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


Geometry
---------

The geometry for this test is a square plate in plane :math:`(x,y)` rotated :math:`30°` with respect to :math:`x` around :math:`z`.


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

Z

Y

.. image:: images/100001CE000014AC000014ACC2F60BD416CBDA3E.svg
    :width: 12
    :height: 12


.. _RefImage_100001CE000014AC000014ACC2F60BD416CBDA3E.svg:

**

.. image:: images/Object_1.svg
    :width: 12
    :height: 12


.. _RefImage_Object_1.svg:

X


.. image:: images/Object_2.svg
    :width: 12
    :height: 12


.. _RefImage_Object_2.svg:

We call

.. image:: images/Object_3.svg
    :width: 12
    :height: 12


.. _RefImage_Object_3.svg:

the length of the deformed plate, we will note :math:`x,y,z` the coordinates of the deformed configuration and :math:`X,Y,Z` the coordinates of the initial configuration


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

We take

.. image:: images/Object_4.svg
    :width: 12
    :height: 12


.. _RefImage_Object_4.svg:


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

We block nodes :math:`\mathit{No1}`, :math:`\mathit{No5}`, and :math:`\mathit{No2}` so that :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}\mathit{DRX}\mathrm{=}\mathit{DRY}\mathrm{=}\mathit{DRZ}\mathrm{=}0`,

and a local displacement :math:`\mathit{Dx}\mathrm{=}100.` is imposed on the nodes :math:`\mathit{No3}`, :math:`\mathit{No4}` and :math:`\mathit{No7}`.