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

Geometry
---------

A rectangular plate of width :math:`a` and length :math:`b`, supported on a spring mat.


.. image:: images/100030FA000069D50000217DD7F22CAC5AE4B35F.svg
    :width: 584
    :height: 184


.. _RefImage_100030FA000069D50000217DD7F22CAC5AE4B35F.svg:

**Figure** 1.1-a **: Diagram of the plate and springs in the plane** :math:`(y,z)` **.**

Dimensions:

:math:`a=1.00m`

:math:`b=2.00m`

:math:`\mathrm{ep}=0.30m`


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

Young's module: :math:`2.0E+11\mathit{Pa}`

Poisson's ratio: :math:`0.3`

Overall spring pad stiffness: :math:`K\mathrm{=}10000.0N\mathrm{/}m`

Spring pad stiffness density: :math:`k=\frac{K}{(ab)}=5000N/{m}^{3}`


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

The load is a pressure loading of the form :math:`P=\mathrm{p.}{(y-b)}^{2}`, with :math:`p=\mathrm{5N}/{m}^{4}`

Displacements imposed on the ends of the springs not connected to the plate:

• in the time interval :math:`[0,1]` the displacement is imposed to 0.0 according to :math:`\mathit{DX}`, :math:`\mathrm{DY}` and :math:`\mathrm{DZ}`,

• in the time interval :math:`[1,2]` the move is imposed to 0.0 according to :math:`\mathrm{DX}` and :math:`\mathrm{DY}`.

Next :math:`\mathrm{DZ}` it is imposed by the :math:`\mathrm{Dz}=(t-1.0)\ast 0.5E-02` function.


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

Not applicable for static analysis.