diff --git a/index.ipynb b/index.ipynb
index cd1f98304395c1118e9b11acfc335a2e18e2ac2f..aa7f9ff0aead933b6d4be95c7057a81598c456c0 100644
--- a/index.ipynb
+++ b/index.ipynb
@@ -155,18 +155,17 @@
"\n",
"## 2 Constant bond-slip law\n",
"\n",
- "### Material\n",
+ "### Material and cross-section\n",
"\n",
"- 2.1 [Pull-out of long fiber from rigid matrix](bmcs_course/2_1_PO_LF_LM_RG.ipynb)\n",
"\n",
- "### Cross-section\n",
+ "### \n",
"\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]\n",
- "- 2.5 [Comparison of several models](bmcs_course/2_4_PO_comparison.ipynb)\n",
+ "- 2.4 [Crack-bridge behavior]\n",
"\n",
- "### Structure \n",
+ "### Cross section and structure \n",
"\n",
"- 2.6 [Anchorage]\n",
"- 2.7 [Multiple cracking]\n",
@@ -289,7 +288,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.1"
+ "version": "3.9.2"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/2_3_PO_ESF_RM.ipynb b/pull_out/2_3_PO_ESF_RM.ipynb
index a1bc548e6f914ffdbe2f32203502ec65879aee43..ca203161f3a08feb7a2d5329ad133a4356aacdbf 100644
--- a/pull_out/2_3_PO_ESF_RM.ipynb
+++ b/pull_out/2_3_PO_ESF_RM.ipynb
@@ -789,7 +789,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.1"
+ "version": "3.9.2"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/2_4_PO_comparison.ipynb b/pull_out/2_4_PO_comparison.ipynb
index 872a12a44e68630c2858341a2842749f77088472..37a3e4ca842732bd45038a01dfef8b016bd6a147 100644
--- a/pull_out/2_4_PO_comparison.ipynb
+++ b/pull_out/2_4_PO_comparison.ipynb
@@ -1702,7 +1702,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.1"
+ "version": "3.9.2"
},
"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 b617bead468b565e508b8fc58ad931c522ee4a48..ca0ced3f38a3fb28ef58122bf07d96a3a4d871f8 100644
--- a/pull_out/2_6_CB_ELF_ELM.ipynb
+++ b/pull_out/2_6_CB_ELF_ELM.ipynb
@@ -69,6 +69,41 @@
""
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "from pull_out import PullOutAModel\n",
+ "from CB_ELF_ELM_Symb import CB_ELF_ELM_Symb "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "68441b5858714d1ba0579def78d6059d",
+ "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": [
+ "PullOutAModel(name='Crack bridge', symb_class=CB_ELF_ELM_Symb).interact()"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {
@@ -114,7 +149,7 @@
}
},
"source": [
- "**Assumption 2:** Symmetry of the fields at the midpoint between two cracks."
+ "**Assumption 3:** Symmetry of the fields at the midpoint between two cracks."
]
},
{
@@ -237,7 +272,7 @@
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -245,7 +280,6 @@
},
"outputs": [],
"source": [
- "%matplotlib widget\n",
"import sympy as sp # symbolic algebra package\n",
"import numpy as np # numerical package\n",
"import matplotlib.pyplot as plt # plotting package\n",
@@ -260,12 +294,14 @@
}
},
"source": [
- "Here we tell `sympy` to remember these variables for further use. The parameter of the `symbols( str )` is a string that contains comma-separated printable symbol definition. One can use latex commands in this string to introduce e.g. Greek symbols like `\\gamma, \\beta`, etc. The number of symbols in `str` must be equal to the number of variables assigned on the left hand side of the `=` sign"
+ "<span style=\"color:gray\">\n",
+ "Here we tell `sympy` to remember these variables for further use. The parameter of the `symbols( str )` is a string that contains comma-separated printable symbol definition. One can use latex commands in this string to introduce e.g. Greek symbols like `\\gamma, \\beta`, etc. The number of symbols in `str` must be equal to the number of variables assigned on the left hand side of the `=` sign\n",
+ " <span>"
]
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -323,7 +359,7 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -342,7 +378,7 @@
"⎝A_\\mathrm{f} A_\\mathrm{m} ⎠"
]
},
- "execution_count": 3,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@@ -493,7 +529,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 51,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -518,7 +554,7 @@
"m{m}⋅E_\\mathrm{m}⎠"
]
},
- "execution_count": 6,
+ "execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
@@ -563,12 +599,12 @@
"\n",
"$\\sigma_\\mathrm{f}(0) = P/A_\\mathrm{f} \\; \\implies \\; P - \\sigma_\\mathrm{f}(0) A_\\mathrm{f} = 0 \\implies C = P / A_\\mathrm{f}$\n",
"\n",
- "$\\sigma_\\mathrm{m}(0) = -P/A_\\mathrm{m} \\; \\implies \\; P + \\sigma_\\mathrm{f}(0) A_\\mathrm{f} = 0 \\implies D = - P / A_\\mathrm{D}$"
+ "$\\sigma_\\mathrm{m}(0) = 0 \\implies D = 0$"
]
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 53,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -587,7 +623,7 @@
"⎝⎩ A_\\mathrm{f}⎭ ⎠"
]
},
- "execution_count": 38,
+ "execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
@@ -608,11 +644,13 @@
}
},
"source": [
- "**`sympy` explanation**: Let us explain the two lines\n",
+ "**`sympy` explanation**: <span style=\"color:gray\"> Let us explain the two lines</span>\n",
"\n",
- "__Line 1__: Defines the equation to solve $P - \\sigma_\\mathrm{f}(x=0) A_\\mathrm{f} = 0$ in curly braces `{}`. The resulting data type is a set. Set is an unordered container. The set was assigned to a variable `eq_C`. \n",
+ "__Line 1__: <span style=\"color:gray\">Defines the equation to solve $P - \\sigma_\\mathrm{f}(x=0) A_\\mathrm{f} = 0$ in curly braces `{}`. The resulting data type is a set. Set is an unordered container. The set was assigned to a variable `eq_C`. \n",
+ "</span>\n",
"\n",
- "__Line 2__: Then we used the `sp.solve` method available in `sympy` package with two parameters. The first parameter is the equation to solve `eq_C` and the second is the variable `C` that we want to resolve. The result is obtained in form of a dictionary defining a key-value pair of the variable and the resolved expression. "
+ "__Line 2__: <span style=\"color:gray\">Then we used the `sp.solve` method available in `sympy` package with two parameters. The first parameter is the equation to solve `eq_C` and the second is the variable `C` that we want to resolve. The result is obtained in form of a dictionary defining a key-value pair of the variable and the resolved expression. \n",
+ " </span>"
]
},
{
@@ -632,40 +670,6 @@
""
]
},
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "__Condition 3__: The displacement of the matrix at the support must be zero, i.e.\n",
- "\n",
- "$u_\\mathrm{m}(0) = 0$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 40,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": "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\n",
- "text/latex": [
- "$\\displaystyle \\left\\{ F : 0\\right\\}$"
- ],
- "text/plain": [
- "{F: 0}"
- ]
- },
- "execution_count": 40,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "F_subs = sp.solve({u_m.subs(x,0) - 0}, F)\n",
- "F_subs"
- ]
- },
{
"cell_type": "markdown",
"metadata": {
@@ -674,12 +678,12 @@
}
},
"source": [
- "__Condition 4__: Let us now require that at the end of unknown debonded length $a < 0$, the slip between the reinforcement and the matrix will be zero, i.e. $u_\\mathrm{f}(a) = u_\\mathrm{m}(a)$."
+ "__Condition 3__: Let us now require that at the end of unknown debonded length $a < 0$, the slip between the reinforcement and the matrix will be zero, i.e. $u_\\mathrm{f}(a) = u_\\mathrm{m}(a)$."
]
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": 55,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -688,31 +692,38 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\left\\{ E : \\frac{- A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} a^{2} p - 2 A_\\mathrm{m} E_\\mathrm{m} P a - A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} a^{2} p}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}}\\right\\}$"
+ "$\\displaystyle \\left\\{ E : \\frac{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m} F - A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} a^{2} p - 2 A_\\mathrm{m} E_\\mathrm{m} P a - A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} a^{2} p}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}}\\right\\}$"
],
"text/plain": [
- "⎧ 2 \n",
- "⎪ - A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅a ⋅p - 2⋅A_\\mathrm{m}⋅E_\\mathrm{m}⋅\n",
+ "⎧ \n",
+ "⎪ 2⋅A_\\mathrm{f}⋅A_\\mathrm{m}⋅E_\\mathrm{f}⋅E_\\mathrm{m}⋅F - A_\\mathrm{f}⋅E_\\\n",
"⎨E: ──────────────────────────────────────────────────────────────────────────\n",
- "⎪ 2⋅A_\\mathrm{f}⋅A_\\mathrm{m}⋅E_\\mathrm{f}\n",
+ "⎪ 2⋅A_\\mathrm{\n",
"⎩ \n",
"\n",
- " 2 ⎫\n",
- "P⋅a - A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\tau}⋅a ⋅p⎪\n",
- "───────────────────────────────────────────────⎬\n",
- "⋅E_\\mathrm{m} ⎪\n",
- " ⎭"
+ " 2 \n",
