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


Geometry
---------

Consider a square with a side of :math:`1m`, shown below:


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


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

The square has anisotropic membrane behavior, characterized by the following coefficients (the coefficients not mentioned are zero):

:math:`\mathrm{\{}\begin{array}{c}{M}_{\mathit{LLLL}}\mathrm{=}3\\ {M}_{\mathit{TTTT}}\mathrm{=}3\\ {M}_{\mathit{LLTT}}\mathrm{=}1\\ {M}_{\mathit{LTLT}}\mathrm{=}2\end{array}`

These coefficients are defined in a coordinate system rotated by 90° around the :math:`(\mathit{Oz})` axis.


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

Two calculations are carried out, corresponding to a tensile stress and a shear load of the membrane. The corresponding limit conditions are shown below:


* **Traction solicitation**

:math:`\mathrm{\{}\begin{array}{c}{u}_{Z}\mathrm{=}0\text{sur}\text{FACE}\\ {u}_{X}\mathrm{=}0\text{sur}\text{X\_NEG}\\ {u}_{Y}\mathrm{=}0\text{sur}\text{Y\_NEG}\\ {F}_{X}\mathrm{=}1\text{sur}\text{X\_POS}\end{array}`


* **Shear load**

:math:`\mathrm{\{}\begin{array}{c}{u}_{Z}\mathrm{=}0\text{sur}\text{FACE}\\ {u}_{Y}\mathrm{=}0\text{sur}\text{X\_NEG}\\ {u}_{X}\mathrm{=}0\text{sur}\text{Y\_NEG}\\ {u}_{X}\mathrm{=}{u}_{Y}\text{sur}\text{POINT}\\ {F}_{Y}\mathrm{=}1\text{sur}\text{X\_POS}\\ {F}_{X}\mathrm{=}1\text{sur}\text{Y\_POS}\end{array}`