ____________ \n",
+ "⎪ √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅\n",
+ "⎪ ───────────────────────────────────────────────────────\n",
+ "⎪ A_\\mathrm{f} \n",
+ "⎪ \n",
+ "⎨ \n",
+ "⎪ \n",
+ "⎪ \n",
+ "⎪ 0 \n",
+ "⎪ \n",
+ "⎪ \n",
+ "⎪ ______________ __________________________\n",
+ "⎪ \\bar{\\tau}⋅p⋅x ╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f}\n",
+ "⎪E_\\mathrm{f} + ────────────── - ─────────────────────────────────────────────\n",
+ "⎪ A_\\mathrm{f} ________\n",
+ "⎪ ╲╱ A_\\math\n",
+ "⎩ \n",
+ "\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "√w + \\bar{\\tau}⋅p⋅x \n",
+ "─────────────────── \n",
+ " \n",
+ " \n",
+ " \n",
+ " ______________ ________\n",
+ " ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\math\n",
+ " for x ≤ ───────────────────────────\n",
+ " \n",
+ " \n",
+ "_________________________________________ 2 \n",
+ " - 2â‹…L_bâ‹…\\bar{\\tau}â‹…p + 2â‹…\\bar{\\tau}â‹…pâ‹…w L_b â‹…\\bar{\\tau}â‹…p \n",
+ "───────────────────────────────────────── for w > ───────────────────────────\n",
+ "______ 2â‹…A_\\mathrm{f}â‹…E_\\mathrm{f}\n",
+ "rm{f} \n",
+ " \n",
+ "\n",
+ " 2 ______________ ___\n",
+ " L_b ⋅\\bar{\\tau}⋅p -√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\n",
+ " for w ≤ ─────────────────────────── ∧ x ≤ ──────────────────────────\n",
+ " 2â‹…A_\\mathrm{f}â‹…E_\\mathrm{f} ____________\n",
+ " ╲╱ \\bar{\\tau} \n",
+ " \n",
+ " 2 ______________ ___\n",
+ " L_b ⋅\\bar{\\tau}⋅p -√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\n",
+ " for w ≤ ─────────────────────────── ∧ x > ──────────────────────────\n",
+ " 2â‹…A_\\mathrm{f}â‹…E_\\mathrm{f} ____________\n",
+ " ╲╱ \\bar{\\tau} \n",
+ " \n",
+ "______ ___________________________________________________________________ \n",
+ "rm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\\bar{\\tau}⋅p + 2⋅\\bar{\\tau}⋅p⋅w -\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " \\bar{\\tau}â‹…p \n",
+ " \n",
+ " ______________ ______________ ___________________________________\n",
+ " ╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} - 2⋅L_b⋅\n",
+ " ∧ x > ───────────────────────────────────────────────────────────────────────\n",
+ " \\bar{\\tau}â‹…\n",
+ " \n",
+ " \n",
+ "\n",
+ "___________ \n",
+ "\\mathrm{f} ⋅√w \n",
+ "─────────────── \n",
+ " \n",
+ "⋅√p \n",
+ " \n",
+ "___________ \n",
+ "\\mathrm{f} ⋅√w \n",
+ "─────────────── \n",
+ " \n",
+ "⋅√p \n",
+ " \n",
+ " 2 \n",
+ " A_\\mathrm{f}â‹…E_\\mathrm{f} L_b â‹…\\bar{\\tau}â‹…p \n",
+ "────────────────────────── ∧ w > ───────────────────────────\n",
+ " 2â‹…A_\\mathrm{f}â‹…E_\\mathrm{f}\n",
+ " \n",
+ "________________________________ \n",
+ "\\bar{\\tau}â‹…p + 2â‹…\\bar{\\tau}â‹…pâ‹…w - A_\\mathrm{f}â‹…E_\\mathrm{f}\n",
+ "────────────────────────────────────────────────────────────\n",
+ "p \n",
+ " \n",
+ " "
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
}
- },
- "outputs": [],
+ ],
"source": [
- "import traits.api as tr\n",
- "\n",
- "class PO_SF_M_RG(tr.HasTraits):\n",
- "\n",
- " get_Pw_pull = sp.lambdify(sp_vars, Pw_short)\n",
- " get_w_L_b = sp.lambdify(sp_vars, w_L_b)\n",
- " get_aw_pull = sp.lambdify(sp_vars, aw_pull_elastic)\n",
- " "
+ "aw_up = -Pw_up_pull/p/tau\n",
+ "bw_down = -Pw_down_pull/p/tau\n",
+ "sig_f_x = sp.Piecewise(\n",
+ " (0, ((w <= w_argmax) & (x <= aw_up)) ),\n",
+ " (-Pw_up_pull/A_f/aw_up*(x-aw_up), ((w <= w_argmax) & (x > aw_up)) ),\n",
+ " (0, ((w > w_argmax) & (x <= bw_down)) ),\n",
+ " (-Pw_down_pull/A_f/bw_down*(x-bw_down), ((w > w_argmax) & (x > bw_down)) ),\n",
+ ")\n",
+ "sp.simplify(sig_f_x)"
]
},
{
"cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
+ "execution_count": 19,
+ "metadata": {},
"outputs": [
{
- "ename": "NameError",
- "evalue": "name 'poui' is not defined",
- "output_type": "error",
- "traceback": [
- "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
- "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
- "\u001b[0;32m<ipython-input-17-c647af14f6fa>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m po = poui.ModelInteract(\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mmodels\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPO_SF_M_RG\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mpy_vars\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpy_vars\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mmap_py2sp\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmap_py2sp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m )\n",
- "\u001b[0;31mNameError\u001b[0m: name 'poui' is not defined"
- ]
+ "data": {
+ "image/png": "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\n",
+ "text/latex": [
+ "$\\displaystyle \\left( w, \\ \\bar{\\tau}, \\ p, \\ L_{b}, \\ A_\\mathrm{f}, \\ A_\\mathrm{m}, \\ E_\\mathrm{f}, \\ E_\\mathrm{m}\\right)$"
+ ],
+ "text/plain": [
+ "(w, \\bar{\\tau}, p, L_b, A_\\mathrm{f}, A_\\mathrm{m}, E_\\mathrm{f}, E_\\mathrm{m}\n",
+ ")"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
}
],
"source": [
- "po = poui.ModelInteract(\n",
- " models=[PO_SF_M_RG],\n",
- " py_vars=list(py_vars),\n",
- " map_py2sp=map_py2sp\n",
- ")"
+ "sp_vars"
]
},
{
"cell_type": "code",
- "execution_count": null,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
+ "execution_count": 20,
+ "metadata": {},
"outputs": [],
"source": [
- "po.interact_geometry()"
+ "get_sig_f_x = sp.lambdify((x,) + sp_vars, sig_f_x)\n",
+ "get_aw_up = sp.lambdify(sp_vars, aw_up)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "2b9ee650254e4287a6602f0dbd024217",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "[<matplotlib.lines.Line2D at 0x7f15279ce820>]"
+ ]
+ },
+ "execution_count": 23,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.warnings.filterwarnings('ignore', category=np.VisibleDeprecationWarning) \n",
+ "w_range = np.linspace(0,2,50)\n",
+ "x_range = np.linspace(-1,0,100)\n",
+ "params = {w: 0.4, A_f:1, E_f:2, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
+ "param_vals = tuple(params[map_py2sp[py_var]] for py_var in py_vars)\n",
+ "get_sig_f_x(0, *param_vals), get_aw_up(*param_vals)\n",
+ "fix, ax = plt.subplots(1,1, figsize=(8,2))\n",
+ "ax.plot(x_range, get_sig_f_x(x_range, *param_vals))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
- "outputs": [],
"source": [
- "ds = 0.2\n",
+ "# ds = 0.2\n",
"po_paper = poui.ModelInteract(\n",
" models=[PO_SF_M_RG],\n",
" py_vars=list(py_vars),\n",
@@ -814,7 +969,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.8"
+ "version": "3.9.1"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/2_6_CB_ELF_ELM.ipynb b/pull_out/2_6_CB_ELF_ELM.ipynb
index 4be30f6d87f836001fc77048ff7c8b99c193341f..4d843ebaaa4fcbe3d1efc3d44f1faa7eb4771613 100644
--- a/pull_out/2_6_CB_ELF_ELM.ipynb
+++ b/pull_out/2_6_CB_ELF_ELM.ipynb
@@ -40,7 +40,7 @@
" - crack positions, and at\n",
" - midpoints between cracks.\n",
"\n",
- "\n"
+ ""
]
},
{
@@ -76,19 +76,70 @@
"outputs": [],
"source": [
"%matplotlib widget\n",
- "from pull_out import PullOutAModel\n",
- "from po_symb.CB_ELF_ELM_Symb import CB_ELF_ELM_Symb "
+ "from pull_out import CB_ELF_ELM"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
+ "outputs": [],
+ "source": [
+ "po = CB_ELF_ELM(E_f=1, E_m=1, A_f=1, A_m=1, p=1, tau=3, L_b=1, w_max=3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/latex": [
+ "$\\displaystyle E_\\mathrm{m} \\left(\\begin{cases} 0 & \\text{for}\\: w \\leq \\frac{L_{b}^{2} \\bar{\\tau} p}{A_\\mathrm{m} E_\\mathrm{m}} + \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\wedge x \\leq - \\frac{\\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) \\left(\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} L_{b}^{2} \\bar{\\tau} p + 2 A_\\mathrm{m}^{2} E_\\mathrm{m}^{2} w} - A_\\mathrm{f} E_\\mathrm{f} L_{b} \\bar{\\tau} p\\right)}{A_\\mathrm{m} E_\\mathrm{m} \\left(A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p\\right)} \\\\- \\frac{\\bar{\\tau} p}{A_\\mathrm{m} E_\\mathrm{m}} & \\text{for}\\: w > \\frac{L_{b}^{2} \\bar{\\tau} p}{A_\\mathrm{m} E_\\mathrm{m}} + \\frac{L_{b}^{2} \\bar{\\tau} p}{2 A_\\mathrm{f} E_\\mathrm{f}} \\vee x > - \\frac{\\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) \\left(\\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} L_{b}^{2} \\bar{\\tau} p + 2 A_\\mathrm{m}^{2} E_\\mathrm{m}^{2} w} - A_\\mathrm{f} E_\\mathrm{f} L_{b} \\bar{\\tau} p\\right)}{A_\\mathrm{m} E_\\mathrm{m} \\left(A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p\\right)} \\end{cases}\\right)$"
+ ],
+ "text/plain": [
+ "E_\\mathrm{m}*Piecewise((0, (w <= L_b**2*\\bar{\\tau}*p/(A_\\mathrm{m}*E_\\mathrm{m}) + L_b**2*\\bar{\\tau}*p/(2*A_\\mathrm{f}*E_\\mathrm{f})) & (x <= -(A_\\mathrm{f}*E_\\mathrm{f} + A_\\mathrm{m}*E_\\mathrm{m})*(sqrt(A_\\mathrm{f})*sqrt(E_\\mathrm{f})*sqrt(\\bar{\\tau})*sqrt(p)*sqrt(A_\\mathrm{f}*E_\\mathrm{f}*L_b**2*\\bar{\\tau}*p + 2*A_\\mathrm{m}**2*E_\\mathrm{m}**2*w) - A_\\mathrm{f}*E_\\mathrm{f}*L_b*\\bar{\\tau}*p)/(A_\\mathrm{m}*E_\\mathrm{m}*(A_\\mathrm{f}*E_\\mathrm{f}*\\bar{\\tau}*p + A_\\mathrm{m}*E_\\mathrm{m}*\\bar{\\tau}*p)))), (-\\bar{\\tau}*p/(A_\\mathrm{m}*E_\\mathrm{m}), (w > L_b**2*\\bar{\\tau}*p/(A_\\mathrm{m}*E_\\mathrm{m}) + L_b**2*\\bar{\\tau}*p/(2*A_\\mathrm{f}*E_\\mathrm{f})) | (x > -(A_\\mathrm{f}*E_\\mathrm{f} + A_\\mathrm{m}*E_\\mathrm{m})*(sqrt(A_\\mathrm{f})*sqrt(E_\\mathrm{f})*sqrt(\\bar{\\tau})*sqrt(p)*sqrt(A_\\mathrm{f}*E_\\mathrm{f}*L_b**2*\\bar{\\tau}*p + 2*A_\\mathrm{m}**2*E_\\mathrm{m}**2*w) - A_\\mathrm{f}*E_\\mathrm{f}*L_b*\\bar{\\tau}*p)/(A_\\mathrm{m}*E_\\mathrm{m}*(A_\\mathrm{f}*E_\\mathrm{f}*\\bar{\\tau}*p + A_\\mathrm{m}*E_\\mathrm{m}*\\bar{\\tau}*p)))))"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "po.symb.sig_w_m_x.diff('x')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "3.0"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "po.symb.get_tau_w_x(-0,50)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "6ab25dda52514d2290f4b140e4ab1c10",
+ "model_id": "ce9361af6d2e4fd08e8371b7c84f51e6",
"version_major": 2,
"version_minor": 0
},
@@ -101,7 +152,7 @@
}
],
"source": [
- "PullOutAModel(name='Crack bridge', symb_class=CB_ELF_ELM_Symb).interact()"
+ "po.interact()"
]
},
{
@@ -272,7 +323,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -301,7 +352,7 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -359,7 +410,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -378,7 +429,7 @@