+ "mathrm{f}⋅\\bar{\\tau}⋅a ⋅p - 2⋅A_\\mathrm{m}⋅E_\\mathrm{m}⋅P⋅a - A_\\mathrm{m}⋅E_\\\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ "f}⋅A_\\mathrm{m}⋅E_\\mathrm{f}⋅E_\\mathrm{m} \n",
+ " \n",
+ "\n",
+ " 2 ⎫\n",
+ "mathrm{m}⋅\\bar{\\tau}⋅a ⋅p⎪\n",
+ "─────────────────────────⎬\n",
+ " ⎪\n",
+ " ⎭"
]
},
- "execution_count": 41,
+ "execution_count": 55,
"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"
]
@@ -725,12 +736,12 @@
}
},
"source": [
- "__Condition 5__: To resolve for $a$ we postulate, that the strains $\\varepsilon_\\mathrm{f}$ and $\\varepsilon_\\mathrm{m}$ are equal if there is no slip between the two components. This means that at the end of the debonded length $\\varepsilon_\\mathrm{f}(a) = \\varepsilon_\\mathrm{m}(a)$:"
+ "__Condition 4__: To resolve for $a$ we postulate, that the strains $\\varepsilon_\\mathrm{f}$ and $\\varepsilon_\\mathrm{m}$ are equal if there is no slip between the two components. This means that at the end of the debonded length $\\varepsilon_\\mathrm{f}(a) = \\varepsilon_\\mathrm{m}(a)$:"
]
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 56,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -751,7 +762,7 @@
"⎩ E_\\mathrm{f} A_\\mathrm{m}⋅E_\\mathrm{m}⎭"
]
},
- "execution_count": 42,
+ "execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
@@ -763,7 +774,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 57,
"metadata": {},
"outputs": [
{
@@ -782,7 +793,7 @@
"au}⋅p⎭"
]
},
- "execution_count": 43,
+ "execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
@@ -812,7 +823,7 @@
},
{
"cell_type": "code",
- "execution_count": 44,
+ "execution_count": 83,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -821,43 +832,43 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\left\\{ C : \\frac{P}{A_\\mathrm{f}}, \\ D : 0, \\ E : \\frac{- A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} a^{2} p - 2 A_\\mathrm{m} E_\\mathrm{m} P a - A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} a^{2} p}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}}, \\ F : 0, \\ a : - \\frac{A_\\mathrm{m} E_\\mathrm{m} P}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p}\\right\\}$"
+ "$\\displaystyle \\left\\{ C : \\frac{P}{A_\\mathrm{f}}, \\ D : 0, \\ E : \\frac{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m} F - A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} a^{2} p - 2 A_\\mathrm{m} E_\\mathrm{m} P a - A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} a^{2} p}{2 A_\\mathrm{f} A_\\mathrm{m} E_\\mathrm{f} E_\\mathrm{m}}, \\ a : - \\frac{A_\\mathrm{m} E_\\mathrm{m} P}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p}\\right\\}$"
],
"text/plain": [
- "⎧ 2 \n",
- "⎪ P - A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅a ⋅p - 2⋅A_\\\n",
+ "⎧ \n",
+ "⎪ P 2⋅A_\\mathrm{f}⋅A_\\mathrm{m}⋅E_\\mathrm{f}⋅E_\\mathrm{\n",
"⎨C: ────────────, D: 0, E: ───────────────────────────────────────────────────\n",
- "⎪ A_\\mathrm{f} 2⋅A_\\mathrm{f}⋅A_\n",
+ "⎪ A_\\mathrm{f} \n",
"⎩ \n",
"\n",
- " 2 \n",
- "mathrm{m}⋅E_\\mathrm{m}⋅P⋅a - A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\tau}⋅a ⋅p \n",
- "──────────────────────────────────────────────────────────────────────, F: 0, \n",
- "\\mathrm{m}⋅E_\\mathrm{f}⋅E_\\mathrm{m} \n",
+ " 2 \n",
+ "m}⋅F - A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅a ⋅p - 2⋅A_\\mathrm{m}⋅E_\\mathrm{m}\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " 2⋅A_\\mathrm{f}⋅A_\\mathrm{m}⋅E_\\mathrm{f}⋅E_\\mathrm{m} \n",
" \n",
"\n",
- " \n",
- " -A_\\mathrm{m}⋅E_\\mathrm{m}⋅P \n",
- "a: ───────────────────────────────────────────────────────────────────────────\n",
- " A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p + A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\ta\n",
+ " 2 \n",
+ "⋅P⋅a - A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\tau}⋅a ⋅p \n",
+ "────────────────────────────────────────────────, a: ─────────────────────────\n",
+ " A_\\mathrm{f}⋅E_\\mathrm{f}\n",
" \n",
"\n",
- " ⎫\n",
- " ⎪\n",
- "────⎬\n",
- "u}⋅p⎪\n",
- " ⎭"
+ " ⎫\n",
+ "-A_\\mathrm{m}⋅E_\\mathrm{m}⋅P ⎪\n",
+ "──────────────────────────────────────────────────────⎬\n",
+ "⋅\\bar{\\tau}⋅p + A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\tau}⋅p⎪\n",
+ " ⎭"
]
},
- "execution_count": 44,
+ "execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "var_subs = {**C_subs,**D_subs,**F_subs,**E_subs,**a_subs}\n",
+ "var_subs = {**C_subs,**D_subs,**E_subs,**a_subs}\n",
"var_subs"
]
},
@@ -874,7 +885,7 @@
},
{
"cell_type": "code",
- "execution_count": 45,
+ "execution_count": 84,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -883,23 +894,33 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\left( \\frac{A_\\mathrm{m} E_\\mathrm{m} P^{2} + \\bar{\\tau} p x \\left(2 P + \\bar{\\tau} p x\\right) \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}, \\ - \\frac{\\bar{\\tau} p x^{2}}{2 A_\\mathrm{m} E_\\mathrm{m}}\\right)$"
+ "$\\displaystyle \\left( \\frac{2 A_\\mathrm{f} E_\\mathrm{f} F \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) + A_\\mathrm{m} E_\\mathrm{m} P^{2} + \\bar{\\tau} p x \\left(2 P + \\bar{\\tau} p x\\right) \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}, \\ F - \\frac{\\bar{\\tau} p x^{2}}{2 A_\\mathrm{m} E_\\mathrm{m}}\\right)$"
],
"text/plain": [
- "⎛ 2 \n",
- "⎜A_\\mathrm{m}⋅E_\\mathrm{m}⋅P + \\bar{\\tau}⋅p⋅x⋅(2⋅P + \\bar{\\tau}⋅p⋅x)⋅(A_\\math\n",
+ "⎛ \n",
+ "⎜2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅F⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\ma\n",
"⎜─────────────────────────────────────────────────────────────────────────────\n",
- "⎝ 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathr\n",
+ "⎝ 2⋅A_\\mathrm{\n",
+ "\n",
+ " 2 \n",
+ "thrm{m}⋅E_\\mathrm{m}) + A_\\mathrm{m}⋅E_\\mathrm{m}⋅P + \\bar{\\tau}⋅p⋅x⋅(2⋅P + \\\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ "f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\math\n",
+ "\n",
+ " \n",
+ "bar{\\tau}⋅p⋅x)⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) \n",
+ "──────────────────────────────────────────────────────────────────────, F - ──\n",
+ "rm{m}) 2⋅\n",
"\n",
- " 2 ⎞\n",
- "rm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) -\\bar{\\tau}⋅p⋅x ⎟\n",
- "───────────────────────────────────────────────, ───────────────────────────⎟\n",
- "m{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) 2⋅A_\\mathrm{m}⋅E_\\mathrm{m}⎠"
+ " 2 ⎞\n",
+ " \\bar{\\tau}⋅p⋅x ⎟\n",
+ "─────────────────────────⎟\n",
+ "A_\\mathrm{m}⋅E_\\mathrm{m}⎠"
]
},
- "execution_count": 45,
+ "execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
@@ -910,9 +931,18 @@
"u_f_x, u_m_x"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "__Condition 5__: The displacement at the end of debonded length $a$ must be continuous, i.e.\n",
+ "\n",
+ "$u_\\mathrm{m}(a) = u_\\mathrm{c}(a)$"
+ ]
+ },
{
"cell_type": "code",
- "execution_count": 46,
+ "execution_count": 85,
"metadata": {},
"outputs": [],
"source": [
@@ -921,7 +951,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 86,
"metadata": {},
"outputs": [],
"source": [
@@ -930,7 +960,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 87,
"metadata": {},
"outputs": [],
"source": [
@@ -939,7 +969,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 88,
"metadata": {},
"outputs": [
{
@@ -954,7 +984,7 @@
" A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}"
]
},
- "execution_count": 17,
+ "execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
@@ -966,7 +996,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 89,
"metadata": {},
"outputs": [],
"source": [
@@ -975,7 +1005,7 @@
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 90,
"metadata": {},
"outputs": [
{
@@ -990,7 +1020,7 @@
"A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}"
]
},
- "execution_count": 47,
+ "execution_count": 90,
"metadata": {},
"output_type": "execute_result"
}
@@ -1002,7 +1032,7 @@
},
{
"cell_type": "code",
- "execution_count": 48,
+ "execution_count": 91,
"metadata": {},
"outputs": [
{
@@ -1023,7 +1053,7 @@
"athrm{m}) "
]
},
- "execution_count": 48,
+ "execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
@@ -1035,7 +1065,7 @@
},
{
"cell_type": "code",
- "execution_count": 49,
+ "execution_count": 97,
"metadata": {},
"outputs": [
{
@@ -1056,26 +1086,64 @@
"\\mathrm{m}) "
]
},
- "execution_count": 49,
+ "execution_count": 97,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "H = sp.symbols('H')\n",
- "u_mh_x = u_m_x + H\n",
- "H_shift = sp.simplify( sp.solve( u_mh_x.subs(x, a_subs[a]) - u_c_a, H)[0] )\n",
- "H_shift"
+ "F_sol = sp.simplify( sp.solve( u_m_x.subs(x, a_subs[a]) - u_c_a, F)[0] )\n",
+ "F_sol"
]
},
{
"cell_type": "code",
- "execution_count": 50,
+ "execution_count": 98,
