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


Geometry
---------


.. image:: images/100013D0000069D500004B73FCB24D9EA571DA94.svg
    :width: 351
    :height: 270


.. _RefImage_100013D0000069D500004B73FCB24D9EA571DA94.svg:

Side of the plate (square) :math:`a=\mathrm{0,04 }m`.

Position of the reference points under the contact surface (:math:`m`)


.. csv-table::

    "", ":math:`x` "," :math:`y` "," :math:`z`"
    ":math:`A` ", "0", "0", "0"
    ":math:`B` ", "0.00125", "0", "0"
    ":math:`C` ", "0.005", "0", "0"
    ":math:`D` ", "0.0075", "0", "0"
    ":math:`E` ", "0.01125", "0", "0"
    ":math:`R` ", "0.03875", "0", "0"



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

**Plaque**:

Poisson's ratio: :math:`\mathrm{0,2}`

Young's module: :math:`\mathrm{1,3}\ast {10}^{11}{\mathit{N.m}}^{-2}`

**Building** (only if it is modelled by elements of the same size as the plate):

Poisson's ratio: :math:`0.2`

Young's module: :math:`{10}^{16}{\mathit{N.m}}^{-2}`

The coefficient of friction under the rigid plane is :math:`\mu =1` **.**


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

The frame, when it has a dimension :math:`N-1` in relation to the dimension of the plate, is blocked:


* by a complete installation.

The frame, when it is of the same size as the plate, is blocked:


* in plane :math:`x=\mathrm{40 }\mathrm{mm}` for trips according to :math:`x` (symmetry of the problem);


* by embedding its underside.

The plate is stuck:


* in plane :math:`x=\mathrm{40 }\mathrm{mm}` for trips according to :math:`x` (symmetry of the problem);


* next :math:`Y` to the node located at the intersection of the plane of symmetry, the contact face and the plane :math:`Z=0` to prevent rigid body movements.

In 3D, to get back to a 2D problem:


* the next move :math:`Z` is blocked for all nodes.

The plate is subjected to two distributed pressures:


* a vertical acting on the top side: :math:`f=–5\ast {10}^{7}{\mathit{N.mm}}^{-2}`;


* a horizontal acting on the face initially in :math:`x=0`, :math:`F=15\ast {10}^{7}{\mathit{N.mm}}^{-2}`.