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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

Geometry of the :math:`(m)` beam:



 :math:`L=1.5`

 :math:`R=0.005`

 :math:`{e}_{p}=0.0005`

Coordinates of points :math:`(m)`:

 :math:`A:(0.0\mathrm{,0}.0\mathrm{,0}.0)`

 :math:`B:(1.\mathrm{,0}.0\mathrm{,0}.0)`

 :math:`C:(1.38\mathrm{,0}.0\mathrm{,0}.0)`

 :math:`D:(1.5\mathrm{,0}.0\mathrm{,0}.0)`


Elastic properties of the material
---------------------------------


* :math:`E=2.0E11\mathrm{Pa}` Young's module


* :math:`\nu =0.3` Poisson's ratio


* :math:`\rho =7900.0{\mathrm{kg.m}}^{-3}` Density


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


* Imposed travel:


* All knots: :math:`\mathrm{DRX}=\mathrm{DRY}=\mathrm{DX}=\mathrm{DZ}=0.0`


* Point :math:`A`: :math:`\mathrm{DY}=\mathrm{DRZ}=0.0`


* Imposed loading:


* Point :math:`B`: random force according to :math:`Y`


* Point :math:`B`: random moment around :math:`Z`


*
    *
        * Obstacle (CERCLE) at point :math:`D`:


    * Game = :math:`0m`


    * standard = :math:`(1.\mathrm{,0}\mathrm{.}\mathrm{,0}\mathrm{.})`


    * origin = :math:`(1.\mathrm{,0}\mathrm{.}\mathrm{,0}\mathrm{.})`


    * Normal stiffness: :math:`\mathrm{RIGI}\text{\_}\mathrm{NOR}={10}^{6}N/m`


    * Friction COULOMB: :math:`\mathrm{COULOMB}=0.3`


.. image:: images/10000200000000D3000000BFD454EEF2F09DD44D.png
    :width: 1.7717in
    :height: 1.6138in


.. _RefImage_10000200000000D3000000BFD454EEF2F09DD44D.png:


*
    *
        * Obstacle (DISCRET) at point :math:`C`:


    * standard = :math:`(1.\mathrm{,0}\mathrm{.}\mathrm{,0}\mathrm{.})`


    * origin = :math:`(1.\mathrm{,0}\mathrm{.}\mathrm{,0}\mathrm{.})`


    * Normal stiffness: :math:`\mathrm{RIGI}\text{\_}\mathrm{NOR}=100.N/m`


    * Friction COULOMB: :math:`\mathrm{COULOMB}=0.3`


.. image:: images/10000200000000EC000000D2D271F1830265DD60.png
    :width: 1.8154in
    :height: 1.6138in


.. _RefImage_10000200000000EC000000D2D271F1830265DD60.png:


*
    * Game1 = :math:`1.0m`


    * Game2 = :math:`1.5m`