"metadata": {},
"outputs": [],
"source": [
- "u_mc_x = u_m_x + H_shift\n",
- "u_fc_x = u_f_x + H_shift"
+ "u_mc_x = u_m_x.subs(F, F_sol)\n",
+ "u_fc_x = u_f_x.subs(F, F_sol)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 99,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp0AAAA5CAYAAAB0x5DvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAakUlEQVR4Ae2d7bXdtBKGnaxTACQVXOggJBUAHeSjgoQOLotf8I9FOgAqyIUOQirgowPoIOF0kPs+OpIje8uWZMve++w9WstHsjSaGb2ascayvc+d9+/fd5YMAUPAEDAEDAFDwBAwBAyBpQh89913H6nvN77/Jz5/rvrrwPMqFCw3BAwBQ8AQMAQMAUPAEDAEFiLwgwLMr0JflX9U+U8dn4a6u6FguSFgCBgChoAhYAgYAoaAIbAQgRcKNL+I+v6g8ieqexDqbKczIGG5IWAIGAKGgCEwgYAWzuyjw4muB9UtecXMt+Iby7CyITCDALucf8y0dxZ0zqFjbYaAIWAIGAKGwA0C2UeHFUC15BWL3YpvLMPKhkASAd30/DRqIAj9R/V/hXp7vB6QONFckxVexj1RDU2tS0bA7POSZ3967Dm7yLVPcz5qS/bRYYV2LXnFYlfzvaVzE2Ng5Y0QqLEN0fJI/bGOz2J1dg86UVoHL5ZayiAgnP4rkv5diAy5azZ8S1AymhYImH22QPEDjzPzXa7zXL+mUq59qt8x67OPDiuUa8krFruK7xKfRviZ2W6M56ryGeJS5LeMW8DxPudnKvdfrgPmMR6v/yK5VYEUipYmDZAL3Zc6Hvo+vF8QD5r3cgDkno4/RA/t6hTJDS/R/iamQS4ynTzlX48nISVcNNwh3Ff+MtU+U2f4jox8BqsmTZoj7Olrzwy7e8e56vtHCr7NZarHRh/pYI5J0P2j47Xaxo8naD+5JD2PZp8ev919fIdJOBvf1Rz9puOBDnbeDmw6174D1tUiEuM4eHRYyrQlr1jmGr7qu9SnUWGV7Ur2UdbtGLuNyqtwKdFpT+wka9av0Vc0bj1U7mIrf049a1x3Z8/f6ZRQjJpJQIE75Fsl8ecHSP9SPtjaDfJU74xceZOgM+I7KVeyXovuoY7/qBwC0tC1z9VGkPpGeVL3nnBUEL3hW4DvCLZVp8IcB/tReW9HKnOHF+yLm49kEh22wvsu/c9JJAlPrFL6noR9evx29/EtpkNjOUvf1bh4qvW58uT1Lte+BdYteEpvNk5Yyw52cmr5t+QVy67hK9pFPo089W1mu+I1uX56WeG62l9v4zGfUrklLiXj2hM7yUr6terdeih9wyYMqnNz1m+27b3TiaH8quMxyulwka/OmybxjXcbp3hz9910sZfcsIP7akIov1mFbi90zO1gErRAW5sM3zJ8a3Gdo2eucKo+yQ5wMOaYRenjviEqRLaCP6xOXt7Uhfid2gc6rhR4dPvUeHb3cS+T69bBzt1KPOl+rr7LdezARyK8cu0Rabq4Zl7UFz+t8hv1YWFlTC0Czma8YnQW6LjUpxHbxHb9PMJv8kZdbVus21xLtvDrJrgASC4dAbspvyUY5QZm8Aql9OvXn6vcYFq1SyhGHV98UGyrFC4i7CzOpb/nGhe05RZCLjCk+zfZ5N+n8SRNUkUNhq8DoxTfCLnVReb8b+H/sY54N4cL59zNVbCVnI0WKSjZXIy3CIZS8k/BPo/h41yzml+3ztl3sUsd/+rodzpig8q1x7Qz5cXzgnzxLfYb0XONYSzO/vx5p7x6A8X3bcIrxmYh32qfRqZktVzXj+HTDGOx/dA5lRrjkhIxrtsVO40v6deqT26yxMrejU+2KksRHPWtchzzrZcTAoQtxLoFXfIGd0w6Z2veJZWvVRi0+6Y1WbgQJd/lE+NgGK+mhEgvHlVUXcDUx/C9ATSL7xTuK+qxIR6RY0+pxAUtlZ5RqX6tbTAlq1md9D0V+zyWjzfDEkbC8xJ8l+vZ0xngcu0zXfdr8nPFDg+v0/C+Kk+2eIzIO9xVqSWvWPASvupT7dPI9LJaruvm0/Fk1pWPgd0iv72qG9diau7mwvZqCKj4sGarxMVgsJhLPpMyCAxUNxUcLtULGQO5gZFkoRPtYDEnl8ApySPwSuSGbzm+CfiWV2kun0z0Zr67mbmmfc4OJtimqyWHHQceFU4FuV+Jxu3oKA+2yMdMz3UQ+GCb7MBTHvyvXJ3H6VTskzEM/ETj2sPHYyxalC/Bd5kn7GZqRzHX3gLnJI8avxGD7KPDCt/K8goKiyc+jW+TYp91N66q+1004TWdYr6O282fJT5Nz9a2az4dTUpl8RjYLfLbq8qBVZPLGVgI4keIIehs+j5lUMzL45R3NNxHSyrjtOixiUzx7SSLSSfFY6WeRZyAm7vJJzoPFwedJtND1XI3XZTEz/Ctw7cI1zVEmhNsgXmPX6buWfo543wQNPUElQXxw164oSIAZteFAHQgWzRxgPtM5ywY+McbHd+r7N4xVk5f6lmIUuno9ikdsXnSrj5+I7LdXz+O+HpxltdGIcZrTGHOUgDm2lN9VtcJ/yq/EX320aGUKvKtQl5hjP0PvqsfT+t+1kGgiQ8zBnzWrSuVfNXNpSqfpofkNF13PD9Ym0+DQkU6InaL/PaqYmxLSQm0wi4nPFgcSSzKW6SwWCLXLbTKkcXP0YSL+hZyw0X1keRwEQiJiUH2IAgIjYmcAJnAoTQZvnX4luK6ho6g7VfN+dTHYsFG44AjKU88CGBZZPgYKPTraX079tXfzKjc6YiDzDH9774Cv+DVgL6vzrHX/jUUTxdnm9qndMGPGCdyeFc2hWHAodjHC/nG49yjfCm+y/Vs7nqfa28+F7IH/KrYb0oU8DzX+NaBGPFkhzNeT1g/2cB47onvjdp9dVVW69Mwr7LdAv8zn66asgFxNXaD3stPFvntpkGnDI3FizuXeOcOJyFh6FskF/xJZr/oqjxeWDvVfaQDB26V3MSL59Tj1lI54FOkl2QZvqWoejrmXcU3Omrsrw9ucuLEH1vH3ubsINjo5E4neuq41sFPAnGzlLxhol1tsa2zmM7ZD7oFemi/1xEnh4topvxja/skEGdHCTlTcxTwC+PopG/Ox0v4OhzEizl0MlzFhz/ohKz4Jjq0Mk9zcx7oXC7aS/JdbHdqLsEj1x4wazYvwr/Wb5wOmT9rfSvFnt+Sjn2fn9HD1pyPKy+2uRRzX1fs09BL5hLbzfnfpj7t9W5mPx63QbYQlwGPhSdLsFsoatCtyG8HPXRyNa5oda4JCItXiMJ71mrjt7jm7nx72gWFB+qTWswxOJe8btxBpnZRPFV1xsT3i2B178oOhm8lYJ5cuHGxrvr901JJ4o1N3VN+YPMjHtjopK14PtiwW1iUY1uf6yhJvOfFBT6Z/Pg75e5CJaKxr6A7wW6QneSTq1T/av/3fYLsOflVPl7B1w1L9KmgslM9O0zcRK+6bqh/NTY5vAvbq3Ar5FlCdk9Ec/OZa3cyhNuW8zLrNyWDlH5ujMqb+ZZ4ja8TT6XL+EaxRL0mNNKn2nZ9n5xfV9lmIc/BmNVnM/tZgstAuXUnVditEzXoXeS3gx46uRpXNDzv30NJ8CRCRuE++UnjsSTBKHdv5ByPdDzXgbORWBT5enC8WHaqC85+sOiqLb5bJDjgk38caJVM9Ucuk0460OmmuurvO1E7x870MnwzAO3ZLBsgIPlUeb/zoLK7sVLe257KwUZfzej3pejij36why98X+cPKl9P9EePXocJGqrxI3ZmxnzQb+qDD/ptZZ/4EIsCO6w8TuTR+oEeqgv4lfp4EV/J2zNdjO96ULFf7GYq5dqn+rWsL/WbEplLfWuWt7d9sOpfh1Ed553y69nO842lPg2XWtvN+p8fF7zNpyviHQBbgB32sjrmQbYSvOb82hGN/1yNK1qceyD4im4q4SBuQQ4E6sOdEIsO75SxmxBejIbPLzrHkTvlDJJdy9RHQY5GbZPBn/q7QFa5261QvlamxHWTCyGNlYkAZYDNuL90Rp7hOwbmSOeaDy6sj5SP39tlIRsHTrM2Kh48uoovvsw1NsFNEj5CO0HZwV272rAbfOcv5bkE34GfqB83Y/jmeBwxr63sk0eGyH3h81hmXJ7FD0L1j328lG8sY7OydLs03wXLezr6G68EuLn2RJd2Vd5eSv2mRPBS3xrwll4hQCDQw1fxea4BMZbf6HzOXwc8J06yPk0/yVliuyX+Zz69LN5hWmqxYx5bxDzIXuS3d+nZMmlAXPAJEseLbSzGRceeNq4P5XgxhDZeRHEQBptKLPKd+Mb0PZ3qg9P0j9r7xuECXCMTFs/4I/6x3lQtSejOblYySYbhm0TmOJVhPiSdHTp24PtDdfxMEUFcnCZtVLQEkxz/izpwUWHRCXzIH0btcRHe8YIUt/Vl8WIxe6ADW3JJdZRZvCb/ZeENpfPFre3Ti0pmk/hBrXHM+XiS4V6VHuNLuzYCr3sPcQbnXPtM1yZNRX5TIklzvMa3xiKwZY53ni/rUp+8rYcPl/r6BYXZNQd+ktVi3ZlSzXz6AzK1scca7OJ4pVYuGi/y26sPY11X8k7Bti1OgpGyEzdYwFQHQETZjkY5F2D+gfzgTk3nYYEVidt5eUshlUSLk/+sA6dwi6jq0CNO0DzUQc6dVwy2o6uR6Troj/oQvCKTBZxzdqj4InLNO1+vxGOsP7zR3fBdj69gbJqYc2yAXcJx4mIe5m7ORnsbEjlfvV9HjLDb2D9w9KnAkmAwdUMVsXPF4H/85Ao7p6T7OnisP8XbEenP5vYZBIVcOmH7c/hBCs2sj0N0jOT1vyjfHeGMvR3szEc0ufaIdJNiqd+UCF/jW2P+rFNs3jiesiNuYllf8HHWV4LR/lG7zpempE/DTPybrTuxcp6v+fQNxvH1nvJkvAOGrbATnyq5yB6lRX57NWKy+NQPIGz1JvmIBgdp4SQ9fy/3SV+xY0Gy5y6kizQRT4LiTgf/8cIFLTBSGQMxfBehul0nzUvqNY+BQD93S22UHdTeDsSYd5ufDwT4E9GVysCOsDP4xrxTbAd19NHR6djNPiUL2y8d20DfUzjx+l+U7wbcNfawEXBwow9Nrj3w2TKXDi1ta7FvjccovbD7wRqjui3W0KRPo4/Xobnter4tcR/Dt+n5VriUKH0K2EmHWb+eG8fducYTafvoCHocQ2Y8TB6xDi42cWPj8jHGegyZjWHbjR0f+zi8lLObyk+orL1x4w41GQQUjmpP+yxUaReya0nhOJV0DD+qlckuPfYylXLtU/3i+lOal7W+FY9rz/Kl+jQYn5L91PpXKxuplbvYb++8f8+vFx0/+YWV7XYewfPRBI8SWGRxBh75MUhyzqF5qXbqFqdjyCxVVrq9Fi0Y5B53FrE8xliPIbMIjFtEJAx5dYMbED6w63S+5tUN+nNx+VcHvz26OHhV303tU/rxHutq2/fj7a8rrfiKz25pPAad34pro/RkN4R3nJM7Zbn23QBuJEjjaeJbjdSpZiP9m/o0CnhMmvrfFjyrwVrZYTwGnW/u06n5WCJXfWb9OgfNyQSdOUUvrd0bZf/V/qWN38bbHgHZFDdr3+ggkOWxOgHB3Ad/Ikkns880Llb7AQHZyGwQk2v/wOn0SxpLM9861mjNp4+F/O2Su9ZvLeg84fnW5HJH8Vj5qt2tEx6iqXaLETD7vMWTt7Hqsg0+UOOjuORuda59Y/WM/QQC5tMTwFi1Q6CF31rQacZkCBgChoAhYAgYAoaAIbA5ArfhQ6LNQTABhoAhYAgYAoaAIWAIGALbImBB57b4GndDwBAwBAwBQ8AQMAQMASFw59tvv+WLuzc6aj6Z58vXwe/76fw0PoO3aTUEDAFDwBAwBAwBQ8AQODkE7J3Ok5sSU8gQMAQMAUPAEDAEDIHzQ8Aer5/fnNqIDAFDwBAwBAwBQ8AQODkErk5OI1PIEDAEDAFDwBA4UQT0KhmvovF7tyR+1o70XPXXN0X7awgYAlMIWNA5hYzVGwKGgCFgCBgChwjw37L6f1Os8o8i+VPHp4ekVmMIGAIxAvZ4PUbDyoaAIWAIGAKGwDwCLxRo8j/WQ+JfM3+iOv7TlyVDwBCYQcCCzhlwrMkQMAQMAUPAEBghwC7nH6M6OzUEDIECBCzoLADJSAwBQ+D8ENDOVHgf7/wGZyNajEDOLtT+k474/U2C0H9UN/gZwcUKWEdD4IwRsKDzjCfXhnaeCLAo6uAdMksLERB+/G/wqsehhvs02GeGDf6FfWST6LChxzo+yxIbgSFgCHT2IZEZgSGwEwIszBL1tRf3UPk7zlVfu0Pyi/pVBUxeZlHmF9wvRYyOJB4lxjs7fL3LWO7RJnpob02SvgQJ95W/rFR6Fe5njusqbHLzsCd2kvWbjgc6eHfzpynd1IYP8D7nZyrH/jHVxeoNgYtHwH4c/uJNwADYAwG/QP2ovA/QVGbBYkflS5V/K9FDdARMLPCdyndK+iylEX/+y9hfypO7OKoPuvdjWiprr37SmYD5zdSYpvQQfTPcxeuscG2JzRT+oX5P7CSLpwmfKz8IKFXnbiCVu6/Y/Xmn/J+gq+WGgCFwiIDtdB5iYjWGwBYIEGD2P7OCAC1Q7HK+UJEg8mPqChIB3q86HqsvjwE3WeTEN3ydOxcMswu0+mdiPAZTges7tQ9wK8BojoR54CdualMT3PfENR6gl4u9TO7cxfSV5SbY5GQeATvsJOW3BJy04b/hiQM2Gp5iqGjJEDAEUghY0JlCxeoMgfYIEMT9rUXqYx3xzglBXVEAqX4sgPEiyK7dVikEga8zAv7OtGebNS4CoS2CoZTsp5JXFcQ2xn03XEeDx1aa20tjbEYqH5zuih12qeNfHQSXsc+yAwqWg/eqRVNlVwejswpD4AIQuHsBY7QhGgKngADBJV+4xotXrNdsQKB+7K68Vc7O5lvfkbqtktvplLzBTqfO+w8sVGYsg/atlGnBV/ryiLxqZ1h9WuN+NrhugE1umo+BHfbyNFZM4+bG8c74iGmsbAgYAmkErtLVVmsIGAItEdAC9WSCn3s8p/bcx0TstoSdlBA48SHPVgm9BgGl5LPoD4LmAr2z+okHu7e8ZjAVeH8lGrcTqhy90OORjuc6CAo5v+/Lc/+OkJ2ywZh0nkutcd8N19zAGrS3xian0jGww16wm7124nMYWLshcKsRsKDzVk+fKX+bEfABFEHT7LtgoiOoih9zh6Bz9fuUKfy8PJp4B9B9tKQyASF6NJUp/rwbRyBLUM7X/ASgAzxEEwfkz3ROsINeb3R8r7L7Cl05fakPj2FVHKSHOit+n1P8muLu+aHQ5rgORr3BSWtscioeETteH8EOLBkChkADBK4a8DAWhoAhsAwBAqRftaDmfrrniWjCLieSwm7jVo/XQ9CGXBfwKUfWa+Uh4EWPVUm82LmCJx9GuaRypyMOMkMT9dD/7ivQh9cV+r46J0DoH/97ujgjcCawLU1VuEsXghOwQw7v747ntRrXAp6lY2lNV4VNA+HV2DWQCQvsZSs/a6SisTEEbg8CFnTenrkyTc8IAQUT7LgRNE09dnejVTtBFDtj8Q7dPQ8Fwc0WieCpk8w++FN5HODR/pGOEABX66G+8I9lEFTO8UOHQA/t9yOhDo8ZvcBtjn/PTjyW4M5uNL9CgBynS8/wprAE1xzPgQjpjZ04OYOGG506tcc3L4GEn8WatcNASC7aJdjELJaUl2C3RM64DzdZqbkc09m5IWAIFCBwVUBjJIaAIdAQAS3avL94T3nYvUlyV3sIog7o1MZvPW61A0NAl3r3sQ98vW6MY7yblxxLYeUz0cWvEQy6SaYLGJWHoGqsIzhdB7pB54oTP7ZOeTHuvk+Q7fRMiKzCtZDnQIz6pILKTvV8RMXNy6r5Uv9Ls8niG5XBRNiJIWAIJBGwoDMJi1UaAtsg4Bf/T5X3O0squ+BR+fjR9Q+qSwYR0g5aFsQ+iZaAgEf28IM/OccjHc91PNVBIpjih+rHQVunuhDQHQR/aov1I+DkJ2VWy0QhnwiMelxCZSJHf3Y9x8Edus998PFO7S5oSvCMq2pxJ5hkntj55b1SHq0P9NB5La5ZnrHCO5ZrsVltHwuwWy0zwhNe2I0lQ8AQaICABZ0NQDQWhkAJAlo8CSQeKR98KKM6gq1UkDL4HcCRjGudu2A11IsvO20EP7zbyK6We99ROXx+Ue527pSziLJrmfooyNGo7SAgVZ1L6u8CWeVu10z5Wpmd54nO4fF5EJfKCeAG+qkfQTCYjLGN+xM0DzCLGymLD7xrcefxNHJf+BxW41SLawnPsYxNzxdic2tt0oPJjV18s7UpxsbcEDh3BCzoPPcZtvGdBAJasAl22IXk/zr3j6m9cl+orn/sGWiVz/2XIrf7Aq2O1KIYB2XQxsEc9CymqUQA3IlnTN/TqZ6gjHGkdiSXyoQ/clPjoK1Pks/OE8G7Gz8NqgNbgr7kvyyExifGxK5vMnk+BOdrcE/yVuUaXKd47lbfCJul9rEGu6UyA7b8C9ikLwQCyw0BQ6AcAQs6y7EySkNgDQI8riY4YkdunNyipoWdgIqAjsCu0zk7boNASnUswOwsOhrlBEkEsoMdPp2z6xcS5bfhZJyLFrk/60A/jk516BEnaB7qIGcXLl7MHZ3qkBMS5UmZgSjKCQbHwXjU3BfDuPnZJD5oIfEbnfz/+lzQ+kp043F16seYmuAuPn3yfFfj2jM8QqElNuJVbB+tsKuROQEv9oa/WTIEDIEGCFw14GEsDAFDIIOAFr/Uo+xBL79Ahsewg7ZwIhoemcc/ExSaFudebmrncjHP2o7SoVQ++BD0EqhX7UDRR0en4wHloKPKBEPNcfd8S8cV1DmpfCtscoM8BeykQ7gBO7jByulv7YaAIZBG4G662moNAUPgjBBgJ2/vtJVMdp7WBAF86HOJO1cE1hynkrayj7nx1crk6QH2YskQMAQaIXDn/Xt+ecWSIWAI3HYEtDPDosrjXB7B82U5/z6Sx/ksnDx6ZhEl5xyal2ofPJZXXVXaU6aX9a8U5IfJF+/2qi+vOoBN7nF8ERZerx53deIL71W8t+BZNJjGRONx6PxW2KT0ZJeTX3iY3QFvDJexMwTOHgELOs9+im2AhsDtR0CLP0HyNzr4iIhH4wQEgy/+VVeU1I/gvP+av6iTEV0UArKRpjcmFwWeDdYQmEHAgs4ZcKzJEDAEzhMBBRXsZD1W3v9qwHmO1EZVi4Bsgg/U+Pe0q3ara+UavSFwCQj8H6b0+yinLK9kAAAAAElFTkSuQmCC\n",
