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


Geometry
---------

The configuration studied consists of two coaxial cylindrical shells 4 meters high:


.. image:: images/100014EE000069F000004D1A83A95521F092C3B2.svg
    :width: 272
    :height: 200


.. _RefImage_100014EE000069F000004D1A83A95521F092C3B2.svg:

The inner shell has an average radius of :math:`1m` and a thickness of :math:`1\mathrm{cm}`.

The outer shell has an average radius of :math:`\mathrm{1,10}m` and a thickness of :math:`1\mathrm{cm}`.


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

The material that makes up the two shells is steel. Its physical characteristics are:


.. csv-table::

    ":math:`\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}` "," :math:`E\mathrm{=}2.{10}^{11}\mathit{Pa}` "," :math:`\nu \mathrm{=}\mathrm{0,3}`"



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

The support conditions are the same for both shells: ends embedded in the lower part (:math:`z\mathrm{=}0`) and free ends in the upper part (:math:`z\mathrm{=}4m`).