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


Geometry
---------


.. image:: images/100000000000030C00000196EE0254946265879F.png
    :width: 5.2744in
    :height: 2.6752in


.. _RefImage_100000000000030C00000196EE0254946265879F.png:

Side :math:`a=\mathrm{1m}`

Thickness :math:`t=\mathrm{0.01m}`

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


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," "," :math:`D` "," "," :math:`G` "," :math:`H` "," :math:`I` "," :math:`J` "," :math:`K`"
    ":math:`x` ", "0. ", "1. ", "1. ", "0. ", "0.5", "0.25", "0.75", "0.75", "0.25"
    ":math:`y` ", "0. ", "0. ", "1. ", "1. ", "0.5", "0.25", "0.25", "0.25", "0.75", "0.75"
    ":math:`z` ", "0. ", "0. ", "0. ", "0. ", "0. ", "0. ", "0. ", "0. ", "0."



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

:math:`E=2.1{10}^{11}\mathrm{Pa}` :math:`\nu =0.3` :math:`\rho =7800\mathrm{kg}/{m}^{3}`


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

Case 1: recessed side :math:`\mathrm{AB}`

for any :math:`P` point such as :math:`{y}_{P}=0`:

:math:`\begin{array}{}u=v=w=0.\\ {\theta }_{x}={\theta }_{y}={\theta }_{z}=0.\end{array}`

Cas2: free plate


Initial conditions
--------------------

Not applicable for modal analysis