+ "text/latex": [
+ "$\\displaystyle - \\frac{A_\\mathrm{m} E_\\mathrm{m} P \\left(A_\\mathrm{m} E_\\mathrm{m} P - 2 L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)\\right) + \\bar{\\tau}^{2} p^{2} x^{2} \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)^{2}}{2 A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)^{2}}$"
+ ],
+ "text/plain": [
+ " ⎛ \n",
+ "-⎝A_\\mathrm{m}⋅E_\\mathrm{m}⋅P⋅(A_\\mathrm{m}⋅E_\\mathrm{m}⋅P - 2⋅L_b⋅\\bar{\\tau}⋅\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " \n",
+ " 2⋅A_\\mathrm{m}⋅E_\\m\n",
+ "\n",
+ " 2 2 2\n",
+ "p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m})) + \\bar{\\tau} ⋅p ⋅x \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " 2\n",
+ "athrm{m}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) \n",
+ "\n",
+ " 2⎞ \n",
+ "⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) ⎠ \n",
+ "───────────────────────────────────────────────────────────\n",
+ " \n",
+ " "
+ ]
+ },
+ "execution_count": 99,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sp.simplify(u_mc_x)"
]
},
{
@@ -1094,7 +1162,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 100,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1114,7 +1182,7 @@
"⎝4 8 2 8 2 ⎠"
]
},
- "execution_count": 23,
+ "execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
@@ -1137,7 +1205,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 101,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1147,20 +1215,20 @@
{
"data": {
"text/plain": [
- "(array([-0.25 , -0.245, -0.23 , -0.205, -0.17 , -0.125, -0.07 , -0.005,\n",
- " 0.07 , 0.155, 0.25 ]),\n",
- " array([-0.5 , -0.405, -0.32 , -0.245, -0.18 , -0.125, -0.08 , -0.045,\n",
- " -0.02 , -0.005, -0. ]))"
+ "(array([0.125, 0.13 , 0.145, 0.17 , 0.205, 0.25 , 0.305, 0.37 , 0.445,\n",
+ " 0.53 , 0.625]),\n",
+ " array([-0.125, -0.03 , 0.055, 0.13 , 0.195, 0.25 , 0.295, 0.33 ,\n",
+ " 0.355, 0.37 , 0.375]))"
]
},
- "execution_count": 35,
+ "execution_count": 101,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "get_u_f_x = sp.lambdify((x, P), u_f_x.subs(data_f))\n",
- "get_u_m_x = sp.lambdify((x, P), u_m_x.subs(data_f))\n",
+ "get_u_f_x = sp.lambdify((x, P), u_fc_x.subs(data_f))\n",
+ "get_u_m_x = sp.lambdify((x, P), u_mc_x.subs(data_f))\n",
"x_range = np.linspace(-1, 0, 11)\n",
"get_u_f_x(x_range, 1), get_u_m_x(x_range, 1)"
]
@@ -1178,7 +1246,7 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 102,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1226,7 +1294,7 @@
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 103,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1236,7 +1304,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "0ba7bad68d044537a830f441e5c403ff",
+ "model_id": "52fd1439850d4e19adfb458951a22723",
"version_major": 2,
"version_minor": 0
},
@@ -1273,7 +1341,7 @@
},
{
"cell_type": "code",
- "execution_count": 220,
+ "execution_count": 114,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1296,7 +1364,7 @@
"au}⋅p⎭"
]
},
- "execution_count": 220,
+ "execution_count": 114,
"metadata": {},
"output_type": "execute_result"
}
@@ -1305,6 +1373,15 @@
"a_subs"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 129,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "P_lin = sp.solve(L_b - a_subs[a], P)[0]"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {
@@ -1313,7 +1390,7 @@
}
},
"source": [
- "so that $a = -1$. The range $x < a$ is beyond our applied model assumptions. We explicitly treated only the range $x \\in (a, 0)$. Thus for nicer postprocessing we have to set $u_f(x) = u_f(a), \\; \\forall x < a$ "
+ "so that $a = -1$. The range $x < a$ is beyond our applied model assumptions. We explicitly treated only the range $x \\in (a, 0)$. Thus for nicer postprocessing we have to set $u_\\mathrm{f}(x) = u_\\mathrm{f}(a), \\; \\forall x < a$ "
]
},
{
@@ -1337,7 +1414,7 @@
},
{
"cell_type": "code",
- "execution_count": 221,
+ "execution_count": 134,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1346,77 +1423,79 @@
"outputs": [],
"source": [
"u_fa_x = sp.Piecewise((u_c_x, x <= var_subs[a]),\n",
- " (u_fc_x, x > var_subs[a]))\n",
+ " (u_fc_x, x > var_subs[a])\n",
+ " )\n",
"u_ma_x = sp.Piecewise((u_c_x, x <= var_subs[a]),\n",
- " (u_mc_x, x > var_subs[a]))\n",
+ " (u_mc_x, x > var_subs[a]),\n",
+ " )\n",
"get_u_fa_x = sp.lambdify((x, P), u_fa_x.subs(data_f))\n",
"get_u_ma_x = sp.lambdify((x, P), u_ma_x.subs(data_f))"
]
},
{
"cell_type": "code",
- "execution_count": 222,
+ "execution_count": 135,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\begin{cases} \\frac{P \\left(L_{b} + x\\right)}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} & \\text{for}\\: x \\leq - \\frac{A_\\mathrm{m} E_\\mathrm{m} P}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p} \\\\- \\frac{P \\left(A_\\mathrm{m} E_\\mathrm{m} P - 2 L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)\\right)}{2 \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)^{2}} + \\frac{A_\\mathrm{m} E_\\mathrm{m} P^{2} + \\bar{\\tau} p x \\left(2 P + \\bar{\\tau} p x\\right) \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)} & \\text{otherwise} \\end{cases}$"
+ "$\\displaystyle \\begin{cases} \\frac{P \\left(L_{b} + x\\right)}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} & \\text{for}\\: x \\leq - \\frac{A_\\mathrm{m} E_\\mathrm{m} P}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p} \\\\\\frac{- \\frac{A_\\mathrm{f} E_\\mathrm{f} P \\left(A_\\mathrm{m} E_\\mathrm{m} P - 2 L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)\\right)}{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} + A_\\mathrm{m} E_\\mathrm{m} P^{2} + \\bar{\\tau} p x \\left(2 P + \\bar{\\tau} p x\\right) \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)} & \\text{otherwise} \\end{cases}$"
],
"text/plain": [
"⎧ \n",
"⎪ \n",
"⎪ \n",
"⎪ \n",
- "⎨ \n",
- "⎪ P⋅(A_\\mathrm{m}⋅E_\\mathrm{m}⋅P - 2⋅L_b⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm\n",
+ "⎨ A_\\mathrm{f}⋅E_\\mathrm{f}⋅P⋅(A_\\mathrm{m}⋅E_\\mathrm{m}⋅P - 2⋅L_b⋅\\bar{\\tau}\n",
"⎪- ───────────────────────────────────────────────────────────────────────────\n",
- "⎪ \n",
- "⎩ 2⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅\n",
- "\n",
- " P⋅(L_b + x) \n",
- " ───────────────────────────────────────────────────── \n",
- " A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
- " \n",
- " 2 \n",
- "{f} + A_\\mathrm{m}⋅E_\\mathrm{m})) A_\\mathrm{m}⋅E_\\mathrm{m}⋅P + \\bar{\\tau}⋅\n",
- "───────────────────────────────── + ──────────────────────────────────────────\n",
- " 2 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\n",
- "E_\\mathrm{m}) \n",
+ "⎪ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\math\n",
+ "⎪─────────────────────────────────────────────────────────────────────────────\n",
+ "⎩ \n",
"\n",
+ " P⋅(L_b + x) \n",
+ " ──────────────────────────────────────────────────\n",
+ " A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm\n",
" \n",
+ "⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m})) \n",
+ "─────────────────────────────────────────────────────────── + A_\\mathrm{m}⋅E_\\\n",
+ "rm{m}⋅E_\\mathrm{m} \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A\n",
+ "\n",
" \n",
+ "─── \n",
+ "{m} \n",
" \n",
+ " 2 \n",
+ "mathrm{m}⋅P + \\bar{\\tau}⋅p⋅x⋅(2⋅P + \\bar{\\tau}⋅p⋅x)⋅(A_\\mathrm{f}⋅E_\\mathrm{f\n",
" \n",
- " \n",
- "p⋅x⋅(2⋅P + \\bar{\\tau}⋅p⋅x)⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm\n",
"──────────────────────────────────────────────────────────────────────────────\n",
- "\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) \n",
- " \n",
+ "_\\mathrm{m}⋅E_\\mathrm{m}) \n",
"\n",
- " -A_\\mathrm{m}⋅E_\\mathrm{m}⋅P \n",
- " for x ≤ ────────────────────────────────────────────────────────────────\n",
- " A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p + A_\\mathrm{m}⋅E_\\mathrm{\n",
+ " -A_\\mathrm{m}\n",
+ " for x ≤ ──────────────────────────────────────\n",
