Description
===========

Geometry
---------

We consider a beam with a length :math:`10m`, oriented to :math:`45°` in the plane :math:`\mathit{XOZ}`.


.. image:: images/100000000000018E0000014C292974E19F411B8D.png
    :width: 2.6744in
    :height: 2.1437in


.. _RefImage_100000000000018E0000014C292974E19F411B8D.png:

The section of the beam is rectangular, :math:`\mathrm{0,1}m` wide, :math:`\mathrm{0,2}m` high.


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

The material uses the following properties:


.. csv-table::

    "Young's module", ":math:`{E}_{b}\mathrm{=}1.0E+10\mathit{Pa}`"
    "Poisson's Ratio", ":math:`{\nu }_{b}\mathrm{=}0.25`"



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

Node :math:`O` is stuck moving in all directions and rotating around :math:`Y`. Node :math:`A` is stuck in motion according to :math:`Y`. In addition, the beam is forbidden to rotate on itself.

The movements of node :math:`A` are imposed as follows: :math:`\mathit{DX}\mathrm{=}\frac{\mathrm{-}\sqrt{2}}{2}\frac{t}{100}` and :math:`\mathit{DZ}\mathrm{=}\frac{\mathrm{-}\sqrt{2}}{2}\frac{t}{100}` with and with :math:`t` taking values from 0 to 1 in increments of :math:`0.1`.

A force of :math:`100N` according to :math:`Y` is applied to node :math:`C` (center of the beam) so that the beam moves in the direction :math:`Y`.


Reference
----------

The reference results are obtained with a non-linear calculation and a beam oriented along the :math:`X` axis. For this orientation the value of the spin angle always remains the same during the calculation, with and without re-updating the results are identical.

For the reference, the displacement imposed on node :math:`A` is: :math:`\mathit{DX}\mathrm{=}\mathrm{-}\frac{t}{100}`

The :math:`\mathit{DY}` displacement of node :math:`C` (center of the beam) gives the reference value.