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


Geometry
---------


.. image:: images/10000E82000026F7000012B5B54AC533B3F9D619.svg
    :width: 502
    :height: 241


.. _RefImage_10000E82000026F7000012B5B54AC533B3F9D619.svg:

Coordinates of the points:


.. csv-table::

    "", ":math:`O` "," :math:`A` "," :math:`B` "," "," :math:`C` "," "," :math:`D` "," :math:`E` "," :math:`F`"
    ":math:`x` ", "0. ", "1. "," :math:`1/\sqrt{2}` ", "0. ", "0.5", "0. ", "0.4"
    ":math:`y` ", "0. ", "0. "," :math:`1/\sqrt{2}` ", "1. ", "0. ", "0.5", "0.4"
    ":math:`z` ", "0", "0. ", "0. ", "0. ", "0. ", "0. ", "0."



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

:math:`E=1\mathrm{Pa}` Young's module

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

:math:`\rho =1\mathrm{kg}/{m}^{3}` Density


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

Mounting on the edge of the plate:

at all :math:`P` points such as :math:`\mathrm{OP}=R`:: :math:`u=v=w=0`, :math:`{\theta }_{x}={\theta }_{y}={\theta }_{z}=0`.

For all the models, except the N model, we have the following loads:


.. csv-table::

    "FORCE_COQUE ", "Uniform pressure", ":math:`P=1N/{m}^{2}`"
    "FORCE_COQUE ", "Normal distributed load", ":math:`\mathrm{F3}=–1N/{m}^{2}`"
    "PESANTEUR "," :math:`g=10m/{s}^{2}` next :math:`Z` from where", ":math:`\mathrm{FZ}=\rho gt=–1N/{m}^{2}`"


These three charges lead to the same solution.

For the N modeling, a loading of pressure :math:`p=0.01172\mathit{MPa}` is imposed on the upper face which corresponds to a maximum displacement along :math:`Z` at the center of the plate of :math:`2\mathit{mm}` (application of the formula in the following paragraph in :math:`r=0`).