"âŽA_\\mathrm{f} A_\\mathrm{m} ⎠"
]
},
- "execution_count": 9,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -529,7 +580,7 @@
},
{
"cell_type": "code",
- "execution_count": 51,
+ "execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -554,7 +605,7 @@
"m{m}⋅E_\\mathrm{m}⎠"
]
},
- "execution_count": 51,
+ "execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@@ -604,7 +655,7 @@
},
{
"cell_type": "code",
- "execution_count": 53,
+ "execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -623,7 +674,7 @@
"âŽâŽ© A_\\mathrm{f}⎠⎠"
]
},
- "execution_count": 53,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -683,7 +734,7 @@
},
{
"cell_type": "code",
- "execution_count": 55,
+ "execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -716,13 +767,12 @@
" âŽ"
]
},
- "execution_count": 55,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "eqns_u_equal = {u_f.subs(C_subs).subs(x,a) - u_m.subs(D_subs).subs(F_subs).subs(x,a)}\n",
"eqns_u_equal = {u_f.subs(C_subs).subs(x,a) - u_m.subs(D_subs).subs(x,a)}\n",
"E_subs = sp.solve(eqns_u_equal,E)\n",
"E_subs"
@@ -741,7 +791,7 @@
},
{
"cell_type": "code",
- "execution_count": 56,
+ "execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -762,7 +812,7 @@
"⎩ E_\\mathrm{f} A_\\mathrm{m}â‹…E_\\mathrm{m}âŽ"
]
},
- "execution_count": 56,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -774,7 +824,7 @@
},
{
"cell_type": "code",
- "execution_count": 57,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -793,7 +843,7 @@
"au}â‹…pâŽ"
]
},
- "execution_count": 57,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -823,7 +873,7 @@
},
{
"cell_type": "code",
- "execution_count": 83,
+ "execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -862,7 +912,7 @@
" âŽ"
]
},
- "execution_count": 83,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@@ -885,7 +935,7 @@
},
{
"cell_type": "code",
- "execution_count": 84,
+ "execution_count": 12,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -920,7 +970,7 @@
"A_\\mathrm{m}⋅E_\\mathrm{m}⎠"
]
},
- "execution_count": 84,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -942,7 +992,7 @@
},
{
"cell_type": "code",
- "execution_count": 85,
+ "execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
@@ -951,7 +1001,7 @@
},
{
"cell_type": "code",
- "execution_count": 86,
+ "execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
@@ -960,7 +1010,7 @@
},
{
"cell_type": "code",
- "execution_count": 87,
+ "execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
@@ -969,7 +1019,7 @@
},
{
"cell_type": "code",
- "execution_count": 88,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -984,7 +1034,7 @@
" A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m}"
]
},
- "execution_count": 88,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -996,7 +1046,7 @@
},
{
"cell_type": "code",
- "execution_count": 89,
+ "execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
@@ -1005,7 +1055,7 @@
},
{
"cell_type": "code",
- "execution_count": 90,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -1020,7 +1070,7 @@
"A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m}"
]
},
- "execution_count": 90,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -1032,7 +1082,7 @@
},
{
"cell_type": "code",
- "execution_count": 91,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -1053,7 +1103,7 @@
"athrm{m}) "
]
},
- "execution_count": 91,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -1065,7 +1115,7 @@
},
{
"cell_type": "code",
- "execution_count": 97,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -1086,7 +1136,7 @@
"\\mathrm{m}) "
]
},
- "execution_count": 97,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -1098,7 +1148,7 @@
},
{
"cell_type": "code",
- "execution_count": 98,
+ "execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
@@ -1108,42 +1158,28 @@
},
{
"cell_type": "code",
- "execution_count": 99,
+ "execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle - \\frac{A_\\mathrm{m} E_\\mathrm{m} P \\left(A_\\mathrm{m} E_\\mathrm{m} P - 2 L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)\\right) + \\bar{\\tau}^{2} p^{2} x^{2} \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)^{2}}{2 A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)^{2}}$"
+ "$\\displaystyle \\frac{P}{A_\\mathrm{f} E_\\mathrm{f}}$"
],
"text/plain": [
- " ⎛ \n",
- "-âŽA_\\mathrm{m}â‹…E_\\mathrm{m}â‹…Pâ‹…(A_\\mathrm{m}â‹…E_\\mathrm{m}â‹…P - 2â‹…L_bâ‹…\\bar{\\tau}â‹…\n",
- "──────────────────────────────────────────────────────────────────────────────\n",
- " \n",
- " 2â‹…A_\\mathrm{m}â‹…E_\\m\n",
- "\n",
- " 2 2 2\n",
- "pâ‹…(A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m})) + \\bar{\\tau} â‹…p â‹…x \n",
- "──────────────────────────────────────────────────────────────────────────────\n",
- " 2\n",
- "athrm{m}â‹…\\bar{\\tau}â‹…pâ‹…(A_\\mathrm{f}â‹…E_\\mathrm{f} + A_\\mathrm{m}â‹…E_\\mathrm{m}) \n",
- "\n",
- " 2⎞ \n",
- "⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) ⎠\n",
- "───────────────────────────────────────────────────────────\n",
- " \n",
- " "
+ " P \n",
+ "─────────────────────────\n",
+ "A_\\mathrm{f}â‹…E_\\mathrm{f}"
]
},
- "execution_count": 99,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "sp.simplify(u_mc_x)"
+ "sp.simplify(u_fc_x).diff(x).subs(x,0)"
]
},
{
@@ -1162,7 +1198,7 @@
},
{
"cell_type": "code",
- "execution_count": 100,
+ "execution_count": 23,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1182,7 +1218,7 @@
"âŽ4 8 2 8 2 ⎠"
]
},
- "execution_count": 100,
+ "execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@@ -1205,7 +1241,7 @@
},
{
"cell_type": "code",
- "execution_count": 101,
+ "execution_count": 24,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1221,7 +1257,7 @@
" 0.355, 0.37 , 0.375]))"
]
},
- "execution_count": 101,
+ "execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@@ -1246,7 +1282,7 @@
},
{
"cell_type": "code",
- "execution_count": 102,
+ "execution_count": 25,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1294,7 +1330,7 @@
},
{
"cell_type": "code",
- "execution_count": 103,
+ "execution_count": 26,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1303,16 +1339,14 @@
"outputs": [
{
"data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "52fd1439850d4e19adfb458951a22723",
- "version_major": 2,
- "version_minor": 0
- },
+ "image/png": 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\n",
"text/plain": [
- "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+ "<Figure size 432x216 with 1 Axes>"
]
},
- "metadata": {},
+ "metadata": {
+ "needs_background": "light"
+ },
"output_type": "display_data"
}
],
@@ -1341,7 +1375,7 @@
},
{
"cell_type": "code",
- "execution_count": 114,
+ "execution_count": 27,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1364,7 +1398,7 @@
"au}â‹…pâŽ"
]
},
- "execution_count": 114,
+ "execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@@ -1375,7 +1409,7 @@
},
{
"cell_type": "code",
- "execution_count": 129,
+ "execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
@@ -2508,7 +2542,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.8"
+ "version": "3.9.1"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/fragmentation.ipynb b/pull_out/fragmentation.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..713e7ffe99814b52c16b2ed6b2234ce6ee640837
--- /dev/null
+++ b/pull_out/fragmentation.ipynb
@@ -0,0 +1,497 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "respiratory-patrol",
+ "metadata": {},
+ "source": [
+ "# 2.3 Tensile behavior of brittle-matrix composite"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "forced-klein",
+ "metadata": {},
+ "source": [
+ "With a basic understanding of the debonding process in the vicinity of a crack bridge studied for various configurations of a pull-out problem ([**pull-out configurations**](pull_out/2_2_1_PO_configuration_explorer.ipynb)) we describe and visualize the process of fragmentation (multiple cracking) in a reinforced composite."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "hairy-planner",
+ "metadata": {},
+ "source": [
+ "## Crack bridge as a key to understanding the behavior of a composite"
+ ]
+ },
+ {
+ "attachments": {
+ "ead9214a-a8c5-4f41-9aff-afe673ecd6d8.png": {
+ "image/png": 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+ }
+ },
+ "cell_type": "markdown",
+ "id": "comparative-interpretation",
+ "metadata": {},
+ "source": [
+ "Matrix cracks develop along a tensile zone of a composite, e.g. in a tensile specimen.\n",
+ "The stress, strain and displacement fields exhibit a periodic structure with symmetry points\n",
+ "at \n",
+ " - crack positions, and at\n",
+ " - midpoints between cracks.\n",
+ "\n",
+ "\n",
+ "Therefore, it the crack bridge model derived for the assumption of a constant bond-slip law can be \n",
+ "conveniently used to describe the tensile response during the multiple cracking process."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "approved-pressing",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "42a4e4377cd5488f8e840614099ea927",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib widget\n",
+ "from pull_out import CB_ELF_ELM\n",
+ "po = CB_ELF_ELM(E_f=1, E_m=1, A_f=1, A_m=1, p=1, tau=3, L_b=1, w_max=3,t=0.4)\n",
+ "po.interact()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "existing-submission",
+ "metadata": {},
+ "source": [
+ "Knowing the matrix stress profile ahead of an existing crack, we know the distance at which no crack will appear. This length is referred to as shielded length."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "olympic-validity",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/latex": [
+ "$\\displaystyle E_\\mathrm{m} \\left(\\begin{cases} \\frac{P}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} & \\text{for}\\: x \\leq - \\frac{A_\\mathrm{m} E_\\mathrm{m} P}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p} \\\\- \\frac{\\bar{\\tau} p x}{A_\\mathrm{m} E_\\mathrm{m}} & \\text{otherwise} \\end{cases}\\right)$"
+ ],
+ "text/plain": [
+ "E_\\mathrm{m}*Piecewise((P/(A_\\mathrm{f}*E_\\mathrm{f} + A_\\mathrm{m}*E_\\mathrm{m}), x <= -A_\\mathrm{m}*E_\\mathrm{m}*P/(A_\\mathrm{f}*E_\\mathrm{f}*\\bar{\\tau}*p + A_\\mathrm{m}*E_\\mathrm{m}*\\bar{\\tau}*p)), (-\\bar{\\tau}*p*x/(A_\\mathrm{m}*E_\\mathrm{m}), True))"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "po.symb.sig_P_m_x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "retired-london",
