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


Geometry
---------

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

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

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

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

 :math:`D:(0.\mathrm{,1}\mathrm{.})`


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


* Mechanics

:math:`E=1.N/{m}^{2}`

:math:`\nu =0.`

:math:`\alpha =1.°{C}^{-1}`


*
    *


* Thermal

:math:`\lambda =1.w/m/°C`

:math:`\rho \mathit{cp}\mathrm{=}1.J\mathrm{/}{m}^{3}°C`


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


* Compulsory trips:


* :math:`A`: :math:`\mathrm{DX}=\mathrm{DY}=0.`


* :math:`B`: :math:`\mathrm{DY}=0.`


* Imposed thermal load:


    *

Two homogeneous thermal evolutions in space are defined:

:math:`\mathrm{ch1}` is a rise in temperature from 10 degrees to 17 degrees :math:`[0.,0.7s]`

:math:`\mathrm{ch2}` is a drop in temperature from 17 degrees to 14 degrees :math:`[0.,0.3s]`

Cycle :math:`[\mathrm{ch1}+\mathrm{ch2}]` is staggered to form the interval :math:`[1.5,2.5s]`. This cycle is repeated periodically and the mechanical calculation is performed over the interval :math:`[0.5,4.5s]`.


*