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


Geometry
---------

We consider a unit element of dimension 2 (quadrangle) or 3 (cube) according to the modeling. The element thickness, when required, is :math:`\mathrm{1m}`.


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

The material is isotropic elastic, whose properties are:


* :math:`E\mathrm{=}1000\mathit{MPa}`


* :math:`\nu \mathrm{=}0.2`

For modeling E, the Poisson's ratio is zero.


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


Modeling A
~~~~~~~~~~~~~~~

The unit-dimensional cube is shown on the. The displacement of the various nodes is imposed in accordance with.




.. image:: images/Cadre1.gif


.. _RefSchema_Cadre1.gif:

Figure 1.3.1-1: Modeling geometry A

.. csv-table::

    "knot", ":math:`\mathit{DX}` "," :math:`\mathit{DY}` "," :math:`\mathit{DZ}`"
    ":math:`A` ", "0.0", "0.0", "0.0"
    ":math:`B` ", "1.0E-3", "0.0", "-6.0E-4"
    ":math:`C` ", "2,0E-3", "-2,0E-3", "-3,0E-3", "-3,0E-3"
    ":math:`D` ", "1,0E-3", "-2,0E-3", "-2,4E-3", "-2,4E-3"
    ":math:`E` ", "0.0", "2.2E-3", "3.0E-3", "3.0E-3"
    ":math:`F` ", "1,0E-3", "2,2E-3", "2,4E-3", "2,4E-3"
    ":math:`G` ", "2,0E-3", "2,0E-3", "2,0E-4", "0.0"
    ":math:`H` ", "1.0E-3", "2.0E-4", "6.0E-4", "6.0E-4"


**Table** 1.3.1-1 **: Moves of** nodes **s**

B, C, and D models
~~~~~~~~~~~~~~~~~~~~~~~~

The geometry of the unit-dimensional quadrangle corresponds to face :math:`\mathit{ABCD}` (). The displacement of the four nodes :math:`A`, :math:`B`, :math:`C` and :math:`D` is imposed in accordance with for the components :math:`X` and :math:`Y`, the component :math:`Z` being zero. When rotational degrees of freedom exist, they are stuck at point :math:`A`.


E modeling
~~~~~~~~~~~~~~~

The geometry of the unit-dimensional quadrangle corresponds to face :math:`\mathit{ABCD}` (). This is an axisymmetric model, whose axis is located :math:`\mathrm{1m}` away from the :math:`\mathit{AD}` edge. The movements of the nodes are zero, except for the :math:`Y` component of the points :math:`C` and :math:`D`, which is equal to :math:`\mathrm{1,0E-4}m`.


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

Néant