+ "metadata": {},
+ "source": [
+ "# Deterministic matrix strength (ACK model)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "toxic-battle",
+ "metadata": {},
+ "source": [
+ "The ACK model developed by Aveston, Cooper and Kelly is an analytical model that represents the composite tensile response by a trilinear law as shown in the following figure. This model is based on the following assumptions:\n",
+ "- The bond behavior is governed by a constant frictional bond in the debonded interface\n",
+ "- The constitutive law for both reinforcement and matrix is assumed to be linear-elastic with brittle failure upon reaching their strengths\n",
+ "- Multiple cracking occurs at a constant level of applied stress, inducing a horizontal branch in the stress-strain behavior"
+ ]
+ },
+ {
+ "attachments": {
+ "fea224a6-5705-4e2d-9e58-9a7c269ac62a.png": {
+ "image/png": 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"
+ }
+ },
+ "cell_type": "markdown",
+ "id": "surface-accused",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "trying-outline",
+ "metadata": {},
+ "source": [
+ "## Stress-strain curve\n",
+ "\n",
+ "The trilinear curve of ACK model represents the composite tensile response by identifying the following characteristic points:\n",
+ "- In the first stage, the matrix is uncracked and perfect bond between matrix and fabric is assumed up to the first cracking stress $\\sigma_{2}$ , which is defined as \n",
+ "\\begin{align}\n",
+ "\\sigma_{2} = E_\\mathrm{c} \\varepsilon_{2}\n",
+ "\\end{align}\n",
+ "where $\\varepsilon_{2}$ is the composite strain value at which the matrix cracks and $E_\\mathrm{c}$ is the composite stiffness. \n",
+ "The strain $\\varepsilon_{2}$ is given as\n",
+ "\\begin{align}\n",
+ "\\varepsilon_{2} = \\dfrac{\\sigma_\\mathrm{mu}}{E_\\mathrm{m}}\n",
+ "\\end{align}\n",
+ "where $\\sigma_\\mathrm{mu}$ and $E_\\mathrm{m}$ are the matrix tensile strength and stiffness, respectively.\n",
+ "The composite stiffness has been obtained using the\n",
+ "[**mixture rule**](../bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb) \n",
+ "and can be expressed here as:\n",
+ "\\begin{align}\n",
+ "E_\\mathrm{c} = E_\\mathrm{f} \\; V_\\mathrm{f} + E_\\mathrm{m} \\; (1 - V_\\mathrm{f})\n",
+ "\\end{align} \n",
+ "where $E_\\mathrm{f}$ is the fiber stiffness, and $V_\\mathrm{f}$ is denoting the fiber volume fraction (reinforcement ratio).\n",
+ "\n",
+ "- The second stage is characterized by the crack propagation. In this phase, the load is\n",
+ "assumed to be constant up to the strain value $\\varepsilon_{3}$ calculated as follows:\n",
+ "\\begin{align}\n",
+ "\\varepsilon_{3} = \\dfrac{\\sigma_\\mathrm{mu}}{E_\\mathrm{m}} \\; (1 + 0.666 \\alpha_\\mathrm{e})\n",
+ "\\end{align}\n",
+ "where where $\\alpha_\\mathrm{e}$ is an homogenization coefficient given as\n",
+ "\\begin{align}\n",
+ "\\alpha_\\mathrm{e} = \\dfrac{E_\\mathrm{m} \\; (1 - V_\\mathrm{f}) }{E_\\mathrm{f} \\; V_\\mathrm{f}}\n",
+ "\\end{align}\n",
+ "\n",
+ "- Finally, in the third stage, when the crack pattern is stabilized the load increases linearly up to the ultimate tensile stress $\\sigma_4$ with a slope equal to $E_\\mathrm{r}$\n",
+ "The ultimate tensile stress is given as\n",
+ "\\begin{align}\n",
+ "\\sigma_4 = \\sigma_\\mathrm{fu} \\; V_\\mathrm{f}\n",
+ "\\end{align}\n",
+ "where $\\sigma_\\mathrm{fu}$ is the tensile strength of the fiber.\n",
+ "The slope $E_\\mathrm{r}$ is given as\n",
+ "\\begin{align}\n",
+ "E_\\mathrm{r} = E_\\mathrm{f} \\; V_\\mathrm{f} \n",
+ "\\end{align}\n",
+ "The composilte strain at failure $\\varepsilon_{4}$ is given as\n",
+ "\\begin{align}\n",
+ "\\varepsilon_{4} = \\varepsilon_{3} + \\dfrac{\\sigma_\\mathrm{4} - \\sigma_\\mathrm{2}}{E_\\mathrm{r}}\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "aerial-synthetic",
+ "metadata": {},
+ "source": [
+ "## Crack spacing\n",
+ "\n",
+ "The final average crack spacing $l_\\mathrm{cs}$ is given as\n",
+ "\\begin{align}\n",
+ "l_\\mathrm{cs} = 1.337 \\; \\dfrac{(1 - V_\\mathrm{f}) \\; \\sigma_\\mathrm{mu}}{ V_\\mathrm{f} \\; T}\n",
+ "\\end{align}\n",
+ "where $T$ is the bond intensity\n",
+ "\\begin{align}\n",
+ " T = \\bar{\\tau} p \\;\\;\\; [\\mathrm{N / mm}]\n",
+ "\\end{align}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "basic-window",
+ "metadata": {},
+ "source": [
+ "But where does this constant 1.337 come from? It is related to a so called \"car parking problem\" "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "approximate-feature",
+ "metadata": {},
+ "source": [
+ "### Matrix cracking is like car parking ?!\n",
+ "\n",
+ "![SegmentLocal](../fig/Cars.gif \"segment\")\n",
+ "\n",
+ "Consider a process where particles (cars) are randomly introduced in a system (along the street). \n",
+ "They must not overlap any previously parked car. What is the average distance between two neighbouring cars?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "mysterious-george",
+ "metadata": {},
+ "source": [
+ "### Example: steel reinforced cross section with 1% reinforcement ratio\n",
+ "Consider the following material parameters"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "enabling-engine",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "E_m = 28000\n",
+ "E_f = 210000\n",
+ "V_f = 0.01\n",
+ "sig_mu = 3\n",
+ "sig_fu = 500"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0f66e3d8-e60d-4ff1-9a43-32ed2a486d7f",
+ "metadata": {},
+ "source": [
+ "The characteristic points of the ACK model deliver the values "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "sunset-trading",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "E_c = E_m * (1 - V_f) + E_f * V_f\n",
+ "alpha_e = E_m * (1 - V_f) / (E_f * V_f)\n",
+ "eps_1, sig_1 = 0, 0\n",
+ "eps_2, sig_2 = sig_mu / E_c, sig_mu\n",
+ "eps_3, sig_3 = sig_mu / E_m * (1 + 0.6666 * alpha_e), sig_mu\n",
+ "sig_4 = sig_fu * V_f\n",
+ "E_r = E_f * V_f\n",
+ "eps_4 = eps_3 + (sig_4 - sig_3) / E_r"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "material-knight",
+ "metadata": {},
+ "source": [
+ "Plot the composite stress-strain curve"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "adult-ribbon",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "ed30c8a8b1094c36b36199f212a8b434",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib widget\n",
+ "import matplotlib.pylab as plt\n",
+ "fig, ax = plt.subplots(1,1,figsize=(7,3))\n",
+ "fig.canvas.toolbar_position = 'top'\n",
+ "fig.canvas.header_visible = False\n",
+ "ax.plot([eps_1, eps_2, eps_3, eps_4], [sig_1, sig_2, sig_3, sig_4]);\n",
+ "ax.set_xlabel(r'$\\varepsilon$ [-]'); ax.set_ylabel(r'$\\sigma$ [MPa]')\n",
+ "ax.plot([0,eps_4],[0,E_r*eps_4], linestyle='dashed');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "comfortable-cowboy",
+ "metadata": {},
+ "source": [
+ "# Probabilistic multiple cracking model\n",
+ "\n",
+ "In reality, the matrix strength $\\sigma_\\mathrm{mu}$ is random. Its profile along the tensile specimen can be described by the probability distribution function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "boxed-scott",
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "from pmcm.api import PMCM"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "regulated-republic",
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "pmcm = PMCM(m=10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "subsequent-coach",
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "63ba009ff6ac49c080b258484966fe0a",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pmcm.interact()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "southwest-bachelor",
+ "metadata": {},
+ "source": [
+ "# Questions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "numeric-nepal",
+ "metadata": {},
+ "source": [
+ "- Given the cross sectional areas $A_\\mathrm{m}, A_\\mathrm{f}$, concrete and reinforcement stiffness $E_\\mathrm{m}, E_\\mathrm{f}$ and strength $\\sigma_\\mathrm{mu}, \\sigma_\\mathrm{fu}$, reinforcement ratio $V_\\mathrm{f}$, bond intensity $T$, calculate the average crack width at failure of a tensile specimen."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "26acec03-96b0-4f31-b890-4e6727d40060",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ph.interact()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "694c155c-bc53-4750-82ef-a9b0b9f0a65d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "import pmcm.pmcm2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "0d586905-6bf3-4f21-8a29-81973da643ff",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pm = pmcm.pmcm2.PMCM()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "11339d52-6dc2-49e0-9c60-7bf01b8d2b4b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "137932dce7424c4091100ca25ef81d0b",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pm.interact()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "be17e48c-81b5-493b-8e14-6f7631019f82",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "base",
+ "language": "python",
+ "name": "base"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/pull_out/pmcm/__init__.py b/pull_out/pmcm/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/pull_out/pmcm/api.py b/pull_out/pmcm/api.py
new file mode 100644
index 0000000000000000000000000000000000000000..c183405df21793738ccf3d0088b5f01d054b588a
--- /dev/null
+++ b/pull_out/pmcm/api.py
@@ -0,0 +1 @@
+from .pmcm import PMCM
\ No newline at end of file
diff --git a/pull_out/pmcm/pmcm.py b/pull_out/pmcm/pmcm.py
new file mode 100644
index 0000000000000000000000000000000000000000..be5586caf4e71d372f3efdf6cfd7b08e17a87cab
--- /dev/null
+++ b/pull_out/pmcm/pmcm.py
@@ -0,0 +1,276 @@
+"""
+Probabilistic multiple cracking model
+"""
+from typing import List, Any, Union
+import bmcs_utils.api as bu
+
+import traits.api as tr
+import numpy as np
+import warnings
+
+from bmcs_utils.trait_types import Float
+from scipy.optimize import newton
+
+warnings.filterwarnings("error", category=RuntimeWarning)
+
+
+class CrackBridgeModel(bu.Model):
+ """
+ Record of all material parameters of the composite. The model components
+ (PullOutModel, CrackBridgeRespSurf, PMCM) are all linked to the database record
+ and access the parameters they require. Some parameters are shared across all
+ three components (Em, Ef, vf), some are specific to a particular type of the
+ PulloutModel.
