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


Geometry
---------


.. image:: images/100002000000080000000627D5EC974C2438846E.png
    :width: 4.6429in
    :height: 3.5693in


.. _RefImage_100002000000080000000627D5EC974C2438846E.png:


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

The properties of the material constituting the plate are:


.. csv-table::

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



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

Boundary conditions: Embedded :math:`\mathit{AD}` side

We are looking for the successive states of equilibrium under the load imposed on side :math:`\mathit{BC}`:


.. csv-table::

    ":math:`p(t)={p}_{\mathrm{cr}}t` ", "", ""
    "with", ":math:`t` ", "pseudo_temps"
    "", ":math:`{p}_{\mathrm{cr}}` ", "Euler critical load"


The load applied corresponds to the critical load of Euler :math:`{p}_{\mathit{cr}}=\frac{{\mathrm{\pi }}^{2}EI}{4{L}^{2}}=\mathrm{1124,21}N`


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

Not applicable