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=== Hyperelasticity === | === Hyperelasticity === | ||
This time we compare the code with the c++ version of DOLFIN. | This time we compare the code with the c++ version of DOLFIN. The problem for an elastic material can be expressed as a minimization problem | ||
[[File:HyperElasticity.png]] | <math> \min_{u \in V} \Pi</math> | ||
<math> \Pi = \int_{\Omega} \psi(u) \, {\rm d} x - \int_{\Omega} B \cdot u \, {\rm d} x - \int_{\partial\Omega} T \cdot u \, {\rm d} s</math> | |||
where \Pi is the total potential energy, \psi is the elastic stored energy, \B is a body force and \T is a traction force. | |||
A complete description of the problem is avilable on the [http://fenicsproject.org/documentation/dolfin/1.2.0/cpp/demo/pde/hyperelasticity/cpp/documentation.html Fenics website.] The final solution will look like this | |||
[[File:HyperElasticity.png|Alignment = center]] | |||
{{Code|HyperElasticity Problem: the ufl file|<syntaxhighlight lang="octave" style="font-size:13px"> | {{Code|HyperElasticity Problem: the ufl file|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
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</div> | </div> | ||
<div style="clear:both"></div> | <div style="clear:both"></div> | ||
=== Incompressible Navier-Stokes equations === | === Incompressible Navier-Stokes equations === | ||