+ """
+
+class CBMConstantBond(CrackBridgeModel):
+ """
+ Return the matrix stress profile of a crack bridge for a given control slip
+ at the loaded end
+ """
+ Em = bu.Float(28000)
+ Ef = bu.Float(180000)
+ vf = bu.Float(0.01)
+ T = bu.Float(8)
+
+ ipw_view = bu.View(
+ bu.Item('Em'),
+ bu.Item('Ef'),
+ bu.Item('vf'),
+ bu.Item('T'),
+ )
+
+ @property
+ def Ec(self):
+ return self.Em * (1 - self.vf) + self.Ef * self.vf # [MPa] mixture rule
+
+class CrackBridgeRespSurface(bu.Model):
+ """
+ Crack bridge response surface that returns the values of matrix stress
+ along ahead of a crack and crack opening for a specified remote stress
+ and boundary conditions.
+ """
+ cb = bu.Instance(CrackBridgeModel)
+
+ def get_sig_m(self, z, sig_c):
+ """Get the profile of matrix stress along the specimen
+ :param z: np.ndarray
+ :type sig_c: float
+ """
+ cb = self.cb
+ sig_m = np.minimum(z * cb.T * cb.vf / (1 - cb.vf), cb.Em * sig_c /
+ (cb.vf * cb.Ef + (1 - cb.vf) * cb.Em))
+ return sig_m
+
+ def get_eps_f(self, z, sig_c):
+ cb = self.cb
+ sig_m = self.get_sig_m(sig_c, z )
+ eps_f = (sig_c - sig_m * (1 - cb.vf)) / cb.vf / cb.Ef
+ return eps_f
+
+ sig_c_slider: float = bu.Float(1.0, BC=True)
+
+ ipw_view = bu.View(
+ bu.Item('sig_c_slider')
+ )
+
+ @staticmethod
+ def subplots(fig):
+ ax = fig.subplots(1,1)
+ ax1 = ax.twinx()
+ return ax, ax1
+
+ def update_plot(self, axes):
+ ax, ax1 = axes
+ x_range = np.linspace(-1000,1000,1000)
+ z_range = np.abs(x_range)
+
+ sig_m_range = self.get_sig_m(self.sig_c_slider, z_range)
+ eps_f_range = self.get_eps_f(self.sig_c_slider, z_range)
+ sig_max = np.max(sig_m_range)
+ eps_max = np.max(eps_f_range)
+
+ ax.plot(x_range, sig_m_range, color='black')
+ ax.fill_between(x_range, sig_m_range, color='gray', alpha=0.1)
+ ax.set_ylim(ymin=-0.03*sig_max)
+ ax1.plot(x_range, eps_f_range, color='blue')
+ ax1.fill_between(x_range, eps_f_range, color='blue', alpha=0.1)
+ ax1.set_ylim(ymin=-0.03*eps_max)
+
+class PMCMHist(bu.Model):
+ pmcm = tr.WeakRef
+
+ K = bu.Int(0)
+ t = bu.Float(0)
+ K_max = tr.Property(depends_on='state_changed')
+ @tr.cached_property
+ def _get_K_max(self):
+ sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K, sig_m_x_K1 = self.pmcm.cracking_history
+ K_max = len(sig_c_K)
+ # ceil the index of current crack
+ self.K = np.min([self.K, K_max])
+ return K_max
+
+ ipw_view = bu.View(
+ bu.Item('K', latex=r'\mathrm{state}', readonly=True),
+ time_editor=bu.HistoryEditor(
+ var='t',
+ var_max='K_max'
+ )
+ )
+
+ @staticmethod
+ def subplots(fig):
+ ax1, ax2 = fig.subplots(1,2)
+ ax11 = ax1.twinx()
+ return ax1, ax11, ax2
+
+ def update_plot(self, axes):
+ ax, ax_cs, ax_sig_x = axes
+ cr = int(self.t * (self.K_max-2))
+ self.K = cr
+ self.pmcm.plot(axes)
+ sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K, sig_m_x_K1 = self.pmcm.cracking_history
+ ax_sig_x.plot(x,sig_m_x_K[cr])
+ ax_sig_x.plot(x,sig_m_x_K1[cr], linestyle='dashed')
+ ax.plot(eps_c_K[cr],sig_c_K[cr],color='magenta',marker='o')
+
+
+class PMCM(bu.Model):
+ name = "PMCM"
+ """
+ Implement the global crack tracing algorithm based on a crack bridge response surface
+ """
+
+ history = bu.Instance(PMCMHist)
+ def _history_default(self):
+ return PMCMHist(pmcm=self)
+
+ cb = bu.Instance(CrackBridgeModel)
+ def _cb_default(self):
+ return CBMConstantBond()
+
+ cb_rs = tr.Property#(depends_on="state_changed")
+ @tr.cached_property
+ def _get_cb_rs(self):
+ return CrackBridgeRespSurface(cb=self.cb)
+
+ tree = ['cb', 'cb_rs', 'history']
+
+ n_x = bu.Int(5000, ALG=True)
+ L_x = bu.Float(500, GEO=True)
+ sig_cu = bu.Float(20, MAT=True)
+ sig_mu = bu.Float(10, MAT=True)
+ m = bu.Float(4, MAT=True)
+
+ ipw_view = bu.View(
+ bu.Item('n_x'),
+ bu.Item('L_x'),
+ bu.Item('sig_cu'),
+ bu.Item('sig_mu'),
+ bu.Item('m'),
+ )
+
+ def get_z_x(self, x, XK): # distance to the closest crack (*\label{get_z_x}*)
+ """Specimen discretization
+ """
+ z_grid = np.abs(x[:, np.newaxis] - np.array(XK)[np.newaxis, :])
+ return np.amin(z_grid, axis=1)
+
+ def get_sig_c_z(self, sig_mu, z, sig_c_pre):
+ """
+ :param sig_c_pre:
+ :type sig_mu: float
+ """
+ # crack initiating load at a material element
+ #print('sig_mu', sig_mu)
+ fun = lambda sig_c: sig_mu - self.cb_rs.get_sig_m(sig_c, z)
+ try: # search for the local crack load level
+ sig_c = newton(fun, sig_c_pre)
+ #print('sig_c', sig_c)
+ return sig_c
+ except (RuntimeWarning, RuntimeError):
+ # solution not found (shielded zone) return the ultimate composite strength
+ return self.sig_cu
+
+ def get_sig_c_K(self, z_x, x, sig_c_pre, sig_mu_x):
+ # crack initiating loads over the whole specimen
+ get_sig_c_x = np.vectorize(self.get_sig_c_z)
+ sig_c_x = get_sig_c_x(sig_mu_x, z_x, sig_c_pre)
+ #print('sig_c_x', z_x, x, sig_c_pre, sig_mu_x)
+ #print('sig_c_x', sig_c_x)
+ y_idx = np.argmin(sig_c_x)
+ return sig_c_x[y_idx], x[y_idx]
+
+ cracking_history = tr.Property(depends_on='state_changed')
+ @tr.cached_property
+ def _get_cracking_history(self):
+ cb = self.cb
+ L_x, n_x, sig_mu, sig_cu, m = self.L_x, self.n_x, self.sig_mu, self.sig_cu, self.m
+ x = np.linspace(0, L_x, n_x) # specimen discretization
+ sig_mu_x: np.ndarray[np.float_] = sig_mu * np.random.weibull(
+ m, size=n_x) # matrix strength
+
+ XK: List[float] = [] # recording the crack postions
+ sig_c_K: List[float] = [0.] # recording the crack initiating loads
+ eps_c_K: List[float] = [0.] # recording the composite strains
+ CS: List[float] = [L_x, L_x / 2] # initial crack spacing
+ sig_m_x_K1: List[float] = [np.zeros_like(x)] # stress profiles at crack states
+ sig_m_x_K: List[float] = [np.zeros_like(x)] # stress profiles after crack states
+
+
+ Ec: float = cb.Ec
+ Em: float = cb.Em
+ idx_0 = np.argmin(sig_mu_x)
+ XK.append(x[idx_0]) # position of the first crack
+ sig_c_0 = sig_mu_x[idx_0] * Ec / Em
+ sig_m_x_K1.append(np.ones_like(x)*sig_mu_x[idx_0]) # matrix stress
+ #print('sig_c_0', sig_c_0)
+ sig_c_K.append(sig_c_0)
+ eps_c_K.append(sig_mu_x[idx_0] / Em)
+
+ while True:
+ z_x = self.get_z_x(x, XK) # distances to the nearest crack
+ sig_m_x_K.append(self.cb_rs.get_sig_m(sig_c_K[-1], z_x)) # matrix stress
+ sig_c_k, y_i = self.get_sig_c_K(z_x, x, sig_c_K[-1], sig_mu_x) # identify next crack
+ sig_m_x_K1.append(self.cb_rs.get_sig_m(sig_c_k, z_x)) # matrix stress
+ if sig_c_k == sig_cu:
+ break
+ XK.append(y_i) # record crack position
+ sig_c_K.append(sig_c_k) # corresponding composite stress
+ eps_c_K.append( # composite strain - integrate the strain field
+ np.trapz(self.cb_rs.get_eps_f(sig_c_k, self.get_z_x(x, XK)), x) / np.amax(x))
+ XK_arr = np.hstack([[0], np.sort(np.array(XK)), [L_x]])
+ CS.append(np.average(XK_arr[1:] - XK_arr[:-1])) # crack spacing
+
+ sig_c_K.append(sig_cu) # the ultimate state
+ eps_c_K.append(np.trapz(self.cb_rs.get_eps_f(sig_cu, self.get_z_x(x, XK) ), x) / np.amax(x))
+ CS.append(CS[-1])
+ return np.array(sig_c_K), np.array(eps_c_K), sig_mu_x, x, np.array(CS), np.array(sig_m_x_K), np.array(sig_m_x_K1)
+
+ @staticmethod
+ def subplots(fig):
+ ax1, ax2 = fig.subplots(1,2)
+ ax11 = ax1.twinx()
+ return ax1, ax11, ax2
+
+ def plot(self, axes):
+ ax, ax_cs, ax_sig_x = axes
+ sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K, sig_m_x_K1 = self.cracking_history
+ n_c = len(eps_c_K) - 2 # numer of cracks
+ ax.plot(eps_c_K, sig_c_K, marker='o', label='%d cracks:' % n_c)
+ ax.set_xlabel(r'$\varepsilon_\mathrm{c}$ [-]');
+ ax.set_ylabel(r'$\sigma_\mathrm{c}$ [MPa]')
+ ax_sig_x.plot(x, sig_mu_x, color='orange')
+ ax_sig_x.fill_between(x, sig_mu_x, 0, color='orange', alpha=0.1)
+ ax_sig_x.set_xlabel(r'$x$ [mm]');
+ ax_sig_x.set_ylabel(r'$\sigma$ [MPa]')
+ ax.legend()
+ eps_c_KK = np.array([eps_c_K[:-1], eps_c_K[1:]]).T.flatten()
+ CS_KK = np.array([CS[:-1], CS[:-1]]).T.flatten()
+ ax_cs.plot(eps_c_KK, CS_KK, color='gray')
+ ax_cs.fill_between(eps_c_KK, CS_KK, color='gray', alpha=0.2)
+ ax_cs.set_ylabel(r'$\ell_\mathrm{cs}$ [mm]');
+
+ def update_plot(self, axes):
+ self.plot(axes)
diff --git a/pull_out/pmcm/pmcm2.py b/pull_out/pmcm/pmcm2.py
new file mode 100644
index 0000000000000000000000000000000000000000..6c34898bde6d54d0f1397d91badec5dea1bc47d4
--- /dev/null
+++ b/pull_out/pmcm/pmcm2.py
@@ -0,0 +1,344 @@
+# %% md
+
+import numpy as np
+from scipy.optimize import newton
+import matplotlib.pylab as plt
+import traits.api as tr
+import bmcs_utils.api as bu
+
+# %%
+import warnings # (*\label{error1}*)
+
+warnings.filterwarnings("error", category=RuntimeWarning) # (*\label{error2}*)
+
+
+class CrackBridgeModel(bu.Model):
+ """
+ Record of all material parameters of the composite. The model components
+ (PullOutModel, CrackBridgeRespSurf, PMCM) are all linked to the database record
+ and access the parameters they require. Some parameters are shared across all
+ three components (Em, Ef, vf), some are specific to a particular type of the
+ PulloutModel.