+ " A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p\n",
" \n",
" \n",
- "{m}) \n",
- "──── otherwise \n",
+ "} + A_\\mathrm{m}⋅E_\\mathrm{m}) \n",
" \n",
+ "────────────────────────────── otherwi\n",
" \n",
"\n",
- " \n",
- "───────────────\n",
- "m}⋅\\bar{\\tau}⋅p\n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " "
+ "⋅E_\\mathrm{m}⋅P \n",
+ "─────────────────────────────────────────\n",
+ " + A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\tau}⋅p\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ "se \n",
+ " "
]
},
- "execution_count": 222,
+ "execution_count": 135,
"metadata": {},
"output_type": "execute_result"
}
@@ -1427,7 +1506,7 @@
},
{
"cell_type": "code",
- "execution_count": 223,
+ "execution_count": 136,
"metadata": {},
"outputs": [],
"source": [
@@ -1448,7 +1527,7 @@
},
{
"cell_type": "code",
- "execution_count": 231,
+ "execution_count": 139,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1458,7 +1537,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "fd20845851ab4ccb88ee8b63a23182e0",
+ "model_id": "a491bca2dc074c0d8b84b9f700f65439",
"version_major": 2,
"version_minor": 0
},
@@ -1475,14 +1554,15 @@
"Text(0, 0.5, '$u$ [mm]')"
]
},
- "execution_count": 231,
+ "execution_count": 139,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "u_fa_x_range = get_u_fa_x(x_range, 3)\n",
- "u_ma_x_range = get_u_ma_x(x_range, 3)\n",
+ "P_ = 2\n",
+ "u_fa_x_range = get_u_fa_x(x_range, P_)\n",
+ "u_ma_x_range = get_u_ma_x(x_range, P_)\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",
@@ -1507,7 +1587,7 @@
},
{
"cell_type": "code",
- "execution_count": 232,
+ "execution_count": 140,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1554,7 +1634,7 @@
" ⎠"
]
},
- "execution_count": 232,
+ "execution_count": 140,
"metadata": {},
"output_type": "execute_result"
}
@@ -1582,7 +1662,7 @@
},
{
"cell_type": "code",
- "execution_count": 233,
+ "execution_count": 141,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1657,7 +1737,7 @@
" ⎠"
]
},
- "execution_count": 233,
+ "execution_count": 141,
"metadata": {},
"output_type": "execute_result"
}
@@ -1684,7 +1764,7 @@
},
{
"cell_type": "code",
- "execution_count": 234,
+ "execution_count": 142,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1711,7 +1791,7 @@
" "
]
},
- "execution_count": 234,
+ "execution_count": 142,
"metadata": {},
"output_type": "execute_result"
}
@@ -1735,7 +1815,7 @@
},
{
"cell_type": "code",
- "execution_count": 235,
+ "execution_count": 143,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1763,7 +1843,7 @@
},
{
"cell_type": "code",
- "execution_count": 241,
+ "execution_count": 144,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1773,7 +1853,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "b02ba005b65a4707b902101bd0a7af19",
+ "model_id": "cfe3597727614eb89d3da5af9539297a",
"version_major": 2,
"version_minor": 0
},
@@ -1838,7 +1918,7 @@
},
{
"cell_type": "code",
- "execution_count": 242,
+ "execution_count": 145,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -1863,7 +1943,7 @@
" ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} "
]
},
- "execution_count": 242,
+ "execution_count": 145,
"metadata": {},
"output_type": "execute_result"
}
@@ -1897,7 +1977,7 @@
},
{
"cell_type": "code",
- "execution_count": 243,
+ "execution_count": 146,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1906,23 +1986,23 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle - w + \\frac{A_\\mathrm{m} E_\\mathrm{m} P^{2}}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}$"
+ "$\\displaystyle - w + \\frac{2 A_\\mathrm{f} E_\\mathrm{f} F \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) + A_\\mathrm{m} E_\\mathrm{m} P^{2}}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)}$"
],
"text/plain": [
- " 2 \n",
- " A_\\mathrm{m}⋅E_\\mathrm{m}⋅P \n",
+ " \n",
+ " 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅F⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A\n",
"-w + ─────────────────────────────────────────────────────────────────────────\n",
- " 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\\n",
+ " 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E\n",
"\n",
- " \n",
- " \n",
- "───────────────────────\n",
- "mathrm{m}⋅E_\\mathrm{m})"
+ " 2\n",
+ "_\\mathrm{m}⋅E_\\mathrm{m}) + A_\\mathrm{m}⋅E_\\mathrm{m}⋅P \n",
+ "────────────────────────────────────────────────────────\n",
+ "_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) "
]
},
- "execution_count": 243,
+ "execution_count": 146,
"metadata": {},
"output_type": "execute_result"
}
@@ -1944,7 +2024,7 @@
},
{
"cell_type": "code",
- "execution_count": 244,
+ "execution_count": 147,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -1953,23 +2033,23 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\left( - \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}, \\ \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}\\right)$"
+ "$\\displaystyle \\left( \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{- F + w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}, \\ - \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}\\right)$"
],
"text/plain": [
- "⎛ _________________\n",
- "⎜ ______________ ______________ ____________ ╱ w \n",
- "⎜-√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ────────────────\n",
- "⎝ ╲╱ A_\\mathrm{m}⋅E_\\\n",
+ "⎛ __________________\n",
+ "⎜ ______________ ______________ ____________ ╱ -F + w \n",
+ "⎜√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ─────────────────\n",
+ "⎝ ╲╱ A_\\mathrm{m}⋅E_\\m\n",
"\n",
- "__________ \n",
- " _______________________________________________________ ___\n",
- "───────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} , √2⋅╲╱ A_\n",
- "mathrm{m} \n",
+ "_________ \n",
+ " _______________________________________________________ ___\n",
+ "──────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} , -√2⋅╲╱ A_\n",
+ "athrm{m} \n",
"\n",
" ___________________________\n",
- "___________ ______________ ____________ ╱ w \n",
+ "___________ ______________ ____________ ╱ -(F - w) \n",
"\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ───────────────────────── \n",
" ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
"\n",
@@ -1979,7 +2059,7 @@
" ⎠"
]
},
- "execution_count": 244,
+ "execution_count": 147,
"metadata": {},
"output_type": "execute_result"
}
@@ -2002,7 +2082,7 @@
},
{
"cell_type": "code",
- "execution_count": 245,
+ "execution_count": 148,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -2011,15 +2091,16 @@
"outputs": [
{
"data": {
- "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIQAAAAZCAYAAADwvIY6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAE+0lEQVRoBe2a7VHcMBCGD4YCLqQD6CAfFeTSQQgdQAcw+QX/MkkHJB0k6SChgkA6CB2EXAfkeTSSxvY5N3CWfZhhZ4TstbTaV1rtrsRNbm5uJtVycnJyQJlVeY/P9Tl6CPPBGp+14diQmej09PQNz6+pDxNvDDX6PkPPyy66ImOjS/+h+kas+4x31HHMXfqfIe91Vc5WeuHDlOd31M8Tb0T1B3R9ju6/RqTzqqqK9Risx6sKSP2Q8ZVyRPmYeJvpgfor5azyPopHwOgdJtQP3hhKY0XeJ6bukFpnECh4CBg7vL2grrmP2KZzFeUni36BwGuKVl5iEd8hy11zL2iEWHUCnyl7TmDyEC6W1lKc4gQZq7REiyFJQ7jkedZlQPpryDvUP7rIKdU36jM2rK77G3QPXiIZxAHM76UmpiHH3VtLUhlcA5xTDFNdSDnJ83SRU6rv6LCyFq6DG/Stk7AJI8Rgni9k9EB6gd/JAivy3dVT+O7yO1OUZ5i7F94hAhgrVtc+hwxBXDGxWkof5IItkx9c1QoDuxvfr9Cvzy5jxfqbSTG3m2xRXlL6MoYJhhYsz8EatPLpAJka0Yy6GYrkG/6eUvRKOS/i2fFCHkM94d07F43K42oR/MgZDGvEUAqvIUNvPTWHUOi1AwxFDOziGCpWjf//O1l4j+KZ+ifFxa6SfarhSSPwPeyMasOSzz1iVc1SeNP672gQ25QiO0QNb0kmk9/i4tW6wDPjNYwtI9vk3W9D3jUyDUHy+JxABgZ/lJkTZ9rr3t0ZV5Q+qThWlS2MN63/tiFjqYdgYL+fx3ZUt6I9+jnZCwTfc685xYJ7hed1rDvZRWq9MY1tlNEkZaYxzZhzfgFfYxFHMwG94FtvBoHsvrCKvSTevHk0CK1DL9FKgPJ76+K0dljCRJbxfZt64QIMnovmrjf+e536jJIWGFYm8wDv4WsETz0n1OYGLn7Vg+gd5nxryjOZ6oUYqzesKoz8knjT+l8bMgYhALhQu9TZM/DspVKI69S/KIJMO1tPUSO+O8lt3qHaTmNLshJfXs07IEsDbBpIat+pRvZQWNWzBF43kDTXIHSZiSGzOMXJf0ndTCKduOyuHJg2GoW72zwhGIv8SPav7vzEr9b2aYaBNt4+8mtGohB4neaC/hraUFhVuQ1bG68VrwKg7CEMGSZiC7vRViWICVI5E6sfPDd39wxe/k9bZTxPCHoDDSAcLWmn8ZiIajDLyF3vogSiveFCwOoRKPJyglnhawx/+a6HuXOYpM/QWFV9ZbwJN7V6G1LnG/4Yhhcn54kM6qKETON0XoyG8P9OPP3USd2CXrz7e4dXt9GRNsnwxPOHolf5TNEbyavdUfCeib4pr7jz/UTsOyhWFe+Ct9Lf3G4v/ECGh7988GSw4ELtsA5Cl2SoeglDwGA/3GFsvZEerfgGaZvLdWJVH8Z3s/lPuU+bUcEv1AuZf/y2lgrlNE7doeHM0rxogtUbmQMMYgwiWCdWxp6igiFWG8j//tbFGrPvG3niUGHP3M1EsRdd4wQZZoamwbFGgN7Z5NwseAgmwZ2oi9RV3htCn28oo27N00mfOh4wblui2+eYkzVhFZNzm+c3/8gWhdyJ59R3zq6V+kjjmwHW2qjgP7XyBsgGIRw+6CHaztB+fqQHNAOstachE8la7piSygCVj7poj2Rm+I/0sGfAMJFvjRPUf49qEgA2q2CVAAAAAElFTkSuQmCC\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\left( - 2 \\sqrt{w}, \\ 2 \\sqrt{w}\\right)$"
+ "$\\displaystyle \\left( 2 \\sqrt{- F + w}, \\ - 2 \\sqrt{- F + w}\\right)$"
],
"text/plain": [
- "(-2⋅√w, 2⋅√w)"
+ "⎛ ________ ________⎞\n",
