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


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Geometry
---------

Coordinates of points :math:`(m)`:


* :math:`A(0.,0.)`


* :math:`B(1.,0.)`


* :math:`C(1.,1.)`


* :math:`D(0.,1.)`


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

Elastic


* :math:`E=178000\mathrm{MPa}` Young's module


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

LEMAITRE


* :math:`n=9.7`


* :math:`K=1920.`


* :math:`\frac{1}{m}=0.`


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

Imposed displacement :math:`(m)`:


* :math:`\mathrm{AB}`: :math:`\mathrm{DY}=0`


* :math:`\mathrm{AD}`: :math:`\mathrm{DX}=0`

Loading


* Uniform pressure on :math:`\mathrm{BC}`: :math:`{\sigma }_{1}`


* Uniform pressure on :math:`\mathrm{CD}`: :math:`{\sigma }_{2}`


* Routes :math:`\mathrm{OA},\mathrm{AB},\mathrm{CD},\mathrm{DE}` and :math:`\mathrm{EF}` lasting 30 seconds


* Trip :math:`\mathrm{BC}` lasting 60 seconds


* Hold time in :math:`A,B` and :math:`D` of 3600 seconds


*


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