.. _linear_elasticity-linear_elastic: linear_elasticity/linear_elastic.py =================================== **Description** Linear elasticity with given displacements. Find :math:`\ul{u}` such that: .. math:: \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) = 0 \;, \quad \forall \ul{v} \;, where .. math:: D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl} \;. This example models a cylinder that is fixed at one end while the second end has a specified displacement of 0.01 in the x direction (this boundary condition is named ``'Displaced'``). There is also a specified displacement of 0.005 in the z direction for points in the region labeled ``'SomewhereTop'``. This boundary condition is named ``'PerturbedSurface'``. The region ``'SomewhereTop'`` is specified as those vertices for which:: (z > 0.017) & (x > 0.03) & (x < 0.07) The displacement field (three DOFs/node) in the ``'Omega region'`` is approximated using P1 (four-node tetrahedral) finite elements. The material is linear elastic and its properties are specified as Lamé parameters :math:`\lambda` and :math:`\mu` (see http://en.wikipedia.org/wiki/Lam%C3%A9_parameters) The output is the displacement for each vertex, saved by default to cylinder.vtk. View the results using:: $ ./postproc.py cylinder.vtk --wireframe -b --only-names=u -d'u,plot_displacements,rel_scaling=1' .. image:: /../gallery/images/linear_elasticity-linear_elastic.png :download:`source code ` .. literalinclude:: /../examples/linear_elasticity/linear_elastic.py