.. _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 LamÃ© 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:: /../doc/images/gallery/linear_elasticity-linear_elastic.png :download:source code  .. literalinclude:: /../examples/linear_elasticity/linear_elastic.py