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


Geometry
---------


.. image:: images/100025FC0000253500001231512A7A40525EAA29.svg
    :width: 480
    :height: 234


.. _RefImage_100025FC0000253500001231512A7A40525EAA29.svg:

Side :math:`a=1.m`, thickness :math:`t=0.01m`, :math:`\alpha =30°`

**Point coordinates** (in :math:`m`):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," :math:`D`"
    ":math:`x` ", "0. "," :math:`a` "," :math:`a(1+\mathrm{sin}\alpha )` "," :math:`a\mathrm{sin}\alpha`"
    ":math:`y` ", "0. ", "0. "," :math:`a\mathrm{cos}\alpha` "," :math:`a\mathrm{cos}\alpha`"
    ":math:`z` ", "0. ", "0. ", "0. ", "0."



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

:math:`E=2.1{10}^{\mathrm{11 }}\mathrm{Pa}`

:math:`\nu =0.3`

:math:`\rho =7800.\mathrm{kg}/{m}^{3}`


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

Embedded 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}`


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

Not applicable for modal analysis.