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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 624
    :height: 225


.. _RefImage_Object_1.svg:

Rectangular recessed plate in :math:`{P}_{1}{P}_{4}` and :math:`{P}_{1}{P}_{4}` subjected in :math:`{P}_{2}{P}_{3}` to a linear couple:

:math:`m=-{\mathrm{me}}_{y};m>0`


Material properties and cross-section characteristics
------------------------------------------------------

Elastic behavior:

:math:`E\mathrm{=}\text{12}\mathrm{\times }{\text{10}}^{6}\text{Pa};\nu \mathrm{=}0`

The fact that the Poisson's ratio (:math:`\nu`) is zero makes the plate solution the same as the beam solution.

:math:`{I}_{y}` is the inertia of the section with a beam model:

:math:`{I}_{y}=\frac{b{h}^{3}}{12}=\frac{1}{12}\times {\text{10}}^{-3}`


Boundary conditions and loading
------------------------------------

Embedding in :math:`{P}_{1}{P}_{4}`. We are looking for the successive states of equilibrium under the load made up of the linear couple in :math:`{P}_{2}{P}_{3}`:

:math:`m(t)=\text{100}t`; :math:`t` pseudo-time.

We are particularly interested in horizontal and vertical movements and the rotation of line :math:`{P}_{2}{P}_{3}`.