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comet-fenics
Commit 5682d82b authored by Jeremy BLEYER's avatar Jeremy BLEYER
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abstract.pdf 0 → 100644
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doc/_build/html/_downloads/axisymmetric_elasticity.ipynb
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...@@ -24,7 +24,7 @@ ...@@ -24,7 +24,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 50, "execution_count": 51,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -879,7 +879,7 @@ ...@@ -879,7 +879,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 43, "execution_count": 52,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -926,7 +926,7 @@ ...@@ -926,7 +926,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 44, "execution_count": 53,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -955,7 +955,7 @@ ...@@ -955,7 +955,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 45, "execution_count": 54,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -979,7 +979,7 @@ ...@@ -979,7 +979,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 46, "execution_count": 55,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1787,7 +1787,7 @@ ...@@ -1787,7 +1787,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 48, "execution_count": 56,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
......
doc/_build/html/_downloads/axisymmetric_elasticity.py
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...@@ -9,7 +9,7 @@ ...@@ -9,7 +9,7 @@
# #
# We will investigate here the case of a hollow hemisphere of inner (resp. outer) radius $R_i$ (resp. $R_e$). Due to the revolution symmetry, the 2D cross-section corresponds to a quarter of a hollow cylinder. # We will investigate here the case of a hollow hemisphere of inner (resp. outer) radius $R_i$ (resp. $R_e$). Due to the revolution symmetry, the 2D cross-section corresponds to a quarter of a hollow cylinder.
# In[50]: # In[51]:
from __future__ import print_function from __future__ import print_function
...@@ -65,7 +65,7 @@ ds = Measure("ds", subdomain_data=facets) ...@@ -65,7 +65,7 @@ ds = Measure("ds", subdomain_data=facets)
# #
# > **Note**: we could also express the strain components in the form of a vector of size 4 in alternative of the 3D tensor representation implemented below. # > **Note**: we could also express the strain components in the form of a vector of size 4 in alternative of the 3D tensor representation implemented below.
# In[43]: # In[52]:
x = SpatialCoordinate(mesh) x = SpatialCoordinate(mesh)
...@@ -104,7 +104,7 @@ def sigma(v): ...@@ -104,7 +104,7 @@ def sigma(v):
# #
# The final formulation is therefore pretty straightforward. Since a uniform pressure loading is applied on the outer boundary, we will also need the exterior normal vector to define the work of external forces form. # The final formulation is therefore pretty straightforward. Since a uniform pressure loading is applied on the outer boundary, we will also need the exterior normal vector to define the work of external forces form.
# In[44]: # In[53]:
n = FacetNormal(mesh) n = FacetNormal(mesh)
...@@ -125,7 +125,7 @@ u = Function(V, name="Displacement") ...@@ -125,7 +125,7 @@ u = Function(V, name="Displacement")
# \quad u_z=0 # \quad u_z=0
# \end{equation} # \end{equation}
# In[45]: # In[54]:
bcs = [DirichletBC(V.sub(1), Constant(0), facets, 1), bcs = [DirichletBC(V.sub(1), Constant(0), facets, 1),
...@@ -135,7 +135,7 @@ print("Inwards radial displacement at (r=Re, theta=0): {:1.7f} (FE) {:1.7f} (Exa ...@@ -135,7 +135,7 @@ print("Inwards radial displacement at (r=Re, theta=0): {:1.7f} (FE) {:1.7f} (Exa
print("Inwards radial displacement at (r=Ri, theta=0): {:1.7f} (FE) {:1.7f} (Exact)".format(-u(Ri, 0.)[0], float(Re**3/(Re**3-Ri**3)*((1-2*nu)*Ri+(1+nu)*Ri/2)*p/E))) print("Inwards radial displacement at (r=Ri, theta=0): {:1.7f} (FE) {:1.7f} (Exact)".format(-u(Ri, 0.)[0], float(Re**3/(Re**3-Ri**3)*((1-2*nu)*Ri+(1+nu)*Ri/2)*p/E)))
# In[46]: # In[55]:
plt.figure() plt.figure()
...@@ -145,7 +145,7 @@ plt.show() ...@@ -145,7 +145,7 @@ plt.show()
# The second loading case corresponds to a fully clamped condition on $z=0$, the vertical boundary remaining in smooth contact. # The second loading case corresponds to a fully clamped condition on $z=0$, the vertical boundary remaining in smooth contact.
# In[48]: # In[56]:
bcs = [DirichletBC(V, Constant((0., 0.)), facets, 1), bcs = [DirichletBC(V, Constant((0., 0.)), facets, 1),
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doc/_build/html/_sources/demo/elasticity/axisymmetric_elasticity.ipynb.txt
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...@@ -24,7 +24,7 @@ ...@@ -24,7 +24,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 50, "execution_count": 51,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -879,7 +879,7 @@ ...@@ -879,7 +879,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 43, "execution_count": 52,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -926,7 +926,7 @@ ...@@ -926,7 +926,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 44, "execution_count": 53,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -955,7 +955,7 @@ ...@@ -955,7 +955,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 45, "execution_count": 54,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -979,7 +979,7 @@ ...@@ -979,7 +979,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 46, "execution_count": 55,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
...@@ -1787,7 +1787,7 @@ ...@@ -1787,7 +1787,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 48, "execution_count": 56,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
......
doc/_build/html/_sources/intro.rst.txt
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...@@ -22,6 +22,18 @@ illustrating the versatility of FEniCS. ...@@ -22,6 +22,18 @@ illustrating the versatility of FEniCS.
