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


Geometry
---------

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


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

     For models A, B, C, and D:


.. csv-table::

    ":math:`E=1\mathit{MPa}` ", "Young's module"
    ":math:`\mathrm{\nu }=0.15` ", "Poisson's ratio"


     For E, F, G, H, H, I, I, I, J, K, L, and M models:


.. csv-table::

    ":math:`E=1\mathit{MPa}` ", "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{BORDX}`, :math:`\text{BORDMX}`, :math:`\text{BORDY}`, :math:`\text{BORDMY}`,, :math:`\text{BORDZ}` and :math:`\text{ESCLAVE}`, 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

    Z\ mathrm {=}\ mathrm {-} 0.2\ mathrm {\ times} (1. + {X} ^ {2} + {Y} ^ {2})\ mathrm {-} 0.3


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

Néant


.. _refheading__31295122: