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


Geometry
---------

The geometry is a beam with a length of 7 m and a rectangular cross section whose neutral fiber is carried by the X axis. The height of the beam is 10 cm. The width of the beam is 15 cm.


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

**Beam:**

.. csv-table::

    "Stiffness", ":math:`E=210{10}^{9}\mathit{Pa}` :math:`\mathrm{\nu }=0.3`"
    "Density", ":math:`\mathrm{\rho }=7800\mathit{kg}/{m}^{3}`"


Boundary conditions
----------------------

The beam is embedded at its end in :math:`x=0`.

The beam is stuck at the nodes on the neutral fiber with abscissa :math:`x=2.5m`, :math:`x=4m`, :math:`x=6m` and :math:`x=7m`. 


Loads
-----------

The simulation lasts 2 seconds.

The impact lasts 0.02s, has a triangular temporal profile, has an amplitude of :math:`F_z=1000N` and is applied to the node on the neutral fiber with abcissa :math:`x=2.5m`.


Meshing
---------

The mesh consists of 280 linear hexahedra. 


Method 
--------

The calculation is carried out in linear transient dynamics on a modal basis enriched with static modes at the blocked nodes.