The full set of demos can be obtained from the *COmputational MEchanics Toolbox* (COMET) available at The full set of demos can be obtained from the *COmputational MEchanics Toolbox* (COMET) available at
https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics. https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics.
If you find these demos useful for your research work, please consider citing them using the following
Zenodo DOI https://doi.org/10.5281/zenodo.1287832
.. code-block:: none
@article{bleyer2018numericaltours,
title={Numerical Tours of Computational Mechanics with FEniCS},
DOI={10.5281/zenodo.1287832},
publisher={Zenodo},
author={Jeremy Bleyer},
year={2018}}
----------------------- -----------------------
How do I get started ? How do I get started ?
......
doc/_build/html/demo/elasticity/axisymmetric_elasticity.html
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...@@ -243,7 +243,7 @@ symmetry, the 2D cross-section corresponds to a quarter of a hollow ...@@ -243,7 +243,7 @@ symmetry, the 2D cross-section corresponds to a quarter of a hollow
cylinder.</p> cylinder.</p>
<div class="nbinput docutils container"> <div class="nbinput docutils container">
<div class="prompt highlight-none"><div class="highlight"><pre> <div class="prompt highlight-none"><div class="highlight"><pre>
<span></span>In [50]: <span></span>In [51]:
</pre></div> </pre></div>
</div> </div>
<div class="input_area highlight-ipython2"><div class="highlight"><pre> <div class="input_area highlight-ipython2"><div class="highlight"><pre>
...@@ -1090,7 +1090,7 @@ a vector of size 4 in alternative of the 3D tensor representation ...@@ -1090,7 +1090,7 @@ a vector of size 4 in alternative of the 3D tensor representation
implemented below.</div></blockquote> implemented below.</div></blockquote>
<div class="nbinput nblast docutils container"> <div class="nbinput nblast docutils container">
<div class="prompt highlight-none"><div class="highlight"><pre> <div class="prompt highlight-none"><div class="highlight"><pre>
<span></span>In [43]: <span></span>In [52]:
</pre></div> </pre></div>
</div> </div>
<div class="input_area highlight-ipython2"><div class="highlight"><pre> <div class="input_area highlight-ipython2"><div class="highlight"><pre>
...@@ -1148,7 +1148,7 @@ need the exterior normal vector to define the work of external forces ...@@ -1148,7 +1148,7 @@ need the exterior normal vector to define the work of external forces
form.</p> form.</p>
<div class="nbinput nblast docutils container"> <div class="nbinput nblast docutils container">
<div class="prompt highlight-none"><div class="highlight"><pre> <div class="prompt highlight-none"><div class="highlight"><pre>
<span></span>In [44]: <span></span>In [53]:
</pre></div> </pre></div>
</div> </div>
<div class="input_area highlight-ipython2"><div class="highlight"><pre> <div class="input_area highlight-ipython2"><div class="highlight"><pre>
...@@ -1175,7 +1175,7 @@ u_r(r) = -\dfrac{R_e^3}{R_e^3-R_i^3}\left((1 − 2\nu)r + (1 + \nu)\dfrac{R_i^3} ...@@ -1175,7 +1175,7 @@ u_r(r) = -\dfrac{R_e^3}{R_e^3-R_i^3}\left((1 − 2\nu)r + (1 + \nu)\dfrac{R_i^3}
\quad u_z=0 \quad u_z=0
\end{equation}</div><div class="nbinput docutils container"> \end{equation}</div><div class="nbinput docutils container">
<div class="prompt highlight-none"><div class="highlight"><pre> <div class="prompt highlight-none"><div class="highlight"><pre>
<span></span>In [45]: <span></span>In [54]:
</pre></div> </pre></div>
</div> </div>
<div class="input_area highlight-ipython2"><div class="highlight"><pre> <div class="input_area highlight-ipython2"><div class="highlight"><pre>
...@@ -1200,7 +1200,7 @@ Inwards radial displacement at (r=Ri, theta=0): 0.0020879 (FE) 0.0020894 (Exact) ...@@ -1200,7 +1200,7 @@ Inwards radial displacement at (r=Ri, theta=0): 0.0020879 (FE) 0.0020894 (Exact)
</div> </div>
<div class="nbinput docutils container"> <div class="nbinput docutils container">
<div class="prompt highlight-none"><div class="highlight"><pre> <div class="prompt highlight-none"><div class="highlight"><pre>
<span></span>In [46]: <span></span>In [55]:
</pre></div> </pre></div>
</div> </div>
<div class="input_area highlight-ipython2"><div class="highlight"><pre> <div class="input_area highlight-ipython2"><div class="highlight"><pre>
...@@ -1996,7 +1996,7 @@ if (IPython.notebook.kernel != null) { ...@@ -1996,7 +1996,7 @@ if (IPython.notebook.kernel != null) {
<span class="math">\(z=0\)</span>, the vertical boundary remaining in smooth contact.</p> <span class="math">\(z=0\)</span>, the vertical boundary remaining in smooth contact.</p>
<div class="nbinput docutils container"> <div class="nbinput docutils container">
<div class="prompt highlight-none"><div class="highlight"><pre> <div class="prompt highlight-none"><div class="highlight"><pre>
<span></span>In [48]: <span></span>In [56]:
</pre></div> </pre></div>
</div> </div>
<div class="input_area highlight-ipython2"><div class="highlight"><pre> <div class="input_area highlight-ipython2"><div class="highlight"><pre>
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doc/_build/html/intro.html
