Commit 95087341 authored by Jeremy BLEYER's avatar Jeremy BLEYER

Finished viscoelastic example

parent 779039e4
...@@ -10,6 +10,7 @@ Contents: ...@@ -10,6 +10,7 @@ Contents:
.. toctree:: .. toctree::
:maxdepth: 1 :maxdepth: 1
demo/viscoelasticity/linear_viscoelasticity.ipynb
demo/2D_plasticity/vonMises_plasticity.py.rst demo/2D_plasticity/vonMises_plasticity.py.rst
......
...@@ -25,7 +25,7 @@ ...@@ -25,7 +25,7 @@
<link rel="index" title="Index" href="../../genindex.html" /> <link rel="index" title="Index" href="../../genindex.html" />
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...@@ -33,7 +33,7 @@ ...@@ -33,7 +33,7 @@
<div class="headertitle"><a <div class="headertitle"><a
href="../../index.html">Numerical tours of continuum mechanics using FEniCS</a></div> href="../../index.html">Numerical tours of continuum mechanics using FEniCS</a></div>
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...@@ -428,6 +428,7 @@ when considering a zero hardening modulus.</p> ...@@ -428,6 +428,7 @@ when considering a zero hardening modulus.</p>
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<li class="toctree-l2 current"><a class="current reference internal" href="#">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2 current"><a class="current reference internal" href="#">Elasto-plastic analysis of a 2D von Mises material</a></li>
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...@@ -461,7 +462,7 @@ when considering a zero hardening modulus.</p> ...@@ -461,7 +462,7 @@ when considering a zero hardening modulus.</p>
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...@@ -238,6 +238,7 @@ writing/reading. Prefered output format is now .xdmf:</p> ...@@ -238,6 +238,7 @@ writing/reading. Prefered output format is now .xdmf:</p>
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<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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......
...@@ -2823,6 +2823,7 @@ if (IPython.notebook.kernel != null) { ...@@ -2823,6 +2823,7 @@ if (IPython.notebook.kernel != null) {
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<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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......
...@@ -216,6 +216,7 @@ that:</p> ...@@ -216,6 +216,7 @@ that:</p>
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<li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -279,6 +279,7 @@ and the beam theory eigenfrequencies :</p> ...@@ -279,6 +279,7 @@ and the beam theory eigenfrequencies :</p>
</ul> </ul>
</li> </li>
<li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
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......
...@@ -2159,6 +2159,7 @@ if (IPython.notebook.kernel != null) { ...@@ -2159,6 +2159,7 @@ if (IPython.notebook.kernel != null) {
</ul> </ul>
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<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -84,6 +84,7 @@ ...@@ -84,6 +84,7 @@
</ul> </ul>
</li> </li>
<li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -213,6 +213,7 @@ so that no term arise in the linear functional):</p> ...@@ -213,6 +213,7 @@ so that no term arise in the linear functional):</p>
</ul> </ul>
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<li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -206,6 +206,7 @@ the thin plate solution.</p> ...@@ -206,6 +206,7 @@ the thin plate solution.</p>
</ul> </ul>
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<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -4345,6 +4345,7 @@ if (IPython.notebook.kernel != null) { ...@@ -4345,6 +4345,7 @@ if (IPython.notebook.kernel != null) {
</ul> </ul>
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<li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -2909,6 +2909,7 @@ Mechanics and Engineering, 85(3), 349-365. ...@@ -2909,6 +2909,7 @@ Mechanics and Engineering, 85(3), 349-365.
</ul> </ul>
</li> </li>
<li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="../../nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -81,6 +81,7 @@ ...@@ -81,6 +81,7 @@
</ul> </ul>
</li> </li>
<li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -89,6 +89,7 @@ ...@@ -89,6 +89,7 @@
</ul> </ul>
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<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
</li> </li>
......
...@@ -73,6 +73,7 @@ ...@@ -73,6 +73,7 @@
</ul> </ul>
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<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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...@@ -118,6 +119,7 @@ ...@@ -118,6 +119,7 @@
</ul> </ul>
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<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
</ul> </ul>
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......
...@@ -94,6 +94,7 @@ ...@@ -94,6 +94,7 @@
</ul> </ul>
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<li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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......
...@@ -24,7 +24,7 @@ ...@@ -24,7 +24,7 @@
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...@@ -56,6 +56,7 @@ ...@@ -56,6 +56,7 @@
<p>Contents:</p> <p>Contents:</p>
<div class="toctree-wrapper compound"> <div class="toctree-wrapper compound">
<ul> <ul>
<li class="toctree-l1"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l1"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l1"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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...@@ -89,6 +90,7 @@ ...@@ -89,6 +90,7 @@
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<li class="toctree-l1 current"><a class="current reference internal" href="#">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1 current"><a class="current reference internal" href="#">Nonlinear problems in solid mechanics</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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...@@ -104,6 +104,7 @@ ...@@ -104,6 +104,7 @@
</ul> </ul>
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<li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="nonlinear_problems.html">Nonlinear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/viscoelasticity/linear_viscoelasticity.html">Linear viscoelasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
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......
