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


Geometry
---------

We consider a square with side :math:`1m`.


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


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

     For A and B models:

.. csv-table::

    ":math:`E=1\mathit{MPa}` ", "Young's module"
    ":math:`\mathrm{\nu }=0.3` ", "Poisson's ratio"


     For C, D, E, and F models:

.. csv-table::

    ":math:`E=\mathrm{1MPa}` ", "Young's module"
    ":math:`\mathrm{\nu }=0.` ", "Poisson's ratio"



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

On edge :math:`\text{HAUT}`, a displacement is imposed (see paragraph :ref:`2 <RefHeading__31295122>`).

On edges :math:`\text{GAUCHE}`, :math:`\text{BAS}` and :math:`\text{DROITE}`, pressure is imposed (see paragraph :ref:`2 <RefHeading__31295122>`).

Throughout the domain, a force of volume is imposed (see paragraph :ref:`2 <RefHeading__31295122>`).

Surface :math:`\text{MAITRE}`, which is paraboloid in nature, is described by the equation:


.. math::
 :label: eq-1

    Y\ mathrm {=}\ mathrm {-} 0.05\ mathrm {\ times} {(X\ mathrm {-} 0.5)}} ^ {2}


Initial conditions
--------------------

Néant


.. _refheading__31295122: