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


YGéométrie
----------

C

D

X

A

B

L=20 cm

Thickness = :math:`\mathrm{0.25cm}`.


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

The material is isotropic elastic whose properties are:


* :math:`E\mathrm{=}3.\mathrm{\times }{10}^{6}N\mathrm{/}{\mathit{cm}}^{2}`


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


* :math:`\alpha \mathrm{=}6.5\mathrm{\times }{10}^{\mathrm{-}6}\mathrm{/}°C`


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

Boundary conditions:


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


* On edge :math:`\mathit{AD}`: :math:`\mathit{DX}\mathrm{=}\mathit{DRY}\mathrm{=}0`


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

Loading


* The load applied is a loading temperature that varies as follows:

Upper skin: :math:`T(x,y)\mathrm{=}100\mathrm{-}5∣x∣\mathrm{-}5∣y∣+\frac{1}{2}∣\mathit{xy}∣`

Lower skin: :math:`T(x,y)\mathrm{=}\mathrm{-}100+5∣x∣+5∣y∣\mathrm{-}\frac{1}{2}∣\mathit{xy}∣`


.. image:: images/Shape16.gif


.. _RefSchema_Shape16.gif:


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

Néant