From e9ee23738c78828a2ffba95d3a0322829ff4c7f7 Mon Sep 17 00:00:00 2001 From: Jeremy Bleyer Date: Thu, 4 Oct 2018 13:58:47 +0200 Subject: [PATCH] Added contact penalty example and licenses --- .../vonMises_plasticity.py.doctree | Bin 66011 -> 66916 bytes .../demo/elasticity/2D_elasticity.py.doctree | Bin 29771 -> 30753 bytes .../axisymmetric_elasticity.doctree | Bin 526913 -> 527861 bytes .../orthotropic_elasticity.py.doctree | Bin 23695 -> 24639 bytes .../cantilever_modal.py.doctree | Bin 34201 -> 35153 bytes .../periodic_homog_elas.doctree | Bin 279449 -> 280148 bytes .../reissner_mindlin_dg.py.doctree | Bin 21056 -> 22020 bytes .../reissner_mindlin_quads.py.doctree | Bin 20451 -> 21395 bytes .../thermoelasticity/thermoelasticity.doctree | Bin 443809 -> 444517 bytes .../thermoelasticity_transient.doctree | Bin 537511 -> 538378 bytes doc/_build/doctrees/environment.pickle | Bin 76496 -> 77212 bytes doc/_build/doctrees/intro.doctree | Bin 13785 -> 15898 bytes 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# -# .. _LinearElasticity2D: # +# .. _LinearElasticity2D: # # ========================= # 2D linear elasticity diff --git a/doc/_build/html/_downloads/cantilever_modal.py b/doc/_build/html/_downloads/cantilever_modal.py index ae6f541..bbc3d4b 100644 --- a/doc/_build/html/_downloads/cantilever_modal.py +++ b/doc/_build/html/_downloads/cantilever_modal.py @@ -1,4 +1,7 @@ -# +raw:: html + +

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+ # .. _ModalAnalysis: # # ========================================== diff --git a/doc/_build/html/_downloads/orthotropic_elasticity.py b/doc/_build/html/_downloads/orthotropic_elasticity.py index aa7920f..a23f4c2 100644 --- a/doc/_build/html/_downloads/orthotropic_elasticity.py +++ b/doc/_build/html/_downloads/orthotropic_elasticity.py @@ -1,5 +1,8 @@ # # .. # gedit: set fileencoding=utf8 : +# .. raw:: html +# +#

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# # .. _OrthotropicElasticity: # @@ -11,10 +14,10 @@ # Introduction # ------------ # -# In this numerical tour, we will show how to tackle the case of orthotropic elasticity (in a 2D setting). The corresponding file can be obtained from +# In this numerical tour, we will show how to tackle the case of orthotropic elasticity (in a 2D setting). The corresponding file can be obtained from # :download:`orthotropic_elasticity.py`. # -# We consider here the case of a square plate perforated by a circular hole of +# We consider here the case of a square plate perforated by a circular hole of # radius :math:`R`, the plate dimension is :math:`2L\times 2L` with :math:`L \gg R` # Only the top-right quarter of the plate will be considered. Loading will consist # of a uniform traction on the top/bottom boundaries, symmetry conditions will also @@ -27,7 +30,7 @@ from mshr import * L, R = 1., 0.1 N = 50 # mesh density - + domain = Rectangle(Point(0.,0.), Point(L, L)) - Circle(Point(0., 0.), R) mesh = generate_mesh(domain, N) @@ -35,7 +38,7 @@ mesh = generate_mesh(domain, N) # Constitutive relation # --------------------- # -# Constitutive relations will be defined using an engineering (or Voigt) notation (i.e. +# Constitutive relations will be defined using an engineering (or Voigt) notation (i.e. # second order tensors will be written as a vector of their components) contrary # to the :ref:`LinearElasticity2D` example which used an intrinsic notation. In # the material frame, which is assumed to coincide here with the global :math:`(Oxy)` @@ -46,13 +49,13 @@ mesh = generate_mesh(domain, N) # .. math:: # \begin{Bmatrix} \varepsilon_{xx} \\ \varepsilon_{yy} \\ 2\varepsilon_{xy} # \end{Bmatrix} = \begin{bmatrix} 1/E_x & -\nu_{xy}/E_x & 0\\ -# -\nu_{yx}/E_y & 1/E_y & 0 \\ 0 & 0 & 1/G_{xy} \end{bmatrix}\begin{Bmatrix} +# -\nu_{yx}/E_y & 1/E_y & 0 \\ 0 & 0 & 1/G_{xy} \end{bmatrix}\begin{Bmatrix} # \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} # \end{Bmatrix} # # with :math:`E_x, E_y` the two Young's moduli in the orthotropy directions, :math:`\nu_{xy}` # the in-plane Poisson ration (with the following relation ensuring the constitutive -# relation symmetry :math:`\nu_{yx}=\nu_{xy}E_y/E_x`) and :math:`G_{xy}` being the +# relation symmetry :math:`\nu_{yx}=\nu_{xy}E_y/E_x`) and :math:`G_{xy}` being the # shear modulus. This relation needs to be inverted to obtain the stress components as a function # of the strain components :math:`\boldsymbol{\sigma}=\mathbf{C}\boldsymbol{\varepsilon}` with # :math:`\mathbf{C}=\mathbf{S}^{-1}`:: @@ -89,7 +92,7 @@ def sigma(v): # Problem position and resolution # -------------------------------- # -# Different parts of the quarter plate boundaries are now defined as well as the +# Different parts of the quarter plate boundaries are now defined as well as the # exterior integration measure ``ds``:: class Top(SubDomain): @@ -127,7 +130,7 @@ a = inner(sigma(du), eps(u_))*dx T = Constant((0, 1e-3)) l = dot(T, u_)*ds(1) -# Symmetric boundary conditions are applied on the ``Top`` and ``Left`` boundaries +# Symmetric boundary conditions are applied on the ``Top`` and ``Left`` boundaries # and the problem is solved:: # symmetry boundary conditions diff --git a/doc/_build/html/_downloads/reissner_mindlin_dg.py b/doc/_build/html/_downloads/reissner_mindlin_dg.py index 7d8822b..c0f3af5 100644 --- a/doc/_build/html/_downloads/reissner_mindlin_dg.py +++ b/doc/_build/html/_downloads/reissner_mindlin_dg.py @@ -1,4 +1,7 @@ -# +raw:: html + +