+ """
+
+
+class CBMConstantBond(CrackBridgeModel):
+ """
+ Return the matrix stress profile of a crack bridge for a given control slip
+ at the loaded end
+ """
+ Em = bu.Float(25e3, MAT=True) # [MPa] matrix modulus
+ Ef = bu.Float(180e3, MAT=True) # [MPa] fiber modulus
+ vf = bu.Float(0.01, CS=True) # [-] reinforcement ratio
+ T = bu.Float(12., MAT=True) # [N/mm^3] bond intensity
+
+ ipw_view = bu.View(
+ bu.Item('Em'),
+ bu.Item('Ef'),
+ bu.Item('vf'),
+ bu.Item('T'),
+ )
+
+class CrackBridgeRespSurface(bu.Model):
+
+ cb = bu.Instance(CrackBridgeModel)
+
+ ## Crack bridge with constant bond
+ def get_sig_m(self, z, sig_c): # matrix stress (*\label{sig_m}*)
+ T = self.cb.T
+ vf = self.cb.vf
+ Em = self.cb.Em
+ Ef = self.cb.Ef
+ sig_m = np.minimum(z * T * vf / (1 - vf), Em * sig_c / (vf * Ef + (1 - vf) * Em))
+ return sig_m
+
+ def get_eps_f(self, z, sig_c): # reinforcement strain (*\label{sig_f}*)
+ vf = self.cb.vf
+ Ef = self.cb.Ef
+ sig_m = self.get_sig_m(z, sig_c)
+ eps_f = (sig_c - sig_m * (1 - vf)) / vf / Ef
+ return eps_f
+
+ sig_c_slider: float = bu.Float(1.0, BC=True)
+
+ ipw_view = bu.View(
+ bu.Item('sig_c_slider')
+ )
+
+ @staticmethod
+ def subplots(fig):
+ ax = fig.subplots(1,1)
+ ax1 = ax.twinx()
+ return ax, ax1
+
+ def update_plot(self, axes):
+ ax, ax1 = axes
+ x_range = np.linspace(-300,300,1000)
+ z_range = np.abs(x_range)
+
+ sig_m_range = self.get_sig_m(z_range, self.sig_c_slider)
+ eps_f_range = self.get_eps_f(z_range, self.sig_c_slider)
+ sig_max = np.max(sig_m_range)
+ eps_max = np.max(eps_f_range)
+
+ ax.plot(x_range, sig_m_range, color='black')
+ ax.fill_between(x_range, sig_m_range, color='gray', alpha=0.1)
+ ax.set_ylim(ymin=-0.03*sig_max)
+ ax1.plot(x_range, eps_f_range, color='blue')
+ ax1.fill_between(x_range, eps_f_range, color='blue', alpha=0.1)
+ ax1.set_ylim(ymin=-0.03*eps_max)
+
+
+class PMCM(bu.Model):
+ name='Fragmentation'
+ sig_cu = bu.Float(10.0, MAT=True) # [MPa] composite strength
+ sig_mu = bu.Float(3.0, MAT=True) # [MPa] matrix strength
+ m = bu.Float(4, MAT=True) # Weibull shape modulus
+ ## Crack tracing algorithm
+ n_x = bu.Int(200, MAT=True)
+ L_x = bu.Float(380, MAT=True)
+
+ cb = bu.Instance(CrackBridgeModel)
+ def _cb_default(self):
+ return CBMConstantBond()
+
+ cb_rs = tr.Property
+ @tr.cached_property
+ def _get_cb_rs(self):
+ return CrackBridgeRespSurface(cb=self.cb)
+ #
+ # # %%
+ #
+ # cb_rs = bu.Instance(CrackBridgeRespSurface, ())
+
+ tree = ['cb', 'cb_rs']
+
+ ipw_view = bu.View(
+ bu.Item('n_x'),
+ bu.Item('L_x'),
+ bu.Item('sig_cu'),
+ bu.Item('sig_mu'),
+ bu.Item('m'),
+ )
+
+
+ ## Specimen discretization
+ def get_z_x(self, x, XK): # distance to the closest crack (*\label{get_z_x}*)
+ z_grid = np.abs(x[:, np.newaxis] - np.array(XK)[np.newaxis, :])
+ return np.amin(z_grid, axis=1)
+
+ def get_sig_c_z(self, sig_mu, z, sig_c_pre):
+ # crack initiating load at a material element
+ fun = lambda sig_c: sig_mu - self.cb_rs.get_sig_m(z, sig_c)
+ try: # search for the local crack load level
+ return newton(fun, sig_c_pre)
+ except (RuntimeWarning, RuntimeError):
+ # solution not found (shielded zone) return the ultimate composite strength
+ return self.sig_cu
+
+ def get_sig_c_K(self, z_x, x, sig_c_pre, sig_mu_x):
+ # crack initiating loads over the whole specimen
+ get_sig_c_x = np.vectorize(self.get_sig_c_z)
+ sig_c_x = get_sig_c_x(sig_mu_x, z_x, sig_c_pre)
+ y_idx = np.argmin(sig_c_x)
+ return sig_c_x[y_idx], x[y_idx]
+
+ cracking_history = tr.Property(depends_on='state_changed')
+ @tr.cached_property
+ def _get_cracking_history(self):
+ return self.get_cracking_history()
+
+ def get_cracking_history(self, update_progress=None):
+ L_x, n_x = self.L_x, self.n_x
+ sig_mu = self.sig_mu
+ m = self.m
+ x = np.linspace(0, L_x, n_x) # specimen discretization (*\label{discrete}*)
+ sig_mu_x = sig_mu * np.random.weibull(m, size=n_x) # matrix strength (*\label{m_strength}*)
+
+ vf = self.cb_rs.cb.vf
+ Em = self.cb_rs.cb.Em
+ Ef = self.cb_rs.cb.Ef
+
+ Ec = Em * (1 - vf) + Ef * vf # [MPa] mixture rule
+
+ XK = [] # recording the crack postions
+ sig_c_K = [0.] # recording the crack initating loads
+ eps_c_K = [0.] # recording the composite strains
+ CS = [L_x, L_x / 2] # crack spacing
+ sig_m_x_K = [np.zeros_like(x)] # stress profiles for crack states
+
+ idx_0 = np.argmin(sig_mu_x)
+ XK.append(x[idx_0]) # position of the first crack
+ sig_c_0 = sig_mu_x[idx_0] * Ec / Em
+ sig_c_K.append(sig_c_0)
+ eps_c_K.append(sig_mu_x[idx_0] / Em)
+
+ while True:
+ z_x = self.get_z_x(x, XK) # distances to the nearest crack
+ sig_m_x_K.append(self.cb_rs.get_sig_m(z_x, sig_c_K[-1])) # matrix stress
+ sig_c_k, y_i = self.get_sig_c_K(z_x, x, sig_c_K[-1], sig_mu_x) # identify next crack
+ if sig_c_k == self.sig_cu: # (*\label{no_crack}*)
+ break
+ if update_progress: # callback to user interface
+ update_progress(sig_c_k)
+ XK.append(y_i) # record crack position
+ sig_c_K.append(sig_c_k) # corresponding composite stress
+ eps_c_K.append( # composite strain - integrate the strain field
+ np.trapz(self.cb_rs.get_eps_f(self.get_z_x(x, XK), sig_c_k), x) / np.amax(x)) # (*\label{imple_avg_strain}*)
+ XK_arr = np.hstack([[0], np.sort(np.array(XK)), [L_x]])
+ CS.append(np.average(XK_arr[1:] - XK_arr[:-1])) # crack spacing
+
+ sig_c_K.append(self.sig_cu) # the ultimate state
+ eps_c_K.append(np.trapz(self.cb_rs.get_eps_f(self.get_z_x(x, XK), self.sig_cu), x) / np.amax(x))
+ CS.append(CS[-1])
+ if update_progress:
+ update_progress(sig_c_k)
+ return np.array(sig_c_K), np.array(eps_c_K), sig_mu_x, x, np.array(CS), np.array(sig_m_x_K)
+
+ @staticmethod
+ def subplots(fig):
+ ax1, ax2 = fig.subplots(1,2)
+ ax11 = ax1.twinx()
+ return ax1, ax11, ax2
+
+ def plot(self, axes):
+ ax, ax_cs, ax_sig_x = axes
+ sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K = self.cracking_history
+ #sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K, sig_m_x_K1 = self.cracking_history
+ n_c = len(eps_c_K) - 2 # numer of cracks
+ ax.plot(eps_c_K, sig_c_K, marker='o', label='%d cracks:' % n_c)
+ ax.set_xlabel(r'$\varepsilon_\mathrm{c}$ [-]');
+ ax.set_ylabel(r'$\sigma_\mathrm{c}$ [MPa]')
+ ax_sig_x.plot(x, sig_mu_x, color='orange')
+ ax_sig_x.fill_between(x, sig_mu_x, 0, color='orange', alpha=0.1)
+ ax_sig_x.set_xlabel(r'$x$ [mm]');
+ ax_sig_x.set_ylabel(r'$\sigma$ [MPa]')
+ ax.legend()
+ eps_c_KK = np.array([eps_c_K[:-1], eps_c_K[1:]]).T.flatten()
+ CS_KK = np.array([CS[:-1], CS[:-1]]).T.flatten()
+ ax_cs.plot(eps_c_KK, CS_KK, color='gray')
+ ax_cs.fill_between(eps_c_KK, CS_KK, color='gray', alpha=0.2)
+ ax_cs.set_ylabel(r'$\ell_\mathrm{cs}$ [mm]');
+
+ def update_plot(self, axes):
+ self.plot(axes)
+
+# %%
+
+def render_widgets():
+ ## Interactive application
+ import ipywidgets as ipw
+
+ n_steps = 20
+ margs_sliders = {
+ name: ipw.FloatSlider(description=desc, value=val,
+ min=minval, max=maxval, step=(maxval - minval) / n_steps,
+ continuous_update=False)
+ for name, desc, val, minval, maxval in [
+ ('Em', r'\(E_\mathrm{m}\;\)[MPa]', 28e3, 1e3, 50e3),
+ ('Ef', r'\(E_\mathrm{f}\;\)[MPa]', 180e3, 1e3, 250e3),
+ ('vf', r'\(V_\mathrm{f}\;\)[-]', 0.01, 0.00001, 0.4),
+ ('T', r'\(T\;\)[N/mm$^3$]', 8, 0.0001, 20),
+ ('sig_cu', r'\(\sigma_\mathrm{cu}\;\)[MPa]', 10, 3, 100),