+ "⎝2⋅╲╱ -F + w , -2⋅╲╱ -F + w ⎠"
]
},
- "execution_count": 245,
+ "execution_count": 148,
"metadata": {},
"output_type": "execute_result"
}
@@ -2042,28 +2123,28 @@
},
{
"cell_type": "code",
- "execution_count": 246,
+ "execution_count": 149,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}$"
+ "$\\displaystyle - \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}$"
],
"text/plain": [
- " ___________________\n",
- " ______________ ______________ ____________ ╱ w \n",
- "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ──────────────────\n",
- " ╲╱ A_\\mathrm{m}⋅E_\\ma\n",
+ " __________________\n",
+ " ______________ ______________ ____________ ╱ -(F - w) \n",
+ "-√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ─────────────────\n",
+ " ╲╱ A_\\mathrm{m}⋅E_\\m\n",
"\n",
- "________ \n",
- " _______________________________________________________\n",
- "─────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
- "thrm{m} "
+ "_________ \n",
+ " _______________________________________________________\n",
+ "──────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ "athrm{m} "
]
},
- "execution_count": 246,
+ "execution_count": 149,
"metadata": {},
"output_type": "execute_result"
}
@@ -2092,7 +2173,7 @@
},
{
"cell_type": "code",
- "execution_count": 247,
+ "execution_count": 150,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -2101,9 +2182,9 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: L_{b} \\geq \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} A_\\mathrm{m} \\sqrt{E_\\mathrm{f}} E_\\mathrm{m} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p} \\\\- \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\left(\\sqrt{2} \\sqrt{A_\\mathrm{f}} A_\\mathrm{m} \\sqrt{E_\\mathrm{f}} E_\\mathrm{m} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} - 2 L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)\\right)}{2 \\sqrt{\\bar{\\tau}} \\sqrt{p} \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)^{\\frac{3}{2}}} + \\frac{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p w \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) - L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) \\left(2 \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} - L_{b} \\bar{\\tau} p\\right)}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)} & \\text{otherwise} \\end{cases}$"
+ "$\\displaystyle \\begin{cases} 0 & \\text{for}\\: L_{b} \\geq - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} A_\\mathrm{m} \\sqrt{E_\\mathrm{f}} E_\\mathrm{m} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}{A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p + A_\\mathrm{m} E_\\mathrm{m} \\bar{\\tau} p} \\\\\\frac{\\frac{\\sqrt{2} A_\\mathrm{f}^{\\frac{3}{2}} E_\\mathrm{f}^{\\frac{3}{2}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\left(- \\sqrt{2} \\sqrt{A_\\mathrm{f}} A_\\mathrm{m} \\sqrt{E_\\mathrm{f}} E_\\mathrm{m} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} - 2 L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)\\right)}{\\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}} - 2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(F - w\\right) \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) - L_{b} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right) \\left(- 2 \\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\bar{\\tau}} \\sqrt{p} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}} - L_{b} \\bar{\\tau} p\\right)}{2 A_\\mathrm{f} E_\\mathrm{f} \\bar{\\tau} p \\left(A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}\\right)} & \\text{otherwise} \\end{cases}$"
],
"text/plain": [
"⎧ \n",
@@ -2113,13 +2194,15 @@
"⎪ \n",
"⎪ \n",
"⎪ \n",
- "⎨ ___________________________ ⎛ \n",
- "⎪ ______________ ______________ ╱ w ⎜ \n",
- "⎪ √2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅ ╱ ───────────────────────── ⋅⎜√2⋅╲╱\n",
- "⎪ ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} ⎝ \n",
- "⎪- ───────────────────────────────────────────────────────────────────────────\n",
+ "⎪ ____________________\n",
+ "⎨ 3/2 3/2 ____________ ╱ -(F - w) \n",
+ "⎪√2⋅A_\\mathrm{f} ⋅E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ───────────────────\n",
+ "⎪ ╲╱ A_\\mathrm{m}⋅E_\\mat\n",
+ "⎪─────────────────────────────────────────────────────────────────────────────\n",
"⎪ \n",
"⎪ \n",
+ "⎪─────────────────────────────────────────────────────────────────────────────\n",
+ "⎪ \n",
"⎩ \n",
"\n",
" \n",
@@ -2129,13 +2212,15 @@
" \n",
" \n",
" \n",
- " \n",
- "______________ ______________ ____________ \n",
- " A_\\mathrm{f} ⋅A_\\mathrm{m}⋅╲╱ E_\\mathrm{f} ⋅E_\\mathrm{m}⋅╲╱ \\bar{\\tau} ⋅√p⋅ \n",
- " ╲╱\n",
+ "_______ ⎛ \n",
+ " ⎜ ______________ ______________ __\n",
+ "────── ⋅⎜- √2⋅╲╱ A_\\mathrm{f} ⋅A_\\mathrm{m}⋅╲╱ E_\\mathrm{f} ⋅E_\\mathrm{m}⋅╲╱ \\\n",
+ "hrm{m} ⎝ \n",
"──────────────────────────────────────────────────────────────────────────────\n",
- " ____________ \n",
- " 2⋅╲╱ \\bar{\\tau} ⋅√p⋅(A_\\mathrm{f}\n",
+ " ______________\n",
+ " ╲╱ A_\\mathrm{f}⋅\n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " \n",
" \n",
"\n",
" \n",
@@ -2145,13 +2230,15 @@
" \n",
" \n",
" \n",
- " ___________________________ \n",
- " ╱ w ______________________________________________\n",
- "╱ ───────────────────────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\m\n",
- " A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ " ___________________________ \n",
+ "__________ ╱ -(F - w) ______________________________\n",
+ "bar{\\tau} ⋅√p⋅ ╱ ───────────────────────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A\n",
+ " ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
"──────────────────────────────────────────────────────────────────────────────\n",
- " 3/2 \n",
- "⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) \n",
+ "_________________________________________ \n",
+ "E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " \n",
" \n",
"\n",
" \n",
@@ -2162,28 +2249,32 @@
" \n",
" \n",
" \n",
- "_________ \n",
- "athrm{m} - 2⋅L_b⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\ma\n",
+ "_________________________ \n",
+ "_\\mathrm{m}⋅E_\\mathrm{m} - 2⋅L_b⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\n",
" \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " 2⋅A_\\mathrm{f}⋅\n",
" \n",
"\n",
" \n",
" \n",
" \n",
" \n",
- " 0 \n",
+ " 0 \n",
" \n",
" \n",
- " ⎞ \n",
- " ⎟ \n",
- "thrm{m})⎟ 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅w⋅(A_\\mathrm{f}⋅E_\\mathrm\n",
- " ⎠ \n",
- "───────── + ──────────────────────────────────────────────────────────────────\n",
+ " ⎞ \n",
+ " ⎟ \n",
+ "\\mathrm{m}⋅E_\\mathrm{m})⎟ \n",
+ " ⎠ \n",
+ "───────────────────────── - 2⋅A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(F - w)⋅(\n",
" \n",
" \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ "E_\\mathrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{\n",
" \n",
"\n",
" \n",
@@ -2195,11 +2286,13 @@
" \n",
" \n",
" \n",
- "{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) - L_b⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f}\n",
" \n",
- "──────────────────────────────────────────────────────────────────────────────\n",
- " 2⋅A_\\mathrm{f}⋅E_\\mat\n",
" \n",
+ "A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) - L_b⋅\\bar{\\tau}⋅p⋅(A_\\\n",
+ " \n",
+ " \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ "m}) \n",
" \n",
"\n",
" \n",
@@ -2209,12 +2302,14 @@
" \n",
" \n",
" \n",
- " ⎛ \n",
- " ⎜ ______________ ______________ ______\n",
- " + A_\\mathrm{m}⋅E_\\mathrm{m})⋅⎜2⋅√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅╲╱ \\bar{\n",
- " ⎝ \n",
+ " \n",
+ " \n",
+ " ⎛ \n",
+ " ⎜ ______________ \n",
+ "mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m})⋅⎜- 2⋅√2⋅╲╱ A_\\mathrm{f} ⋅╲\n",
+ " ⎝ \n",
+ " \n",
"──────────────────────────────────────────────────────────────────────────────\n",
- "hrm{f}⋅\\bar{\\tau}⋅p⋅(A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m}) \n",
" \n",
" \n",
"\n",
@@ -2225,65 +2320,91 @@
" \n",
" \n",
" \n",
- " ___________________________ \n",
- "______ ╱ w __________________________________\n",
- "\\tau} ⋅√p⋅ ╱ ───────────────────────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\ma\n",
- " ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ " \n",
+ " \n",
+ " ___________________________ \n",
+ " ______________ ____________ ╱ -(F - w) __________\n",
+ "╱ E_\\mathrm{f} ⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ───────────────────────── ⋅╲╱ A_\\mathrm\n",
+ " ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ " \n",
"──────────────────────────────────────────────────────────────────────────────\n",
" \n",
" \n",
+ "\n",
