Commit 5682d82b by Jeremy BLEYER

### Added citation instructions

parent 4c8e7114
abstract.pdf 0 → 100644
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 ... ... @@ -24,7 +24,7 @@ }, { "cell_type": "code", "execution_count": 50, "execution_count": 51, "metadata": {}, "outputs": [ { ... ... @@ -879,7 +879,7 @@ }, { "cell_type": "code", "execution_count": 43, "execution_count": 52, "metadata": {}, "outputs": [], "source": [ ... ... @@ -926,7 +926,7 @@ }, { "cell_type": "code", "execution_count": 44, "execution_count": 53, "metadata": {}, "outputs": [], "source": [ ... ... @@ -955,7 +955,7 @@ }, { "cell_type": "code", "execution_count": 45, "execution_count": 54, "metadata": {}, "outputs": [ { ... ... @@ -979,7 +979,7 @@ }, { "cell_type": "code", "execution_count": 46, "execution_count": 55, "metadata": {}, "outputs": [ { ... ... @@ -1787,7 +1787,7 @@ }, { "cell_type": "code", "execution_count": 48, "execution_count": 56, "metadata": {}, "outputs": [ { ... ...
 ... ... @@ -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. # In[50]: # In[51]: from __future__ import print_function ... ... @@ -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. # In[43]: # In[52]: x = SpatialCoordinate(mesh) ... ... @@ -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. # In[44]: # In[53]: n = FacetNormal(mesh) ... ... @@ -125,7 +125,7 @@ u = Function(V, name="Displacement") # \quad u_z=0 # # In[45]: # In[54]: 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 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() ... ... @@ -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. # In[48]: # In[56]: bcs = [DirichletBC(V, Constant((0., 0.)), facets, 1), ... ...
 ... ... @@ -24,7 +24,7 @@ }, { "cell_type": "code", "execution_count": 50, "execution_count": 51, "metadata": {}, "outputs": [ { ... ... @@ -879,7 +879,7 @@ }, { "cell_type": "code", "execution_count": 43, "execution_count": 52, "metadata": {}, "outputs": [], "source": [ ... ... @@ -926,7 +926,7 @@ }, { "cell_type": "code", "execution_count": 44, "execution_count": 53, "metadata": {}, "outputs": [], "source": [ ... ... @@ -955,7 +955,7 @@ }, { "cell_type": "code", "execution_count": 45, "execution_count": 54, "metadata": {}, "outputs": [ { ... ... @@ -979,7 +979,7 @@ }, { "cell_type": "code", "execution_count": 46, "execution_count": 55, "metadata": {}, "outputs": [ { ... ... @@ -1787,7 +1787,7 @@ }, { "cell_type": "code", "execution_count": 48, "execution_count": 56, "metadata": {}, "outputs": [ { ... ...
 ... ... @@ -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 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 ? ... ...
 ... ... @@ -243,7 +243,7 @@ symmetry, the 2D cross-section corresponds to a quarter of a hollow cylinder.

In [50]:
In [51]:

...  ...  @@ -1090,7 +1090,7 @@ a vector of size 4 in alternative of the 3D tensor representation
implemented below.
In [43]:
In [52]:

...  ...  @@ -1148,7 +1148,7 @@ need the exterior normal vector to define the work of external forces
form.

In [44]:
In [53]:

...  ...  @@ -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}

In [45]:
In [54]:

...  ...  @@ -1200,7 +1200,7 @@ Inwards radial displacement at (r=Ri, theta=0): 0.0020879 (FE) 0.0020894 (Exact)

In [46]:
In [55]:

...  ...  @@ -1996,7 +1996,7 @@ if (IPython.notebook.kernel != null) {
$$z=0$$, the vertical boundary remaining in smooth contact.

In [48]:
In [56]:

...  ...
 ... ... @@ -64,6 +64,16 @@ getting started with FEniCS using solid mechanics examples.

illustrating the versatility of FEniCS.

The full set of demos can be obtained from the COmputational MEchanics Toolbox (COMET) available at 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

@article{bleyer2018numericaltours,
title={Numerical Tours of Computational Mechanics with FEniCS},
DOI={10.5281/zenodo.1287832},
publisher={Zenodo},
author={Jeremy Bleyer},
year={2018}}