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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

Thickness = :math:`\mathrm{0.1m}`.


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

The material is isotropic elastic whose properties are:


* :math:`E\mathrm{=}20000\mathit{Pa}`


* :math:`\nu \mathrm{=}0.3`


* :math:`\alpha \mathrm{=}{10}^{\mathrm{-}5}\mathrm{/}°C`


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

Boundary conditions:


* On edges :math:`\mathit{AB}` and :math:`\mathit{CD}`: :math:`\mathit{DX}\mathrm{=}\mathit{DZ}\mathrm{=}0`


* On edge :math:`\mathit{BC}`: :math:`\mathit{DY}\mathrm{=}0`

Loading


* The load applied is a loading temperature


    * Constant following :math:`X` and :math:`Z`


    * Variable along the :math:`Y` axis: :math:`T(Y)\mathrm{=}\mathrm{50Y}\mathrm{-}50`


.. image:: images/Shape2.gif


.. _RefSchema_Shape2.gif:


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

Néant