Introduction
============


Geometry
---------

The study concerns a thick steel plate. Its geometry is simple. It is a simple flattened cube:

length :math:`\mathrm{2,0}` meters, width :math:`\mathrm{2,0}` meters and thickness :math:`\mathrm{0,03}` meters [].

The plate is firmly embedded on one of its sides (ENCAS) and fixed on a vibrating table.

We want to calculate the displacement of a point located on the upper face in a corner of a plate, opposite to the embedment (point P) [].


.. image:: images/Object_12.png
    :width: 5.4917in
    :height: 2.672in


.. _RefSchema_Object_12.png:

Figure 1.1-1


.. image:: images/Object_2.png
    :width: 3.998in
    :height: 2.8354in


.. _RefSchema_Object_2.png:

Figure 1.1-2


Materials
---------

For linear analyses, steel is considered to be an isotropic, linear elastic material:


* Young's modulus: :math:`E\mathrm{=}200000.{10}^{+6}\mathit{Pa}`,


* Poisson's ratio: :math:`\nu \mathrm{=}\mathrm{0,3}`,


* density: :math:`\rho \mathrm{=}8000\mathit{kg}\mathrm{/}{m}^{3}`

For non-linear analysis, this is a VMIS_ISOT_LINE behavior with :math:`\text{D\_SIGM\_EPSI}=2\mathit{GPa}` (Young's modulus divided by 100) and an elastic limit :math:`\mathit{SY}=200\mathit{MPa}`.


Boundary conditions and loading
------------------------------------

The plate is embedded on one of its sides.

The input signal is a simple sine with frequency :math:`15\mathit{Hz}`.

The amplitude is :math:`\mathrm{30g}` horizontally and :math:`\mathrm{30g}` vertically downwards (:math:`g=10m/{s}^{2}`).

The duration of the signal is :math:`0.5s`.