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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 501
    :height: 157


.. _RefImage_Object_1.svg:


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

The properties of the material from which the beam is made are:


.. csv-table::

    ":math:`E\mathrm{=}2.{10}^{11}\mathit{Pa}` ", "Young's modulus"
    ":math:`\nu \mathrm{=}0.3` ", "Poisson's ratio"


The material follows a perfectly plastic law of elastic behavior:


.. csv-table::

    ":math:`{\sigma }_{e}\mathrm{=}2.35{10}^{8}\mathit{Pa}` ", "Elastic limit"
    ":math:`{\varepsilon }_{e}\mathrm{=}1.175{10}^{\mathrm{-}3}` ", "Elastic deformation limit"



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


* Boundary conditions: :math:`\mathit{AB}` and :math:`\mathit{CD}` sides embedded


* Imposed move following :math:`Z` in :math:`E` (:math:`x\mathrm{=}L\mathrm{/}2`):

:math:`{\mathit{DZ}}_{e}\mathrm{=}{6.60910}^{\mathrm{-}3}m` (

.. image:: images/Object_6.svg
    :width: 501
    :height: 157


.. _RefImage_Object_6.svg:

)

:math:`\mathit{DZ}(E)` varies from :math:`0` to :math:`30{\mathit{DZ}}_{e}`


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

Not applicable