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


Geometry
---------


.. image:: images/100000000000038A000002ADE16397DE6AC269A3.jpg
    :width: 6.5181in
    :height: 4.7571in


.. _RefImage_100000000000038A000002ADE16397DE6AC269A3.jpg:


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


.. csv-table::

    "**Beam:**", "Young's modulus:", ":math:`E={2.10}^{11}\mathrm{Pa}`"
    "", "Poisson's ratio:", ":math:`\nu \mathrm{=}0.3`"
    "", "density:", ":math:`\rho \mathrm{=}8000\mathit{kg}\mathrm{/}{m}^{3}`"
    "C**ontact:**", "penalty coefficients:", ":math:`{E}_{n}={10}^{14}\mathrm{Pa}`"
    "", "", ":math:`{E}_{t}=0`"
    "", "Coulomb coefficient:", ":math:`\mu =0`"



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

The problem is unidirectional according to :math:`z`.

We consider a quarter of the beam with the symmetry conditions: we block the movements

according to :math:`x` on map :math:`x=0` and travel according to :math:`y` on map :math:`y=0`.


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

At all the nodes of the beam mesh are imposed according to the :math:`z` axis:


* the initial move: :math:`{u}_{0}=2\mathrm{mm}`


* initial speed: :math:`{v}_{0}=-100m/s`