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+ # .. _ReissnerMindlinDG: # # ============================================================== diff --git a/doc/_build/html/_downloads/reissner_mindlin_quads.py b/doc/_build/html/_downloads/reissner_mindlin_quads.py index b6eb975..8da6c11 100644 --- a/doc/_build/html/_downloads/reissner_mindlin_quads.py +++ b/doc/_build/html/_downloads/reissner_mindlin_quads.py @@ -1,4 +1,7 @@ -# +raw:: html + +

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+ # .. _ReissnerMindlinQuads: # # ========================================== diff --git a/doc/_build/html/_sources/demo/2D_plasticity/vonMises_plasticity.py.rst.txt b/doc/_build/html/_sources/demo/2D_plasticity/vonMises_plasticity.py.rst.txt index 95444e1..215cf08 100644 --- a/doc/_build/html/_sources/demo/2D_plasticity/vonMises_plasticity.py.rst.txt +++ b/doc/_build/html/_sources/demo/2D_plasticity/vonMises_plasticity.py.rst.txt @@ -1,6 +1,10 @@ .. _vonMisesPlasticity: +.. raw:: html + +

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+ ================================================== Elasto-plastic analysis of a 2D von Mises material ================================================== diff --git a/doc/_build/html/_sources/demo/elasticity/2D_elasticity.py.rst.txt b/doc/_build/html/_sources/demo/elasticity/2D_elasticity.py.rst.txt index 6d2d53f..ec8b17b 100644 --- a/doc/_build/html/_sources/demo/elasticity/2D_elasticity.py.rst.txt +++ b/doc/_build/html/_sources/demo/elasticity/2D_elasticity.py.rst.txt @@ -1,8 +1,11 @@ .. # gedit: set fileencoding=utf8 : +.. raw:: html + +

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-.. _LinearElasticity2D: +.. _LinearElasticity2D: ========================= 2D linear elasticity diff --git a/doc/_build/html/_sources/demo/elasticity/orthotropic_elasticity.py.rst.txt b/doc/_build/html/_sources/demo/elasticity/orthotropic_elasticity.py.rst.txt index 757385d..84408aa 100644 --- a/doc/_build/html/_sources/demo/elasticity/orthotropic_elasticity.py.rst.txt +++ b/doc/_build/html/_sources/demo/elasticity/orthotropic_elasticity.py.rst.txt @@ -1,5 +1,8 @@ .. # gedit: set fileencoding=utf8 : +.. raw:: html + +

