Reference problem
=====================


Geometry
---------

Geometry is a square with side :math:`L=100\mathrm{mm}`.

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Material properties
----------------------

The material is incompressible elastic and has the following properties:

:math:`E=100\mathrm{MPa}`

:math:`\nu =0.4999`


Boundary conditions and loads
-------------------------------------

Given the antisymmetric nature of the problem, only half of the massif is modelled with the following boundary conditions:

On :math:`\mathrm{OE}`:

:math:`\mathrm{DX}(\mathrm{OE})=0`

On :math:`\mathrm{OD}`:

:math:`\mathrm{DX}(O)=\mathrm{DY}(O)=0`

:math:`\mathrm{DX}(D)=0`

:math:`\mathrm{fsx}=\frac{\mathrm{8y}}{L}\mathrm{.}{\sigma }_{d}`

:math:`\mathrm{fsy}=-(1-\frac{{\mathrm{4y}}^{2}}{\mathrm{L²}})\mathrm{.}{\sigma }_{d}`

On :math:`\mathrm{BC}`:

:math:`\mathrm{fsy}=+(1-\frac{{\mathrm{4y}}^{2}}{\mathrm{L²}})\mathrm{.}{\sigma }_{d}`

With :math:`{\sigma }_{d}` a given constraint, which we will take equal to 1 in the test. :math:`{\sigma }_{d}=1\mathrm{MPa}`