+ ('sig_mu', r'\(\sigma_\mathrm{mu}\;\)[MPa]', 5.0, 1, 10),
+ ('m', r'\(m\;\)[-]', 4, 0.8, 100),
+ ('L_x', r'\(L\;\)[mm]', 500, 200, 2000)
+ ]
+ }
+ pmcm_args = ['sig_cu', 'sig_mu', 'm', 'L_x', 'n_x']
+ cb_args = ['Em', 'Ef', 'vf', 'T']
+
+ margs_sliders['n_x'] = ipw.IntSlider(description='$n_\mathrm{points}$', value=200,
+ min=20, max=1000, step=10, continuous_update=False)
+ crack_slider = ipw.IntSlider(description='crack', value=0, min=0, max=1, step=1)
+ progress = ipw.FloatProgress(min=0, max=1) # instantiate the bar
+
+ fig, (ax, ax_sig_x) = plt.subplots(1, 2, figsize=(8, 3), tight_layout=True)
+ ax_cs = ax.twinx()
+
+
+ def update_progress(sig):
+ progress.value = sig
+
+
+ pmcm = PMCM()
+
+ def init():
+ for key, sl in margs_sliders.items():
+ globals()[key] = sl.value
+ sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K = pmcm.get_cracking_history(update_progress) # (*\label{calc_curve}*)
+ progress.max = margs_sliders['sig_cu'].value
+ ax.plot(eps_c_K, sig_c_K, marker='o') # (*\label{show_curve1}*)
+ ax_sig_x.plot(x, sig_mu_x, color='red')
+
+
+ current_sig_m_x_K = []
+ current_x = []
+
+
+ def reset_crack_slider(x, sig_m_x_K):
+ global current_sig_m_x_K, current_x, sig_m_line, sig_eps_marker
+ current_sig_m_x_K = sig_m_x_K
+ current_x = x
+ n_cracks = len(sig_m_x_K)
+ crack_slider.max = n_cracks - 1
+ crack_slider.value = 0
+ sig_m_line, = ax_sig_x.plot(x, sig_m_x_K[0])
+ sig_eps_marker, = ax.plot([0], [0], color='magenta', marker='o')
+
+
+ def update_crack_slider(crack):
+ global sig_m_line, sig_eps_marker
+ global sig_c_K, eps_c_K
+ if len(current_sig_m_x_K) > 0:
+ sig_m_line.set_ydata(current_sig_m_x_K[crack])
+ sig_eps_marker.set_data(eps_c_K[crack], sig_c_K[crack])
+
+
+ def update(**mparams):
+ global sig_c_K, eps_c_K
+ for key, val in mparams.items():
+ globals()[key] = val
+ ax.clear()
+ ax_cs.clear()
+ ax_sig_x.clear()
+ ax.set_title('stress-strain and crack spacing')
+ ax_sig_x.set_title('matrix strength and stress profiles')
+ sig_c_K, eps_c_K, sig_mu_x, x, CS, sig_m_x_K = pmcm.get_cracking_history(update_progress) # (*\label{calc_curve}*)
+ n_c = len(eps_c_K) - 2 # numer of cracks
+ ax.plot(eps_c_K, sig_c_K, marker='o', label='%d cracks:' % n_c) # (*\label{show_curve1}*)
+ ax.set_xlabel(r'composite strain $\varepsilon_\mathrm{c}$ [-]');
+ ax.set_ylabel(r'composite stress $\sigma_\mathrm{c}$ [MPa]')
+ ax_sig_x.plot(x, sig_mu_x, color='orange')
+ ax_sig_x.fill_between(x, sig_mu_x, 0, color='orange', alpha=0.1)
+ ax_sig_x.set_xlabel(r'$x$ [mm]');
+ ax_sig_x.set_ylabel(r'matrix stress $\sigma_\mathrm{m}$ [MPa]')
+ ax.legend()
+ eps_c_KK = np.array([eps_c_K[:-1], eps_c_K[1:]]).T.flatten()
+ CS_KK = np.array([CS[:-1], CS[:-1]]).T.flatten()
+ ax_cs.plot(eps_c_KK, CS_KK, color='gray')
+ ax_cs.fill_between(eps_c_KK, CS_KK, color='gray', alpha=0.2)
+ ax_cs.set_ylabel(r'crack spacing $\ell_\mathrm{cs}$ [mm]');
+ reset_crack_slider(x, sig_m_x_K)
+
+
+ def slider_layout():
+ hbox_pr = ipw.HBox([progress])
+ hbox = ipw.HBox([crack_slider])
+ pmcm_layout = ipw.Layout(grid_template_columns='1fr')
+ pmcm_list = [ipw.Label('Crack tracing parameters')] + \
+ [margs_sliders[arg] for arg in pmcm_args]
+ pmcm_col = ipw.GridBox(pmcm_list, layout=pmcm_layout)
+ cb_layout = ipw.Layout(grid_template_columns='1fr')
+ cb_list = [ipw.Label('Crack bridge parameters')] + \
+ [margs_sliders[arg] for arg in cb_args]
+ cb_col = ipw.GridBox(cb_list, layout=cb_layout)
+ alg_params = ipw.HBox([pmcm_col, cb_col])
+ box = ipw.VBox([hbox_pr, hbox, alg_params])
+ display(box)
+
+
+ init()
+ slider_layout()
+ ipw.interactive_output(update_crack_slider, {'crack': crack_slider})
+ ipw.interactive_output(update, margs_sliders);
diff --git a/pull_out/po_symb/CB_ELF_ELM_Symb.py b/pull_out/po_symb/CB_ELF_ELM_Symb.py
index fe497f8de8a4e9f5673dc1899553b5f7a7f0820e..96065f939ac2fee2ed7229b2c0dd6f286dbc5e33 100644
--- a/pull_out/po_symb/CB_ELF_ELM_Symb.py
+++ b/pull_out/po_symb/CB_ELF_ELM_Symb.py
@@ -47,48 +47,67 @@ class CB_ELF_ELM_Symb(bu.SymbExpr):
u_c_x_ = P / A_c / E_c * x + G
G_subs = sp.solve( u_c_x_.subs(x, -L_b), G)[0]
- u_c_x = sp.simplify(u_c_x_.subs(G, G_subs).subs(var_subs))
- u_c_a = sp.simplify( u_c_x.subs(x,var_subs[a]) )
+ u_P_c_x = sp.simplify(u_c_x_.subs(G, G_subs).subs(var_subs))
+ u_c_a = sp.simplify(u_P_c_x.subs(x,var_subs[a]) )
F_sol = sp.simplify( sp.solve( u_m_x.subs(x, a_subs[a]) - u_c_a, F)[0] )
- u_mc_x = u_m_x.subs(F, F_sol)
- u_fc_x = u_f_x.subs(F, F_sol)
-
- u_fa_x = sp.Piecewise((u_c_x, x <= var_subs[a]),
- (u_fc_x, x > var_subs[a])
- )
- u_ma_x = sp.Piecewise((u_c_x, x <= var_subs[a]),
- (u_mc_x, x > var_subs[a]),
+ u_P_mc_x = u_m_x.subs(F, F_sol)
+ u_P_fc_x = u_f_x.subs(F, F_sol)
+
+ u_P_f_x = sp.Piecewise((u_P_c_x, x <= var_subs[a]),
+ (u_P_fc_x, x > var_subs[a])
+ )
+ u_P_m_x = sp.Piecewise((u_P_c_x, x <= var_subs[a]),
+ (u_P_mc_x, x > var_subs[a]),
)
- eps_f_x = sp.diff(u_fa_x,x)
- eps_m_x = sp.diff(u_ma_x,x)
-
- sig_f_x = E_f * eps_f_x
- sig_m_x = E_m * eps_m_x
+ eps_P_f_x = sp.diff(u_P_f_x,x)
+ eps_P_m_x = sp.diff(u_P_m_x,x)
+ sig_P_f_x = E_f * eps_P_f_x
+ sig_P_m_x = E_m * eps_P_m_x
+ tau_P_x = sig_P_f_x.diff(x) * A_f / p
- tau_x = sig_f_x.diff(x) * A_f / p
+ P_w_pull_min, P_w_pull_pls = sp.solve(u_P_fc_x.subs(x,0) - w, P)
+ P_w_pull_ = P_w_pull_min
- eps_f_0 = P / E_f / A_f
- eps_m_0 = -P / E_m / A_m
- a_subs = sp.solve({P - p * tau * a}, a)
- w_el = sp.Rational(1,2) * ( eps_f_0 - eps_m_0) * a
- Pw_pull_ = sp.solve(w_el.subs(a_subs) - w, P)[1]
+ a_w_pull = a_subs[a].subs(P, P_w_pull_)
+ w_argmax1 = sp.solve(sp.Eq(a_w_pull, -L_b), w)[0]
- w_L_b = u_fa_x.subs(x, -L_b).subs(P, Pw_pull_)
+ d_Pw_pull_dw = sp.diff(P_w_pull_, w)
- aw_pull = a_subs[a].subs(P, Pw_pull_)
-
- P_max = p * tau * L_b
- w_argmax = sp.solve(P_max - Pw_pull_, w)[0]
- d_Pw_pull_dw = sp.diff(Pw_pull_, w)
+ w_argmax = w_argmax1
K_c = sp.simplify(d_Pw_pull_dw.subs({w: w_argmax}))
- Pw_clamped = sp.Piecewise(
- (Pw_pull_, w < w_argmax),
- (P_max + K_c * (w - w_argmax), w >= w_argmax)
+ P_c = P_w_pull_.subs(w, w_argmax)
+ P_w_clamped = sp.Piecewise(
+ (P_w_pull_, w < w_argmax),
+ (P_c + K_c * (w - w_argmax), w >= w_argmax)
)
- Pw_pull = Pw_clamped
+
+ P_w_pull = P_w_clamped
+ w_L_b = P_w_pull * 1e-9
+
+ u_w_c_x = u_P_c_x.subs(P, P_w_pull_)
+ u_w_fc_x = u_P_fc_x.subs(P, P_w_pull_)
+ u_w_mc_x = u_P_mc_x.subs(P, P_w_pull_)
+
+ P_d = P_w_pull_ - P_c
+ u_d = P_d / A_f / E_f * (x + L_b)
+
+ u_w_f_x = sp.Piecewise((u_w_c_x, ((w <= w_argmax) & (x <= a_w_pull))),
+ (u_w_fc_x, ((w <= w_argmax) & (x > a_w_pull))),
+ (u_d + u_w_fc_x.subs(w, w_argmax), (w > w_argmax))
+ )
+ u_w_m_x = sp.Piecewise((u_w_c_x, ((w <= w_argmax) & (x <= a_w_pull))),
+ (u_w_mc_x, ((w <= w_argmax) & (x > a_w_pull))),
+ (u_w_mc_x.subs(w, w_argmax), (w > w_argmax))
+ )
+ eps_w_f_x = u_w_f_x.diff(x)
+ sig_w_f_x = E_f * eps_w_f_x
+ eps_w_m_x = u_w_m_x.diff(x)
+ sig_w_m_x = E_m * eps_w_m_x
+ tau_w_x = A_f / p * sig_w_f_x.diff(x)
+ tau_w_x = -A_m / p * sig_w_m_x.diff(x)
#-------------------------------------------------------------------------
# Declaration of the lambdified methods
@@ -97,14 +116,14 @@ class CB_ELF_ELM_Symb(bu.SymbExpr):
symb_model_params = ['E_f', 'A_f', 'E_m', 'A_m', 'tau', 'p', 'L_b']
symb_expressions = [
- ('eps_f_x', ('x','P',)),
- ('eps_m_x', ('x','P',)),
- ('sig_f_x', ('x','P',)),
