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


Geometry
---------


.. image:: images/10000000000003C0000002D09AB0F97673C6F9DF.png
    :width: 5.9055in
    :height: 2.4528in


.. _RefImage_10000000000003C0000002D09AB0F97673C6F9DF.png:

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

 :math:`A:(0.,6.\cdot {10}^{-3})`

 :math:`B:(48.\cdot {10}^{-\mathrm{3,}}6.\cdot {10}^{-3})`

 :math:`C:(48.\cdot {10}^{-\mathrm{3,}}-6.\cdot {10}^{-3})`

 :math:`D:(0.,-6.\cdot {10}^{-3})`

 Plate geometry (:math:`m`):

 Thickness: :math:`h=\mathrm{0,001}`

 Width: :math:`L=0.048`

 Height: :math:`H=0.012`

 Mesh group: :math:`\text{BORD\_CH}` right surface (:math:`\mathrm{BC}`)

 Mesh group: :math:`\mathrm{ENCAST}` left surface (:math:`\mathrm{AD}`)

 Mesh group: :math:`\mathrm{SURF}` inner surface


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


* :math:`E=3.\cdot {10}^{10}\mathrm{Pa}`


* :math:`\nu =0.25`


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


* Imposed travel:


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


* Charging:


    * Parabolic distribution over height, constant over thickness.


.. csv-table::

    ":math:`Y(m)` ", "-0.006", "-0.003", "-0.003", "0", "0.003", "0.006"
    "2D Shear Stress (:math:`\mathrm{Pa.m}`)", "0", "3.75E6", "3.75E6", "3.75E6", "0"




     The integration of this constraint on the height :math:`H` leads to a constraint resulting from :math:`80.{10}^{3}\mathrm{Pa.m}` which is noted :math:`P` in the following.