.. _linear_elasticity-linear_elastic_tractions: linear_elasticity/linear_elastic_tractions.py ============================================= **Description** Linear elasticity with pressure traction load on a surface and constrained to one-dimensional motion. Find :math:\ul{u} such that: .. math:: \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) = - \int_{\Gamma_{right}} \ul{v} \cdot \ull{\sigma} \cdot \ul{n} \;, \quad \forall \ul{v} \;, where .. math:: D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl} \;. and :math:\ull{\sigma} \cdot \ul{n} = \bar{p} \ull{I} \cdot \ul{n} with given traction pressure :math:\bar{p}. The function :func:verify_tractions() is called after the solution to verify that the inner surface tractions correspond to the load applied to the external surface. Try running the example with different approximation orders and/or uniform refinement levels: - the default options:: python simple.py examples/linear_elasticity/linear_elastic_tractions.py -O refinement_level=0 -d approx_order=1 - refine once:: python simple.py examples/linear_elasticity/linear_elastic_tractions.py -O refinement_level=1 -d approx_order=1 - use the tri-quadratic approximation (Q2):: python simple.py examples/linear_elasticity/linear_elastic_tractions.py -O refinement_level=0 -d approx_order=2 .. image:: /../doc/images/gallery/linear_elasticity-linear_elastic_tractions.png :download:source code  .. literalinclude:: /../examples/linear_elasticity/linear_elastic_tractions.py