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...@@ -64,6 +64,16 @@ getting started with FEniCS using solid mechanics examples.</p> ...@@ -64,6 +64,16 @@ getting started with FEniCS using solid mechanics examples.</p>
illustrating the versatility of FEniCS.</p> illustrating the versatility of FEniCS.</p>
<p>The full set of demos can be obtained from the <em>COmputational MEchanics Toolbox</em> (COMET) available at <p>The full set of demos can be obtained from the <em>COmputational MEchanics Toolbox</em> (COMET) available at
<a class="reference external" href="https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics">https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics</a>.</p> <a class="reference external" href="https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics">https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics</a>.</p>
<p>If you find these demos useful for your research work, please consider citing them using the following
Zenodo DOI <a class="reference external" href="https://doi.org/10.5281/zenodo.1287832">https://doi.org/10.5281/zenodo.1287832</a></p>
<div class="highlight-none"><div class="highlight"><pre><span></span>@article{bleyer2018numericaltours,
title={Numerical Tours of Computational Mechanics with FEniCS},
DOI={10.5281/zenodo.1287832},
publisher={Zenodo},
author={Jeremy Bleyer},
year={2018}}
</pre></div>
</div>
</div> </div>
<div class="section" id="how-do-i-get-started"> <div class="section" id="how-do-i-get-started">
<h2>How do I get started ?<a class="headerlink" href="#how-do-i-get-started" title="Permalink to this headline"></a></h2> <h2>How do I get started ?<a class="headerlink" href="#how-do-i-get-started" title="Permalink to this headline"></a></h2>
...@@ -107,12 +117,14 @@ a joint research unit of <a class="reference external" href="http://www.enpc.fr" ...@@ -107,12 +117,14 @@ a joint research unit of <a class="reference external" href="http://www.enpc.fr"
<li class="toctree-l1"><a class="reference internal" href="linear_problems.html">Linear problems in solid mechanics</a><ul> <li class="toctree-l1"><a class="reference internal" href="linear_problems.html">Linear problems in solid mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/elasticity/2D_elasticity.py.html">2D linear elasticity</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/elasticity/2D_elasticity.py.html">2D linear elasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/elasticity/orthotropic_elasticity.py.html">Orthotropic linear elasticity</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/elasticity/orthotropic_elasticity.py.html">Orthotropic linear elasticity</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity.html">Linear thermoelasticity evolution problem</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/elasticity/axisymmetric_elasticity.html">Axisymmetric formulation for elastic structures of revolution</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity.html">Linear thermoelasticity (weak coupling)</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/thermoelasticity/thermoelasticity_transient.html">Thermo-elastic evolution problem (full coupling)</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo/modal_analysis_dynamics/cantilever_modal.py.html">Modal analysis of an elastic structure</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/modal_analysis_dynamics/cantilever_modal.py.html">Modal analysis of an elastic structure</a></li>
</ul> </ul>
</li> </li>
<li class="toctree-l1"><a class="reference internal" href="homogenization.html">Homogenization of heterogeneous materials</a><ul> <li class="toctree-l1"><a class="reference internal" href="homogenization.html">Homogenization of heterogeneous materials</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo/periodic_homog_elas/periodic_homog_elas.html">Periodic homogenization of linear materials</a></li> <li class="toctree-l2"><a class="reference internal" href="demo/periodic_homog_elas/periodic_homog_elas.html">Periodic homogenization of linear elastic materials</a></li>
</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>
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doc/_build/html/searchindex.js
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doc/intro.rst
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...@@ -22,6 +22,18 @@ illustrating the versatility of FEniCS. ...@@ -22,6 +22,18 @@ illustrating the versatility of FEniCS.
The full set of demos can be obtained from the *COmputational MEchanics Toolbox* (COMET) available at The full set of demos can be obtained from the *COmputational MEchanics Toolbox* (COMET) available at
https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics. https://gitlab.enpc.fr/jeremy.bleyer/comet-fenics.
If you find these demos useful for your research work, please consider citing them using the following
Zenodo DOI https://doi.org/10.5281/zenodo.1287832
.. code-block:: none
@article{bleyer2018numericaltours,
title={Numerical Tours of Computational Mechanics with FEniCS},
DOI={10.5281/zenodo.1287832},
publisher={Zenodo},
author={Jeremy Bleyer},
year={2018}}
----------------------- -----------------------
How do I get started ? How do I get started ?
......
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