Commit 411bbced authored by Jeremy BLEYER's avatar Jeremy BLEYER

Some polishing and added tips and tricks section

parent 1028fd84
=========================
2D elasticity in Fenics
=========================
:math:`\int_{\Omega}\underline{\underline{\sigma}}:\underline{\underline{\varepsilon}}[v]d\Omega`
=========================
2D elasticity in Fenics
=========================
......@@ -15,6 +15,7 @@ Contents:
linear_problems
nonlinear_problems
demo/reissner_mindlin/reissner_mindlin.rst
tips_and_tricks
Tips and Tricks
================
In construction...
.. _TipsTricksProjection:
------------------------------------------------
Efficient projection on DG or Quadrature spaces
------------------------------------------------
For projecting a Function on a DG or Quadrature space, that is a space with no coupling between elements, the projection can be performed element-wise. For this purpose, using the LocalSolver is much faster than performing a global projection::
metadata={"quadrature_degree": deg}
def local_project(v,V):
dv = TrialFunction(V)
v_ = TestFunction(V)
a_proj = inner(dv,v_)*dx(metadata=metadata)
b_proj = inner(v,v_)*dx(metadata=metadata)
solver = LocalSolver(a_proj,b_proj)
solver.factorize()
u = Function(V)
solver.solve_local_rhs(u)
return u
Local factorizations can be cached if projection is performed many times.
......@@ -259,7 +259,7 @@ the stress and strain tensors. These nonlinear expressions must then be projecte
back onto the associated Quadrature spaces. Since these fields are defined locally
in each cell (in fact only at their associated Gauss point), this projection can
be performed locally. For this reason, we define a ``local_project`` function
that use the ``LocalSolver`` to gain in efficiency (see also :ref:`TipsStressProjection`_)
that use the ``LocalSolver`` to gain in efficiency (see also :ref:`TipsTricksProjection`)
for more details::
def local_project(v, V, u=None):
......
###############
Linear problems
###############
Elastostatics :
standard continuous galerkin
* 2D plane stress/strain
* 3D isotropic, orthotropic
discontinous galerkin
-> volumetric locking
mixed formulation using Hu-Wahizu
-> volumetric locking
Elastodynamics
* time integration Newmark scheme, theta
* modal analysis with SLEPC
Poroelasticity
Mixing continuum and interfaces
* elastic interfaces/supports (beam on elastic foundation)
Linear Fracture Mechanics
* G-theta method to compute J-integral and stress intensity factors
Homogenization in elasticity
-> treatment of rigid particles with Lagrange multipliers
Linear Buckling
##################
Nonlinear problems
##################
Hyperelasticity :
-> compressible neo-hookean
-> incompressible neo-hookean
Viscoelasticity
* Maxwell model
* Kelvin-Voigt model
Elasto-plasticity
* radial return for von Mises/Drucker Prager
* limit analysis with augmented Lagrangian
Viscoplasticity
* yield stress fluids
Contact
* resolution of normal contact with TAO
* contact with AL
Von-Karman plates
################
Beams and Plates
################
Love-Kirchhoff plates with DG
Reissner-Mindlin plates
Higher-order plate models (warping, Bending-Gradient)
#####
Misc
#####
Topology Optimization
(undocumented example)
Linear Matching Method
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