- ('sig_m_x', ('x','P',)),
- ('tau_x', ('x','P',)),
- ('u_fa_x', ('x','P',)),
- ('u_ma_x', ('x','P',)),
+ ('eps_w_f_x', ('x','w',)),
+ ('eps_w_m_x', ('x','w',)),
+ ('sig_w_f_x', ('x','w',)),
+ ('sig_w_m_x', ('x','w',)),
+ ('tau_w_x', ('x','w',)),
+ ('u_w_f_x', ('x','w',)),
+ ('u_w_m_x', ('x','w',)),
('w_L_b', ('w',)),
- ('aw_pull', ('w',)),
- ('Pw_pull', ('w',)),
+ ('a_w_pull', ('w',)),
+ ('P_w_pull', ('w',)),
]
diff --git a/pull_out/po_symb/PO_ELF_ELM_Symb.py b/pull_out/po_symb/PO_ELF_ELM_Symb.py
index de25c8e5bf64c6f25279425370c70a902e5b061b..a6c7a713067dad2bee566458085a33dada3d8a73 100644
--- a/pull_out/po_symb/PO_ELF_ELM_Symb.py
+++ b/pull_out/po_symb/PO_ELF_ELM_Symb.py
@@ -42,30 +42,32 @@ class PO_ELF_ELM_Symb(bu.SymbExpr):
u_f_x = u_f.subs(var_subs)
u_m_x = u_m.subs(var_subs)
- u_fa_x = sp.Piecewise((u_f_x.subs(x, var_subs[a]), x <= var_subs[a]),
+ u_P_f_x = sp.Piecewise((u_f_x.subs(x, var_subs[a]), x <= var_subs[a]),
(u_f_x, x > var_subs[a]))
- u_ma_x = sp.Piecewise((u_m_x.subs(x, var_subs[a]), x <= var_subs[a]),
+ u_P_m_x = sp.Piecewise((u_m_x.subs(x, var_subs[a]), x <= var_subs[a]),
(u_m_x, x > var_subs[a]))
- eps_f_x = sp.diff(u_fa_x, x)
- eps_m_x = sp.diff(u_ma_x, x)
+ eps_P_f_x = sp.diff(u_P_f_x, x)
+ eps_P_m_x = sp.diff(u_P_m_x, x)
- sig_f_x = E_f * eps_f_x
- sig_m_x = E_m * eps_m_x
+ sig_P_f_x = E_f * eps_P_f_x
+ sig_P_m_x = E_m * eps_P_m_x
- tau_x = sig_f_x.diff(x) * A_f / p
+ tau_P_x = sig_P_f_x.diff(x) * A_f / p
- eps_f_0 = P / E_f / A_f
- eps_m_0 = -P / E_m / A_m
- a_subs = sp.solve({P - p * tau * a}, a)
- w_el = sp.Rational(1, 2) * (eps_f_0 - eps_m_0) * a
- Pw_pull_elastic = sp.solve(w_el.subs(a_subs) - w, P)[1]
+ Pw_push, P_w_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)
- Pw_push, Pw_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)
+ w_L_b = u_P_f_x.subs(x, -L_b).subs(P, P_w_pull)
- w_L_b = u_fa_x.subs(x, -L_b).subs(P, Pw_pull)
+ a_w_pull = a_subs[a].subs(P, P_w_pull)
- aw_pull = a_subs[a].subs(P, Pw_pull)
+ eps_w_f_x = eps_P_f_x.subs(P, P_w_pull)
+ eps_w_m_x = eps_P_m_x.subs(P, P_w_pull)
+ sig_w_f_x = sig_P_f_x.subs(P, P_w_pull)
+ sig_w_m_x = sig_P_m_x.subs(P, P_w_pull)
+ u_w_f_x = u_P_f_x.subs(P, P_w_pull)
+ u_w_m_x = u_P_m_x.subs(P, P_w_pull)
+ tau_w_x = tau_P_x.subs(P, P_w_pull)
#-------------------------------------------------------------------------
# Declaration of the lambdified methods
@@ -74,14 +76,14 @@ class PO_ELF_ELM_Symb(bu.SymbExpr):
symb_model_params = ['E_f', 'A_f', 'E_m', 'A_m', 'tau', 'p', 'L_b']
symb_expressions = [
- ('eps_f_x', ('x','P',)),
- ('eps_m_x', ('x','P',)),
- ('sig_f_x', ('x','P',)),
- ('sig_m_x', ('x','P',)),
- ('tau_x', ('x','P',)),
- ('u_fa_x', ('x','P',)),
- ('u_ma_x', ('x','P',)),
+ ('eps_w_f_x', ('x','w',)),
+ ('eps_w_m_x', ('x','w',)),
+ ('sig_w_f_x', ('x','w',)),
+ ('sig_w_m_x', ('x','w',)),
+ ('tau_w_x', ('x','w',)),
+ ('u_w_f_x', ('x','w',)),
+ ('u_w_m_x', ('x','w',)),
('w_L_b', ('w',)),
- ('aw_pull', ('w',)),
- ('Pw_pull', ('w',)),
+ ('a_w_pull', ('w',)),
+ ('P_w_pull', ('w',)),
]
diff --git a/pull_out/po_symb/PO_ELF_RLM_Symb.py b/pull_out/po_symb/PO_ELF_RLM_Symb.py
index ee50dc434be782c03c5a04d359e55e8ba34a6c46..a4167f16a777b4768eb70d077c369f609d38241a 100644
--- a/pull_out/po_symb/PO_ELF_RLM_Symb.py
+++ b/pull_out/po_symb/PO_ELF_RLM_Symb.py
@@ -34,26 +34,35 @@ class PO_ELF_RLM_Symb(bu.SymbExpr):
u_f_x = u_f.subs(var_subs)
- u_fa_x = sp.Piecewise((u_f_x, x > var_subs[a]),
- (0, x <= var_subs[a]))
+ u_P_f_x = sp.Piecewise((u_f_x, x > var_subs[a]),
+ (0, x <= var_subs[a]))
- eps_f_x = sp.diff(u_fa_x,x)
+ eps_P_f_x = sp.diff(u_P_f_x,x)
- sig_f_x = E_f * eps_f_x
+ sig_P_f_x = E_f * eps_P_f_x
- tau_x = sp.simplify(sig_f_x.diff(x) * A_f / p)
+ tau_P_x = sp.simplify(sig_P_f_x.diff(x) * A_f / p)
- u_f_x.subs(x, 0) - w
+ P_w_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)[0]
- Pw_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)[0]
+ w_L_b = u_P_f_x.subs(x, -L_b).subs(P, P_w_pull)
- w_L_b = u_fa_x.subs(x, -L_b).subs(P, Pw_pull)
+ a_w_pull = a_subs[a].subs(P, P_w_pull)
- aw_pull = a_subs[a].subs(P, Pw_pull)
+ sig_w_f_x = sp.Piecewise(
+ (0, (x < a_w_pull)),
+ (P_w_pull / A_f * (x - a_w_pull), True)
+ )
+
+ sig_w_f_x = sig_P_f_x.subs(P,P_w_pull)
+ eps_w_f_x = eps_P_f_x.subs(P,P_w_pull)
+ u_w_f_x = u_P_f_x.subs(P,P_w_pull)
+ tau_w_x = tau_P_x.subs(P,P_w_pull)
+
+ eps_w_m_x = eps_w_f_x * 1e-8
+ sig_w_m_x = sig_w_f_x * 1e-8
+ u_w_m_x = u_w_f_x * 1e-8
- eps_m_x = eps_f_x * 1e-8
- sig_m_x = sig_f_x * 1e-8
- u_ma_x = u_fa_x * 1e-8
#-------------------------------------------------------------------------
# Declaration of the lambdified methods
#-------------------------------------------------------------------------
@@ -61,14 +70,15 @@ class PO_ELF_RLM_Symb(bu.SymbExpr):
symb_model_params = ['E_f', 'A_f', 'tau', 'p', 'L_b']
symb_expressions = [
- ('eps_f_x', ('x','P',)),
- ('eps_m_x', ('x','P',)),
- ('sig_f_x', ('x','P',)),
- ('sig_m_x', ('x','P',)),
- ('tau_x', ('x','P',)),
- ('u_fa_x', ('x','P',)),
- ('u_ma_x', ('x','P',)),
+ ('eps_w_f_x', ('x','w',)),
+ ('eps_w_m_x', ('x','w',)),
+ ('sig_w_f_x', ('x','w',)),
+ ('sig_w_f_x', ('x','w',)),
+ ('sig_w_m_x', ('x','w',)),
+ ('tau_w_x', ('x','w',)),
+ ('u_w_f_x', ('x','w',)),
+ ('u_w_m_x', ('x','w',)),
('w_L_b', ('w',)),
- ('aw_pull', ('w',)),
- ('Pw_pull', ('w',)),
+ ('a_w_pull', ('w',)),
+ ('P_w_pull', ('w',)),
]
diff --git a/pull_out/po_symb/PO_ESF_RLM_Symb.py b/pull_out/po_symb/PO_ESF_RLM_Symb.py
index b00ccc1efdc05394dd5903af4e0e73e45c2c4485..b6b4ecb7cd0bda56200f5d53ca982b5dd3ad61ce 100644
--- a/pull_out/po_symb/PO_ESF_RLM_Symb.py
+++ b/pull_out/po_symb/PO_ESF_RLM_Symb.py
@@ -1,6 +1,8 @@
import bmcs_utils.api as bu
import sympy as sp
+import numpy as np
+np.warnings.filterwarnings('ignore', category=np.VisibleDeprecationWarning)
class PO_ESF_RLM_Symb(bu.SymbExpr):
@@ -33,49 +35,64 @@ class PO_ESF_RLM_Symb(bu.SymbExpr):
u_f_x = u_f.subs(var_subs)
- u_fa_x = sp.Piecewise((u_f_x, x > var_subs[a]),
+ u_P_f_x = sp.Piecewise((u_f_x, x > var_subs[a]),
(0, x <= var_subs[a]))
- eps_f_x = sp.diff(u_fa_x,x)
+ eps_P_f_x = sp.diff(u_P_f_x,x)
- sig_f_x = E_f * eps_f_x
+ sig_P_f_x = E_f * eps_P_f_x
- tau_x = sp.simplify(sig_f_x.diff(x) * A_f / p)
+ tau_P_x = sp.simplify(sig_P_f_x.diff(x) * A_f / p)
- u_f_x.subs(x, 0) - w
+ P_w_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)[0]
- Pw_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)[0]
+ w_L_b = u_P_f_x.subs(x, -L_b).subs(P, P_w_pull)
- w_L_b = u_fa_x.subs(x, -L_b).subs(P, Pw_pull)
-
- aw_pull = a_subs[a].subs(P, Pw_pull)
-
- eps_m_x = eps_f_x * 1e-8
- sig_m_x = sig_f_x * 1e-8
- u_ma_x = u_fa_x * 1e-8
+ a_w_pull = a_subs[a].subs(P, P_w_pull)
P_max = p * tau * L_b
- w_argmax = sp.solve(P_max - Pw_pull, w)[0]
- Pw_up_pull = Pw_pull
+ w_argmax = sp.solve(P_max - P_w_pull, w)[0]
+ P_w_up_pull = P_w_pull
b, P_down = sp.symbols(r'b, P_\mathrm{down}')
sig_down = P_down / A_f
eps_down = 1 / E_f * sig_down
w_down = (L_b + b) - sp.Rational(1, 2) * eps_down * b
- Pw_down_pull, Pw_down_push = sp.solve(
+ P_w_down_pull, P_w_down_push = sp.solve(
w_down.subs(b, -P_down / p / tau) - w,
P_down
)
- Pw_short = sp.Piecewise((0, w <= 0),
- (Pw_up_pull, w <= w_argmax),
- (Pw_down_pull, w <= L_b),
+
+ P_w_short = sp.Piecewise((0, w <= 0),
