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

Geometry
---------


.. image:: images/10000A360000286900000C672CE68324F7CC406D.svg
    :width: 521
    :height: 159


.. _RefImage_10000A360000286900000C672CE68324F7CC406D.svg:

The length of the beam is equal to: :math:`L=1m`

The section of the beam is full circular with radius: :math:`R=0.1m`

The gap between the beam and the elastic support is equal to: :math:`J={10}^{-4}m`


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

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

:math:`\nu =0.3`

:math:`\mathrm{\rho }={10}^{6}\mathit{kg}/{m}^{3}`

The stiffness of the contact spring is equal to: :math:`{K}_{c}={10}^{8}N/m`


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

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

At point :math:`A`: :math:`\mathrm{DY}=\mathrm{DRZ}=0`.

At the free end of the beam: from instant :math:`t=0s`, :math:`\mathrm{Fy}=–1000.N`


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

Structure initially at rest.