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.. _OrthotropicElasticity: @@ -11,10 +14,10 @@ Introduction ------------ -In this numerical tour, we will show how to tackle the case of orthotropic elasticity (in a 2D setting). The corresponding file can be obtained from +In this numerical tour, we will show how to tackle the case of orthotropic elasticity (in a 2D setting). The corresponding file can be obtained from :download:`orthotropic_elasticity.py`. -We consider here the case of a square plate perforated by a circular hole of +We consider here the case of a square plate perforated by a circular hole of radius :math:`R`, the plate dimension is :math:`2L\times 2L` with :math:`L \gg R` Only the top-right quarter of the plate will be considered. Loading will consist of a uniform traction on the top/bottom boundaries, symmetry conditions will also @@ -27,7 +30,7 @@ between a rectangle and a circle:: L, R = 1., 0.1 N = 50 # mesh density - + domain = Rectangle(Point(0.,0.), Point(L, L)) - Circle(Point(0., 0.), R) mesh = generate_mesh(domain, N) @@ -35,7 +38,7 @@ between a rectangle and a circle:: Constitutive relation --------------------- -Constitutive relations will be defined using an engineering (or Voigt) notation (i.e. +Constitutive relations will be defined using an engineering (or Voigt) notation (i.e. second order tensors will be written as a vector of their components) contrary to the :ref:`LinearElasticity2D` example which used an intrinsic notation. In the material frame, which is assumed to coincide here with the global :math:`(Oxy)` @@ -46,13 +49,13 @@ frame, the orthotropic constitutive law writes :math:`\boldsymbol{\varepsilon}=\ .. math:: \begin{Bmatrix} \varepsilon_{xx} \\ \varepsilon_{yy} \\ 2\varepsilon_{xy} \end{Bmatrix} = \begin{bmatrix} 1/E_x & -\nu_{xy}/E_x & 0\\ - -\nu_{yx}/E_y & 1/E_y & 0 \\ 0 & 0 & 1/G_{xy} \end{bmatrix}\begin{Bmatrix} + -\nu_{yx}/E_y & 1/E_y & 0 \\ 0 & 0 & 1/G_{xy} \end{bmatrix}\begin{Bmatrix} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} \end{Bmatrix} with :math:`E_x, E_y` the two Young's moduli in the orthotropy directions, :math:`\nu_{xy}` the in-plane Poisson ration (with the following relation ensuring the constitutive -relation symmetry :math:`\nu_{yx}=\nu_{xy}E_y/E_x`) and :math:`G_{xy}` being the +relation symmetry :math:`\nu_{yx}=\nu_{xy}E_y/E_x`) and :math:`G_{xy}` being the shear modulus. This relation needs to be inverted to obtain the stress components as a function of the strain components :math:`\boldsymbol{\sigma}=\mathbf{C}\boldsymbol{\varepsilon}` with :math:`\mathbf{C}=\mathbf{S}^{-1}`:: @@ -89,7 +92,7 @@ second-order tensor or using the Voigt engineering notation:: Problem position and resolution -------------------------------- -Different parts of the quarter plate boundaries are now defined as well as the +Different parts of the quarter plate boundaries are now defined as well as the exterior integration measure ``ds``:: class Top(SubDomain): @@ -101,7 +104,7 @@ exterior integration measure ``ds``:: class Bottom(SubDomain): def inside(self, x, on_boundary): return near(x[1],0) and on_boundary - + # exterior facets MeshFunction facets = MeshFunction("size_t", mesh, 1) facets.set_all(0) @@ -122,12 +125,12 @@ on the top boundary:: u_ = TestFunction(V) u = Function(V, name='Displacement') a = inner(sigma(du), eps(u_))*dx - + # uniform traction on top boundary T = Constant((0, 1e-3)) l = dot(T, u_)*ds(1) -Symmetric boundary conditions are applied on the ``Top`` and ``Left`` boundaries +Symmetric boundary conditions are applied on the ``Top`` and ``Left`` boundaries and the problem is solved:: # symmetry boundary conditions @@ -135,12 +138,12 @@ and the problem is solved:: DirichletBC(V.sub(1), Constant(0.), facets, 3)] solve(a == l, u, bc) - + import matplotlib.pyplot as plt p = plot(sigma(u)[1,1]/T[1], mode='color') plt.colorbar(p) plt.title(r"$\sigma_{yy}$",fontsize=26) - + The :math:`\sigma_{xx}` and :math:`\sigma_{yy}` components should look like that: diff --git a/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt b/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt index d52f9e8..c3d082b 100644 --- a/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt +++ b/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt @@ -1,3 +1,6 @@ +.. raw:: html + +

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.. _ModalAnalysis: diff --git a/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_dg.py.rst.txt b/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_dg.py.rst.txt index 6e4ab39..fa70b4f 100644 --- a/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_dg.py.rst.txt +++ b/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_dg.py.rst.txt @@ -1,3 +1,6 @@ +.. raw:: html + +

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.. _ReissnerMindlinDG: diff --git a/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_quads.py.rst.txt b/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_quads.py.rst.txt index cb192fd..3fd1a0f 100644 --- a/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_quads.py.rst.txt +++ b/doc/_build/html/_sources/demo/reissner_mindlin/reissner_mindlin_quads.py.rst.txt @@ -1,3 +1,6 @@ +.. raw:: html + +

