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


Geometry
---------

Consider the following structure:


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

The tube has an outer radius :math:`{R}_{\mathit{ext}}=11.11{10}^{-3}m` and a thickness of :math:`\mathit{ep}=1.27{10}^{-3}m`


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

The material is isotropic elastic whose properties are:


* :math:`E=2.056{10}^{11}\mathit{Pa}`


* :math:`\nu \mathrm{=}0.3`


* :math:`\rho \mathrm{=}8357\mathit{kg}\mathrm{/}{m}^{3}`


* Shock stiffness: :math:`{K}_{\mathit{choc}}=4{10}^{6}N/m`


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

The game at the ring contact level is :math:`e=2.9{10}^{-4}m`.

Ring contacts have been removed from :math:`0.1e` of the contact nodes.