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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

Geometry of plate :math:`(m)`:

 :math:`L=1`

 :math:`e=0.001` thickness

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

 :math:`O(0.0,0.0)`

 :math:`E(-0.1,-0.1)`

Mesh group:

 :math:`\mathrm{CONT}\text{\_}\mathrm{NO}`: :math:`\mathrm{AB},\mathrm{BC},\mathrm{CD},\mathrm{DA}` sides

 :math:`\mathrm{COND2}\text{\_}\mathrm{NO}`: Face :math:`\mathrm{ABCD}` except point :math:`E`


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


* :math:`E=7.1E10\mathrm{Pa}` Young's module


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


* :math:`\rho =7820.0{\mathrm{kg.m}}^{-3}` Density


* :math:`\mathrm{AMOR}\text{\_}\mathrm{ALPHA}=0.5{\mathrm{N.s.m}}^{-1}`


* :math:`\mathrm{AMOR}\text{\_}\mathrm{BETA}=0.1{\mathrm{N.kg}}^{-1}`


    *
        *

The coefficients :math:`\alpha` and :math:`\beta` make it possible to build a viscous damping matrix that is proportional to stiffness and mass: :math:`[C]=\alpha [K]+\beta [M]`.


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


*
    * Imposed travel:


*
    *
        *
            * :math:`\mathrm{CONT}\text{\_}\mathrm{NO}`: zero movements and rotations


            * :math:`\mathrm{COND2}\text{\_}\mathrm{NO}`: zero movements and rotations


*
    *
        * Excitation force :math:`(N)`:


*
    *
        *
            * Point :math:`E`: :math:`\mathrm{Fz}=1`