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.. _ReissnerMindlinQuads: diff --git a/doc/_build/html/_sources/intro.rst.txt b/doc/_build/html/_sources/intro.rst.txt index 362f765..3f00475 100644 --- a/doc/_build/html/_sources/intro.rst.txt +++ b/doc/_build/html/_sources/intro.rst.txt @@ -11,10 +11,10 @@ What is it about ? ------------------------ -These numerical tours will introduce you to a wide variety of topics in -computational continuum and structural mechanics using the finite element software FEniCS. +These numerical tours will introduce you to a wide variety of topics in +computational continuum and structural mechanics using the finite element software FEniCS. Many covered topics can be considered as standard and will help the reader in -getting started with FEniCS using solid mechanics examples. +getting started with FEniCS using solid mechanics examples. Other topics will also be more exploratory and will reflect currently investigated research topics, illustrating the versatility of FEniCS. @@ -22,33 +22,40 @@ 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. +-------------------- +Citing and license +-------------------- + 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}, + @article{bleyer2018numericaltours, + title={Numerical Tours of Computational Mechanics with FEniCS}, + DOI={10.5281/zenodo.1287832}, + publisher={Zenodo}, + author={Jeremy Bleyer}, year={2018}} +All this work is licensed under the `Creative Commons Attribution-ShareAlike 4.0 International License `_ |license|. + +.. |license| image:: https://i.creativecommons.org/l/by-sa/4.0/88x31.png ----------------------- -How do I get started ? +How do I get started ? ----------------------- -You can find instructions on how to install FEniCS on the FEniCS project website -http://fenicsproject.org. In the following numerical tours, we will use the +You can find instructions on how to install FEniCS on the FEniCS project website +http://fenicsproject.org. In the following numerical tours, we will use the Python interface for the different FEniCS scripts. These demos have been written using FEniCS 2017.2.0 but many should work with older versions. -FEniCS is also distributed along with an important number of documented or -undocumented examples, some of them will be revisited in these tours but do not +FEniCS is also distributed along with an important number of documented or +undocumented examples, some of them will be revisited in these tours but do not hesitate over looking at other interesting examples. -In the following, we will assume that readers possess basic knowledge of FEniCS commands. +In the following, we will assume that readers possess basic knowledge of FEniCS commands. In particular, we advise you to go first through the documentation and tutorials https://fenicsproject.org/tutorial/ if this is not the case. @@ -56,9 +63,9 @@ if this is not the case. About the author ---------------------- -`Jeremy Bleyer `_ is a researcher -in Solid and Structural Mechanics at `Laboratoire Navier `_, -a joint research unit of `Ecole Nationale des Ponts et Chaussées `_, +`Jeremy Bleyer `_ is a researcher +in Solid and Structural Mechanics at `Laboratoire Navier `_, +a joint research unit of `Ecole Nationale des Ponts et Chaussées `_, `IFSTTAR `_ and `CNRS `_ (UMR 8205). email: jeremy.bleyer@enpc.fr diff --git a/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html b/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html index 8be996a..000fd76 100644 --- a/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html +++ b/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html @@ -51,8 +51,8 @@
-
-

Elasto-plastic analysis of a 2D von Mises material¶

+

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+

Elasto-plastic analysis of a 2D von Mises material¶

Introduction¶

This example is concerned with the incremental analysis of an elasto-plastic @@ -410,6 +410,7 @@ when considering a zero hardening modulus.

  • Introduction diff --git a/doc/_build/html/demo/elasticity/2D_elasticity.py.html b/doc/_build/html/demo/elasticity/2D_elasticity.py.html index d8b290f..4fa50fe 100644 --- a/doc/_build/html/demo/elasticity/2D_elasticity.py.html +++ b/doc/_build/html/demo/elasticity/2D_elasticity.py.html @@ -51,7 +51,7 @@
    -
    +

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    2D linear elasticity¶

    Introduction¶

    @@ -220,6 +220,7 @@ writing/reading. Prefered output format is now .xdmf:

    • Introduction diff --git a/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html b/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html index 75109eb..2932a80 100644 --- a/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html +++ b/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html @@ -217,7 +217,7 @@ div.nboutput div.output_area.stderr { .ansi-bold { font-weight: bold; } .ansi-underline { text-decoration: underline; } -
      +

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      The corresponding files can be obtained from:

      • Jupyter Notebook: axisymmetric_elasticity.ipynb
      • @@ -2805,6 +2805,7 @@ if (IPython.notebook.kernel != null) {
        • Introduction diff --git a/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html b/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html index 0d4fbf3..032ca66 100644 --- a/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html +++ b/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html @@ -51,7 +51,7 @@
          -
          +

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          Orthotropic linear elasticity¶

          Introduction¶

          @@ -198,6 +198,7 @@ that:

          • Introduction diff --git a/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html b/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html index 8af8582..d47a170 100644 --- a/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html +++ b/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html @@ -51,7 +51,7 @@
            -

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