+ " \n",
+ " \n",
+ " -\n",
+ " \n",
+ " for L_b ≥ ─\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " ⎞ \n",
+ "_____________________________________________ ⎟ \n",
+ "{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} - L_b⋅\\bar{\\tau}⋅p⎟ \n",
+ " ⎠ \n",
+ " \n",
+ "───────────────────────────────────────────────────────────────── \n",
+ " \n",
" \n",
"\n",
" \n",
- " ______________ \n",
- " √2⋅╲╱ A_\\mathrm{f} ⋅A_\\ma\n",
+ " ______________ ______________ ____________ \n",
+ "√2⋅╲╱ A_\\mathrm{f} ⋅A_\\mathrm{m}⋅╲╱ E_\\mathrm{f} ⋅E_\\mathrm{m}⋅╲╱ \\bar{\\tau} ⋅\n",
+ " \n",
+ "──────────────────────────────────────────────────────────────────────────────\n",
+ " A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\t\n",
+ " \n",
+ " \n",
+ " \n",
" \n",
- " for L_b ≥ ─────────────────────────\n",
" \n",
" \n",
- " ⎞ \n",
- "_____________________ ⎟ \n",
- "thrm{m}⋅E_\\mathrm{m} - L_b⋅\\bar{\\tau}⋅p⎟ \n",
- " ⎠ \n",
- "───────────────────────────────────────── \n",
" \n",
" \n",
+ " oth\n",
+ " \n",
" \n",
"\n",
- " __________________\n",
- " ______________ ____________ ╱ w \n",
- "thrm{m}⋅╲╱ E_\\mathrm{f} ⋅E_\\mathrm{m}⋅╲╱ \\bar{\\tau} ⋅√p⋅ ╱ ─────────────────\n",
- " ╲╱ A_\\mathrm{m}⋅E_\\m\n",
+ " ___________________________ \n",
+ " ╱ -(F - w) _________________________________________\n",
+ "√p⋅ ╱ ───────────────────────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}\n",
+ " ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
"──────────────────────────────────────────────────────────────────────────────\n",
- " A_\\mathrm{f}⋅E_\\mathrm{f}⋅\\bar{\\tau}⋅p + A_\\mathrm{m}⋅E_\\m\n",
+ "au}⋅p + A_\\mathrm{m}⋅E_\\mathrm{m}⋅\\bar{\\tau}⋅p \n",
+ " \n",
" \n",
" \n",
" \n",
" \n",
" \n",
- " otherwise \n",
" \n",
" \n",
+ "erwise \n",
+ " \n",
" \n",
"\n",
- "_________ \n",
- " _______________________________________________________\n",
- "──────── ⋅╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
- "athrm{m} \n",
- "───────────────────────────────────────────────────────────────────\n",
- "athrm{m}⋅\\bar{\\tau}⋅p \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " \n",
- " "
+ " \n",
+ "______________ \n",
+ "⋅E_\\mathrm{m} \n",
+ " \n",
+ "───────────────\n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " "
]
},
- "execution_count": 247,
+ "execution_count": 150,
"metadata": {},
"output_type": "execute_result"
}
@@ -2306,7 +2427,7 @@
},
{
"cell_type": "code",
- "execution_count": 248,
+ "execution_count": 151,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -2315,29 +2436,29 @@
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
- "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{\\frac{w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}}$"
+ "$\\displaystyle - \\frac{\\sqrt{2} \\sqrt{A_\\mathrm{f}} \\sqrt{E_\\mathrm{f}} \\sqrt{- \\frac{F - w}{A_\\mathrm{m} E_\\mathrm{m}}} \\sqrt{A_\\mathrm{f} E_\\mathrm{f} + A_\\mathrm{m} E_\\mathrm{m}}}{\\sqrt{\\bar{\\tau}} \\sqrt{p}}$"
],
"text/plain": [
- " ___________________________ \n",
- " ______________ ______________ ╱ w _______\n",
- "√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅ ╱ ───────────────────────── ⋅╲╱ A_\\mat\n",
- " ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ " ___________________________ \n",
+ " ______________ ______________ ╱ -(F - w) ______\n",
+ "-√2⋅╲╱ A_\\mathrm{f} ⋅╲╱ E_\\mathrm{f} ⋅ ╱ ───────────────────────── ⋅╲╱ A_\\ma\n",
+ " ╲╱ A_\\mathrm{m}⋅E_\\mathrm{m} \n",
"──────────────────────────────────────────────────────────────────────────────\n",
- " ____________ \n",
- " ╲╱ \\bar{\\tau} ⋅√p \n",
- "\n",
- " \n",
- "________________________________________________\n",
- "hrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
- " \n",
- "────────────────────────────────────────────────\n",
- " \n",
- " "
+ " ____________ \n",
+ " ╲╱ \\bar{\\tau} ⋅√p \n",
+ "\n",
+ " \n",
+ "_________________________________________________ \n",
+ "thrm{f}⋅E_\\mathrm{f} + A_\\mathrm{m}⋅E_\\mathrm{m} \n",
+ " \n",
+ "──────────────────────────────────────────────────\n",
+ " \n",
+ " "
]
},
- "execution_count": 248,
+ "execution_count": 151,
"metadata": {},
"output_type": "execute_result"
}
@@ -2348,1695 +2469,19 @@
]
},
{
- "cell_type": "code",
- "execution_count": 249,
+ "cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
- "outputs": [],
"source": [
- "import traits.api as tr\n",
+ "## Virtual experiments\n",
"\n",
- "class PO_LF_LM_EL(tr.HasTraits):\n",
+ "Exercise the relation between $P$ and $\\tau(x)$ and between $w$ and $\\varepsilon(x)$.\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": 40,
- "metadata": {
- "hide_input": false,
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "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",
- "\n",
- " this.waiting = false;\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",
- "\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\", \"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"
- ],
- "text/plain": [
- "<IPython.core.display.Javascript object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "text/html": [
- "<img src=\"data:image/png;base64,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\" width=\"899.3\">"
- ],
- "text/plain": [
- "<IPython.core.display.HTML object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "5c51964df7934170b3808eb6ab042c7a",
- "version_major": 2,
- "version_minor": 0
- },
- "text/plain": [
- "VBox(children=(HBox(children=(FloatSlider(value=1e-05, description='\\\\(t\\\\)', max=1.0, min=1e-05, step=0.05), …"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "po.interact_fields()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "source": [
- "## Let's learn from the model\n",
- "\n",
- "Exercise the relation between $P$ and $\\tau(x)$ and between $w$ and $\\varepsilon(x)$.\n",
- "\n",
- " 1. Is the originally postulated assumption of rigid matrix relevant for the RILEM test?\n",
- " 4. What is the role of debonded length $a$ in view of general non-linear simulation?\n",
- " 5. When does the pull-out fail?\n",
- " 6. What happens with $a$ upon unloading?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 41,
- "metadata": {
- "slideshow": {
- "slide_type": "slide"
- }
- },
- "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",
- "\n",
- " this.waiting = false;\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",
- "\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\", \"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"
- ],
- "text/plain": [
- "<IPython.core.display.Javascript object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "text/html": [
- "<img src=\"data:image/png;base64,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\" width=\"799.6333333333333\">"
- ],
- "text/plain": [
- "<IPython.core.display.HTML object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "44198f7f12eb47189edc39f04e7241d7",
- "version_major": 2,
- "version_minor": 0
- },
- "text/plain": [
- "VBox(children=(HBox(children=(FloatSlider(value=1e-05, description='\\\\(t\\\\)', max=1.0, min=1e-05, step=0.05), …"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "po.interact_geometry()"
+ " 1. Given a rectangular cross section with area $A = 100$ identify a carbon reinforcement area \n",
+ " that induces 10 mm crack spacing"
]
},
{
@@ -4063,7 +2508,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.1"
+ "version": "3.9.2"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/2_6_CB_SF_M_RG-.ipynb b/pull_out/2_6_CB_SF_M_RG-.ipynb
index 33f8f16c76983bf34831f1a0c0af95e78facb2b9..827816b22b614d2c1334d004c7fac8513d0649c5 100755
--- a/pull_out/2_6_CB_SF_M_RG-.ipynb
+++ b/pull_out/2_6_CB_SF_M_RG-.ipynb
@@ -371,7 +371,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "19e7440236214fe999a8a8ce5a661559",
+ "model_id": "9f439c975c474279aa3e78a26de3015b",
"version_major": 2,
"version_minor": 0
},
@@ -412,7 +412,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -436,7 +436,7 @@
" ╲╱ A_\\mathrm{f}⋅E_\\mathrm{f} "
]
},
- "execution_count": 22,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -526,7 +526,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "8d3fa0dbfc8a486abe92045e7ac205fe",
+ "model_id": "5cdd067c1c7845d29d777c958b901886",
"version_major": 2,
"version_minor": 0
},
@@ -840,7 +840,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.1"
+ "version": "3.9.2"
},
"toc": {
"base_numbering": 1,
diff --git a/pull_out/CB_ELF_ELM_Symb.py b/pull_out/CB_ELF_ELM_Symb.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe497f8de8a4e9f5673dc1899553b5f7a7f0820e
--- /dev/null
+++ b/pull_out/CB_ELF_ELM_Symb.py
@@ -0,0 +1,110 @@
+
+import bmcs_utils.api as bu
+import sympy as sp
+
+