+ (P_w_up_pull, w <= w_argmax),
+ (P_w_down_pull, w < L_b),
(0, True)
- )
- w_L_b_a = L_b - Pw_down_pull / p / tau
+ )
+
+ w_L_b_a = L_b - P_w_down_pull / p / tau
w_L_b = sp.Piecewise((0, w <= w_argmax),
(w_L_b_a, (w > w_argmax) & (w <= L_b)),
(w, True))
- aw_pull = - (Pw_short / p / tau)
- Pw_pull = Pw_short
+ a_w_pull = - (P_w_short / p / tau)
+ P_w_pull = P_w_short
+
+ a_w_up = -P_w_up_pull / p / tau
+ b_w_down = -P_w_down_pull / p / tau
+
+ u_w_f_up = sp.integrate(-P_w_up_pull / E_f/ A_f / a_w_up * (x - a_w_up),(x, a_w_up, x))
+ u_w_f_do = sp.integrate(-P_w_down_pull / E_f/ A_f / b_w_down * (x - b_w_down),(x, b_w_down, x))
+ u_w_f_x = sp.Piecewise(
+ (0, ((w <= w_argmax) & (x <= a_w_up))),
+ (u_w_f_up, ((w <= w_argmax) & (x > a_w_up))),
+ (0, ((w > w_argmax) & (x <= b_w_down))),
+ (u_w_f_do + w_L_b, ((w > w_argmax) & (x > b_w_down))),
+ )
+ eps_w_f_x = u_w_f_x.diff(x)
+ sig_w_f_x = E_f * eps_w_f_x
+ tau_w_x = sig_w_f_x.diff(x)
+
+ eps_w_m_x = x * 1e-9
+ sig_w_m_x = x * 1e-9
+ u_w_m_x = x * 1e-9 # u_w_f_x * 1e-8
#-------------------------------------------------------------------------
# Declaration of the lambdified methods
@@ -84,15 +101,17 @@ class PO_ESF_RLM_Symb(bu.SymbExpr):
symb_model_params = ['E_f', 'A_f', 'E_m', 'A_m', 'tau', 'p', 'L_b']
symb_expressions = [
- ('eps_f_x', ('x','P',)),
- ('eps_m_x', ('x','P',)),
- ('sig_f_x', ('x','P',)),
- ('sig_m_x', ('x','P',)),
- ('tau_x', ('x','P',)),
- ('u_fa_x', ('x','P',)),
- ('u_ma_x', ('x','P',)),
+ ('u_w_f_x', ('x','w',)),
+ ('u_w_m_x', ('x','w',)),
+ ('eps_w_f_x', ('x','w',)),
+ ('eps_w_m_x', ('x','w',)),
+ ('sig_w_f_x', ('x','w',)),
+ ('sig_w_f_x', ('x','w',)),
+ ('sig_w_m_x', ('x','w',)),
+ ('sig_w_m_x', ('x','w',)),
+ ('tau_w_x', ('x','w',)),
('w_L_b', ('w',)),
- ('aw_pull', ('w',)),
- ('Pw_pull', ('w',)),
+ ('a_w_pull', ('w',)),
+ ('P_w_pull', ('w',)),
]
diff --git a/pull_out/pull_out.py b/pull_out/pull_out.py
index 3e2dc728244547c1425531950a57ad0bd7d39df1..8beec3205c4d9494de825498f8ed72b9ebb5fb99 100644
--- a/pull_out/pull_out.py
+++ b/pull_out/pull_out.py
@@ -51,12 +51,12 @@ class PullOutAModel(bu.Model, bu.InjectSymbExpr):
def plot_Pw(self, ax):
w = self.t * self.w_max
- P = 0.001*self.symb.get_Pw_pull(w)
+ P = 0.001*self.symb.get_P_w_pull(w)
w_L_b = self.symb.get_w_L_b(w)
ax.plot(w,P,marker='o', color='blue')
ax.plot(w_L_b,P,marker='o', color='blue')
- P_range = self.symb.get_Pw_pull(self.w_range)
+ P_range = self.symb.get_P_w_pull(self.w_range)
w_L_b_range = self.symb.get_w_L_b(self.w_range)
ax.plot(self.w_range, P_range * 0.001, color='blue', label=r'$w(0)$')
ax.plot(w_L_b_range, P_range * 0.001, color='blue', linestyle='dashed',
@@ -78,74 +78,76 @@ class PullOutAModel(bu.Model, bu.InjectSymbExpr):
L_b = self.L_b
x_range = np.linspace(-L_b, 0, 100)
w_max = self.w_max
+ w_range = self.w_range
+ P_range = self.symb.get_P_w_pull(self.w_range)
+ w_argmax = w_range[np.argmax(P_range)]
w = self.t * w_max
- P = self.symb.get_Pw_pull(w)
- eps_f_range = self.symb.get_eps_f_x(x_range, P)
- sig_f_range = self.symb.get_sig_f_x(x_range, P)
+ eps_f_range = self.symb.get_eps_w_f_x(x_range, w)
+ sig_f_range = self.symb.get_sig_w_f_x(x_range, w)
N_f_range = self.A_f * sig_f_range
- u_f_range = self.symb.get_u_fa_x(x_range, P)
- eps_m_range = self.symb.get_eps_m_x(x_range, P)
- sig_m_range = self.symb.get_sig_m_x(x_range, P)
+ u_f_range = self.symb.get_u_w_f_x(x_range, w)
+ eps_m_range = self.symb.get_eps_w_m_x(x_range, w)
+ sig_m_range = self.symb.get_sig_w_m_x(x_range, w)
N_m_range = self.A_m * sig_m_range
- u_m_range = self.symb.get_u_ma_x(x_range, P)
- tau_range = self.symb.get_tau_x(x_range, P)
+ u_m_range = self.symb.get_u_w_m_x(x_range, w)
+ tau_range = self.symb.get_tau_w_x(x_range, w) * np.ones_like(x_range)
T_range = self.p * tau_range
- P_max = self.symb.get_Pw_pull(w_max)
- eps_max = np.max(self.symb.get_eps_f_x(x_range, P_max))
- sig_max = np.max(self.symb.get_sig_f_x(x_range, P_max))
+ eps_max = np.max(self.symb.get_eps_w_f_x(x_range, w_argmax))
+ sig_max = np.max(self.symb.get_sig_w_f_x(x_range, w_argmax))
N_max = self.A_f * sig_max
- u_max = np.max(self.symb.get_u_fa_x(x_range, P_max))
- eps_min = np.min(self.symb.get_eps_m_x(x_range, P_max))
- sig_min = np.min(self.symb.get_sig_m_x(x_range, P_max))
+ u_max = w_max
+ eps_min = np.min(self.symb.get_eps_w_m_x(x_range, w_argmax))
+ sig_min = np.min(self.symb.get_sig_w_m_x(x_range, w_argmax))
N_min = self.A_m * sig_min
- u_min = np.min(self.symb.get_u_ma_x(x_range, P_max))
- tau_max = self.symb.get_tau_x(0, P_max)
+ u_min = np.min(self.symb.get_u_w_m_x(x_range, w_argmax))
+ tau_max = self.tau
T_max = self.p * tau_max
x_min = -L_b
x_max = 0
+
self.plot_filled_var(
ax_u, x_range, u_f_range,
color='brown', alpha=0.2,
- ylim=(u_min, u_max), xlim=(x_min,0)
+ ylim=(u_min, u_max), xlim=(x_min,x_max)
)
self.plot_filled_var(
ax_u, x_range, u_m_range,
xlabel='$x$ [mm]', ylabel='$u$ [mm]',
color='black', alpha=0.2,
- ylim=(u_min, u_max), xlim=(x_min,0)
+ ylim=(u_min, u_max), xlim=(x_min,x_max)
)
self.plot_filled_var(
ax_eps, x_range, eps_f_range,
xlabel='$x$ [mm]', ylabel=r'$\varepsilon$ [mm]', color='green',
- ylim=(eps_min, eps_max), xlim=(x_min,0)
+ ylim=(eps_min, eps_max), xlim=(x_min,x_max)
)
self.plot_filled_var(
ax_eps, x_range, eps_m_range,
xlabel='$x$ [mm]', ylabel=r'$\varepsilon$ [mm]', color='green',
- ylim=(eps_min, eps_max), xlim=(x_min,0)
+ ylim=(eps_min, eps_max), xlim=(x_min,x_max)
)
self.plot_filled_var(
ax_sig, x_range, N_f_range,
xlabel='$x$ [mm]', ylabel=r'$N$ [N]', color='blue',
- ylim=(sig_min, sig_max), xlim=(x_min,0)
+ ylim=(sig_min, sig_max), xlim=(x_min,x_max)
)
self.plot_filled_var(
ax_sig, x_range, N_m_range,
xlabel='$x$ [mm]', ylabel=r'$N$ [N]', color='blue',
- ylim=(N_min, N_max), xlim=(x_min,0)
+ ylim=(N_min, N_max), xlim=(x_min,x_max)
)
self.plot_filled_var(
ax_tau, x_range, T_range,
xlabel='$x$ [mm]', ylabel=r'$T$ [N/mm]', color='red',
- ylim=(0, T_max), xlim=(x_min,0)
+ ylim=(0, T_max), xlim=(x_min,x_max)
)
def update_plot(self, axes):
@@ -168,7 +170,7 @@ class PullOutAModel(bu.Model, bu.InjectSymbExpr):
x_min, x_max = xlim
dx = x_max - x_min
ax.set_xlim(x_min-0.05*dx, x_max+0.05*dx)
- ax.fill_between(xdata, ydata, color=color, alpha=alpha);
+ ax.fill_between(xdata, ydata, 0, color=color, alpha=alpha);
return line
class PO_ELF_RLM(PullOutAModel):
diff --git a/tension/fragmentation.ipynb b/tension/fragmentation.ipynb
deleted file mode 100644
index 8dbab71db0bcc833bb03d9e0777551c537c18c64..0000000000000000000000000000000000000000
--- a/tension/fragmentation.ipynb
+++ /dev/null
@@ -1,79 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": 2,
- "id": "prime-protocol",
- "metadata": {},
- "outputs": [],
- "source": [
- "%matplotlib widget\n",
- "from pmcm.api import PMCM"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "id": "union-agriculture",
- "metadata": {},
- "outputs": [],
- "source": [
- "pmcm = PMCM()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "id": "fallen-frederick",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "834752290e104f5586ad7392a14c56ae",
- "version_major": 2,
- "version_minor": 0
- },
- "text/plain": [
- "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "pmcm.interact()"
- ]
- },
- {
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