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


Geometry
---------


.. image:: images/100009BA0000191D00001A9031085C6B3F5E32A3.svg
    :width: 324
    :height: 342


.. _RefImage_100009BA0000191D00001A9031085C6B3F5E32A3.svg:

The length of the beams is worth: :math:`L=1m`

The beams have a circular cross section:


* radius: :math:`R=0.1m`


* thickness: :math:`\mathrm{ep}=0.01m`

The play between the beams is worth: :math:`\mathrm{Jeu}=1{10}^{-3}m`


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

:math:`E=1.{10}^{10}\mathrm{Pa}`

:math:`\nu =0.3`

:math:`\rho =1.{10}^{8}\mathrm{kg}/{m}^{3}`

The stiffness of the contact spring is: :math:`{K}_{c}={1.10}^{8}N/m`


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

On the whole structure: :math:`\mathrm{DX}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0`.

At the upper and lower ends of the beams: :math:`\mathrm{DY}=\mathrm{DRZ}=0`.

In the middle of the left beam: from moment :math:`t=0s`, :math:`\mathrm{Fy}=–1.{10}^{6}N`


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

Structure initially at rest.