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


Geometry
---------


.. image:: images/100020AE0000254F00001653987876792F1F7F49.svg
    :width: 481
    :height: 288


.. _RefImage_100020AE0000254F00001653987876792F1F7F49.svg:

internal radius :math:`a=0.1m`

outer radius :math:`b=0.2m`

Point coordinates:


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," "," :math:`D` "," :math:`E` "," :math:`F`"
    ":math:`x` ", "0.100", "0.200"," :math:`0.1\mathrm{cos}(22.5)` "," "," :math:`0.2\mathrm{cos}(22.5)` "," :math:`1/\sqrt{2}` "," :math:`\sqrt{2}`"
    ":math:`y` ", "0. ", "0. "," :math:`0.1\mathrm{sin}(22.5)` "," :math:`0.2\mathrm{sin}(22.5)` "," :math:`1/\sqrt{2}` "," :math:`\sqrt{2}`"
    ":math:`z` ", "0. ", "0. ", "0. ", "0. ", "0. ", "0."



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

:math:`E=26N/{m}^{2}`

:math:`\nu =0.3`

:math:`\rho =35\mathrm{Kg}/{m}^{3}`

There is nothing physical about the very low value of Young's modulus.


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


.. csv-table::

    "Internal pressure :math:`P=p{e}^{j\omega t}` ", "with :math:`p=1\mathrm{Mpa}` ", "and", ":math:`\omega =0.2\mathrm{rad}/s`"



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


* without initial conditions,


* direct calculation of the harmonic solution.