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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


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

Young's module: :math:`E\mathrm{=}{2.10}^{11}\mathit{Pa}`

Poisson's ratio: :math:`\nu =0.3`

Expansion coefficient: :math:`\alpha ={1.10}^{-5}°{C}^{-1}`


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

Sides :math:`\mathrm{AB}`, :math:`\mathrm{BC}`, :math:`\mathrm{CD}`, and :math:`\mathrm{DA}` are embedded. The temperature is constant on the upper side and is equal to :math:`{T}_{s}=100°C`.

The temperature is constant on the underside and is equal to :math:`{T}_{i}=0°C`; the temperature gradient is assumed to be linear in thickness.