This diff is collapsed.
...@@ -10,6 +10,7 @@ Contents: ...@@ -10,6 +10,7 @@ Contents:
.. toctree:: .. toctree::
:maxdepth: 1 :maxdepth: 1
demo/viscoelasticity/linear_viscoelasticity.ipynb
demo/2D_plasticity/vonMises_plasticity.py.rst demo/2D_plasticity/vonMises_plasticity.py.rst
......
.. Numerical tours of continuum mechanics using FEniCS documentation master file, created by
sphinx-quickstart on Wed Jun 8 21:25:10 2016.
You can adapt this file completely to your liking, but it should at least
contain the root `toctree` directive.
Reissner-Mindlin plates
=======================
Contents:
.. toctree::
:maxdepth: 1
reissner_mindlin_quads.py.rst
reissner_mindlin_dg.py.rst
...@@ -30,7 +30,7 @@ ...@@ -30,7 +30,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 72, "execution_count": 1,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -63,7 +63,8 @@ ...@@ -63,7 +63,8 @@
"(dw, dtheta) = split(du)\n", "(dw, dtheta) = split(du)\n",
"\n", "\n",
"\n", "\n",
"k_form = EI*inner(grad(theta_), grad(dtheta))*dx + kappa*GS*dot(grad(w_)[0]-theta_, grad(dw)[0]-dtheta)*dx\n", "k_form = EI*inner(grad(theta_), grad(dtheta))*dx + \\\n",
" kappa*GS*dot(grad(w_)[0]-theta_, grad(dw)[0]-dtheta)*dx\n",
"l_form = Constant(1.)*u_[0]*dx" "l_form = Constant(1.)*u_[0]*dx"
] ]
}, },
...@@ -73,12 +74,12 @@ ...@@ -73,12 +74,12 @@
"raw_mimetype": "text/restructuredtext" "raw_mimetype": "text/restructuredtext"
}, },
"source": [ "source": [
"As in the :ref:`ModalAnalysis` tour, a dummy linear form `l_form` is used to call the `assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`." "As in the :ref:`ModalAnalysis` tour, a dummy linear form :code:`l_form` is used to call the :code:`assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`."
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 78, "execution_count": 5,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -117,7 +118,7 @@ ...@@ -117,7 +118,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 70, "execution_count": 3,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -142,7 +143,7 @@ ...@@ -142,7 +143,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 71, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
......
...@@ -30,7 +30,7 @@ ...@@ -30,7 +30,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 72, "execution_count": 1,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -63,7 +63,8 @@ ...@@ -63,7 +63,8 @@
"(dw, dtheta) = split(du)\n", "(dw, dtheta) = split(du)\n",
"\n", "\n",
"\n", "\n",
"k_form = EI*inner(grad(theta_), grad(dtheta))*dx + kappa*GS*dot(grad(w_)[0]-theta_, grad(dw)[0]-dtheta)*dx\n", "k_form = EI*inner(grad(theta_), grad(dtheta))*dx + \\\n",
" kappa*GS*dot(grad(w_)[0]-theta_, grad(dw)[0]-dtheta)*dx\n",
"l_form = Constant(1.)*u_[0]*dx" "l_form = Constant(1.)*u_[0]*dx"
] ]
}, },
...@@ -73,12 +74,12 @@ ...@@ -73,12 +74,12 @@
"raw_mimetype": "text/restructuredtext" "raw_mimetype": "text/restructuredtext"
}, },
"source": [ "source": [
"As in the :ref:`ModalAnalysis` tour, a dummy linear form `l_form` is used to call the `assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`." "As in the :ref:`ModalAnalysis` tour, a dummy linear form :code:`l_form` is used to call the :code:`assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`."
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 78, "execution_count": 5,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -117,7 +118,7 @@ ...@@ -117,7 +118,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 70, "execution_count": 3,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -142,7 +143,7 @@ ...@@ -142,7 +143,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 79, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -946,9 +947,9 @@ ...@@ -946,9 +947,9 @@
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"Critical buckling loads:\n", "Critical buckling loads:\n",
"Exact: 0.00032 FE: 0.31805 Rel. gap 99914.49%%\n", "Exact: 0.31800 FE: 0.31805 Rel. gap 0.01%%\n",
"Exact: 0.00094 FE: 0.94033 Rel. gap 99940.30%%\n", "Exact: 0.93995 FE: 0.94033 Rel. gap 0.04%%\n",
"Exact: 0.00187 FE: 1.87415 Rel. gap 99978.99%%\n" "Exact: 1.87267 FE: 1.87415 Rel. gap 0.08%%\n"
] ]
} }
], ],
......
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"nbsphinx": "hidden"
},
"source": [
"This notebook is part of the `nbsphinx` documentation: http://nbsphinx.readthedocs.io/."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Markdown Cells\n",