+class CB_ELF_ELM_Symb(bu.SymbExpr):
+
+ E_m, A_m = sp.symbols(r'E_\mathrm{m}, A_\mathrm{m}', nonnegative=True)
+ E_f, A_f = sp.symbols(r'E_\mathrm{f}, A_\mathrm{f}', nonnegative=True)
+ tau, p = sp.symbols(r'\bar{\tau}, p', nonnegative=True)
+ C, D, E, F = sp.symbols('C, D, E, F')
+ P, w = sp.symbols('P, w')
+ x, a, L_b = sp.symbols('x, a, L_b')
+
+ d_sig_f = p * tau / A_f
+ d_sig_m = -p * tau / A_m
+
+ sig_f = sp.integrate(d_sig_f, x) + C
+ sig_m = sp.integrate(d_sig_m, x) + D
+
+ eps_f = sig_f / E_f
+ eps_m = sig_m / E_m
+
+ u_f = sp.integrate(eps_f, x) + E
+ u_m = sp.integrate(eps_m, x) + F
+
+ eq_C = {P - sig_f.subs({x:0}) * A_f}
+ C_subs = sp.solve(eq_C,C)
+ eq_D = {sig_m.subs({x:0}) * A_m}
+ D_subs = sp.solve(eq_D,D)
+
+ eqns_u_equal = {u_f.subs(C_subs).subs(x,a) - u_m.subs(D_subs).subs(x,a)}
+ E_subs = sp.solve(eqns_u_equal,E)
+
+ eqns_eps_equal = {eps_f.subs(C_subs).subs(x,a) - eps_m.subs(D_subs).subs(x,a)}
+
+ a_subs = sp.solve(eqns_eps_equal,a)
+
+ var_subs = {**C_subs,**D_subs,**E_subs,**a_subs}
+
+ u_f_x = sp.simplify( u_f.subs(var_subs) )
+ u_m_x = sp.simplify( u_m.subs(var_subs) )
+
+ A_c = A_m + A_f
+ E_c = (E_m * A_m + E_f * A_f) / (A_c)
+ G = sp.symbols('G')
+ 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]) )
+
+ 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]),
+ )
+ 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
+
+ tau_x = sig_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_ = sp.solve(w_el.subs(a_subs) - w, P)[1]
+
+ w_L_b = u_fa_x.subs(x, -L_b).subs(P, Pw_pull_)
+
+ 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)
+ 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)
+ )
+
+ Pw_pull = Pw_clamped
+
+ #-------------------------------------------------------------------------
+ # Declaration of the lambdified methods
+ #-------------------------------------------------------------------------
+
+ 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',)),
+ ('w_L_b', ('w',)),
+ ('aw_pull', ('w',)),
+ ('Pw_pull', ('w',)),
+ ]
diff --git a/pull_out/pull_out.py b/pull_out/pull_out.py
index 9a1db0ba4b245d4b380fdce937a1cb3abdac2e4d..e1d0b36dd488e0618103d322fb853a1e9afff8a8 100644
--- a/pull_out/pull_out.py
+++ b/pull_out/pull_out.py
@@ -251,102 +251,6 @@ class PO_ESF_RLM_Symb(bu.SymbExpr):
('Pw_pull', ('w',)),
]
-class CB_ELF_RLM_Symb(bu.SymbExpr):
-
- E_m, A_m = sp.symbols(r'E_\mathrm{m}, A_\mathrm{m}', nonnegative=True)
- E_f, A_f = sp.symbols(r'E_\mathrm{f}, A_\mathrm{f}', nonnegative=True)
- tau, p = sp.symbols(r'\bar{\tau}, p', nonnegative=True)
- C, D, E, F = sp.symbols('C, D, E, F')
- P, w = sp.symbols('P, w')
- x, a, L_b = sp.symbols('x, a, L_b')
-
- d_sig_f = p * tau / A_f
- d_sig_m = -p * tau / A_m
-
- sig_f = sp.integrate(d_sig_f, x) + C
- sig_m = sp.integrate(d_sig_m, x) + D
-
- eps_f = sig_f / E_f
- eps_m = sig_m / E_m
-
- u_f = sp.integrate(eps_f, x) + E
- u_m = sp.integrate(eps_m, x) + F
-
- eq_C = {P - sig_f.subs({x: 0}) * A_f}
- C_subs = sp.solve(eq_C, C)
- eq_D = {sig_m.subs({x: 0}) * A_m}
- D_subs = sp.solve(eq_D, D)
-
- F_subs = sp.solve({u_m.subs(x, 0) - 0}, F)
-
- eqns_u_equal = {u_f.subs(C_subs).subs(x, a) - u_m.subs(D_subs).subs(F_subs).subs(x, a)}
- E_subs = sp.solve(eqns_u_equal, E)
-
- eqns_eps_equal = {eps_f.subs(C_subs).subs(x, a) - eps_m.subs(D_subs).subs(x, a)}
- a_subs = sp.solve(eqns_eps_equal, a)
- var_subs = {**C_subs, **D_subs, **F_subs, **E_subs, **a_subs}
-
- 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_f_x, x > var_subs[a]))
- u_ma_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)
-
- sig_f_x = E_f * eps_f_x
- sig_m_x = E_m * eps_m_x
-
- tau_x = sig_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, Pw_pull = sp.solve(u_f_x.subs({x: 0}) - w, P)
-
- P_max = p * tau * L_b
- w_argmax = sp.solve(P_max - Pw_pull, w)[0]
- Pw_pull = Pw_pull
-
- d_Pw_pull_dw = sp.diff(Pw_pull, w)
- 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)
- )
- Pw_clamped
-
- w_L_b = Pw_clamped * 1e-10
- aw_pull = - (Pw_clamped / p / tau)
- Pw_pull = Pw_clamped
-
- #-------------------------------------------------------------------------
- # Declaration of the lambdified methods
- #-------------------------------------------------------------------------
-
- 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',)),
- ('w_L_b', ('w',)),
- ('aw_pull', ('w',)),
- ('Pw_pull', ('w',)),
- ]
-
-
class PullOutAModel(bu.Model, bu.InjectSymbExpr):
"""
General pullout elastic long fiber and rigid long matrix
@@ -403,12 +307,12 @@ class PullOutAModel(bu.Model, bu.InjectSymbExpr):
tau_range = self.symb.get_tau_x(x_range, P)
P_max = self.symb.get_Pw_pull(w_max)
- eps_f_max = self.symb.get_eps_f_x(0, P_max)
- sig_f_max = self.symb.get_sig_f_x(0, P_max)
- u_f_max = self.symb.get_u_fa_x(0, P_max)
- eps_m_max = self.symb.get_eps_m_x(0, P_max)
- sig_m_max = self.symb.get_sig_m_x(0, P_max)
- u_m_max = self.symb.get_u_ma_x(0, P_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))
+ 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_min = np.min(self.symb.get_u_ma_x(x_range, P_max))
tau_max = self.symb.get_tau_x(0, P_max)
ax11.plot(x_range, eps_f_range, color='blue')
@@ -417,7 +321,7 @@ class PullOutAModel(bu.Model, bu.InjectSymbExpr):
ax11.fill_between(x_range, eps_m_range, 0, color='blue', alpha=0.3)
ax11.set_xlabel(r'$x$ [mm]')
ax11.set_ylabel(r'$\varepsilon$ [-]')
- ax11.set_ylim(ymin=eps_m_max,ymax=eps_f_max)
+ ax11.set_ylim(ymin=eps_min,ymax=eps_max)
ax21.plot(x_range, sig_f_range, color='green')
ax21.plot(x_range, sig_m_range, color='green', linestyle='dashed')
@@ -425,15 +329,16 @@ class PullOutAModel(bu.Model, bu.InjectSymbExpr):
ax21.fill_between(x_range, sig_m_range, 0, alpha=0.3, color='green')
ax21.set_xlabel(r'$x$ [mm]')
ax21.set_ylabel(r'$\sigma$ [MPa]')
- ax21.set_ylim(ymin=sig_m_max,ymax=sig_f_max)
+ ax21.set_ylim(ymin=sig_min,ymax=sig_max)
- ax12.plot(x_range, u_f_range, color='orange')
- ax12.plot(x_range, u_m_range, color='orange', linestyle='dashed')
- ax12.fill_between(x_range, u_f_range, 0, alpha=0.1, color='orange')
- ax12.fill_between(x_range, u_m_range, 0, alpha=0.3, color='orange')
+ disp_color='black'
+ ax12.plot(x_range, u_f_range, color=disp_color)
+ ax12.plot(x_range, u_m_range, color=disp_color, linestyle='dashed')
+ ax12.fill_between(x_range, u_f_range, 0, alpha=0.1, color=disp_color)
+ ax12.fill_between(x_range, u_m_range, 0, alpha=0.3, color=disp_color)
ax12.set_xlabel(r'$x$ [mm]')
ax12.set_ylabel(r'$u$ [mm]')
- ax12.set_ylim(ymin=u_m_max,ymax=u_f_max)
+ ax12.set_ylim(ymin=u_min,ymax=u_max)
ax22.plot(x_range, tau_range, color='red')
ax22.fill_between(x_range, tau_range, 0, alpha=0.1, color='red')
diff --git a/tension/fragmentation.ipynb b/tension/fragmentation.ipynb
index cc54195f932f6446d6e13cb6943d484fa44601ee..02f1117095a9662acde230401635f34b4acb90bf 100644
--- a/tension/fragmentation.ipynb
+++ b/tension/fragmentation.ipynb
@@ -3,7 +3,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "thick-postcard",
+ "id": "grand-papua",
"metadata": {},
"outputs": [],
"source": [
@@ -14,7 +14,7 @@
{
"cell_type": "code",
"execution_count": 2,
- "id": "affected-mother",
+ "id": "republican-antarctica",
"metadata": {},
"outputs": [],
"source": [
@@ -24,13 +24,13 @@
{
"cell_type": "code",
"execution_count": 3,
- "id": "colored-clause",
+ "id": "considered-citation",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "24abea4c54174a62a893fbdd1127c3d9",
+ "model_id": "18ea497b4aa24c02b072dc773977e5eb",
"version_major": 2,
"version_minor": 0
},
@@ -49,7 +49,7 @@
{
"cell_type": "code",
"execution_count": 4,
- "id": "european-colombia",
+ "id": "widespread-microwave",
"metadata": {},
"outputs": [],
"source": [
@@ -59,7 +59,7 @@
{
"cell_type": "code",
"execution_count": 5,
- "id": "scientific-silly",
+ "id": "later-albert",
"metadata": {},
"outputs": [
{
@@ -84,7 +84,7 @@
{
"cell_type": "code",
"execution_count": 9,
- "id": "lonely-dairy",
+ "id": "lovely-commissioner",
"metadata": {},
"outputs": [],
"source": [
@@ -94,7 +94,7 @@
{
"cell_type": "code",
"execution_count": 10,
- "id": "accessory-citizenship",
+ "id": "material-hampshire",
"metadata": {},
"outputs": [],
"source": [
@@ -104,7 +104,7 @@
{
"cell_type": "code",
"execution_count": 12,
- "id": "subsequent-watershed",
+ "id": "silent-maryland",
"metadata": {},
"outputs": [],
"source": [
@@ -114,7 +114,7 @@
{
"cell_type": "code",
"execution_count": 13,
- "id": "several-holiday",
+ "id": "million-carter",
"metadata": {},
"outputs": [
{
@@ -139,7 +139,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "neural-lesson",
+ "id": "contrary-ferry",
"metadata": {},
"outputs": [],
"source": []
@@ -161,7 +161,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.3"
+ "version": "3.9.1"
}
},
"nbformat": 4,