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

Geometry
---------

The problem being treated is planar. The structure studied is 1 rectangle cut into 2 squares :math:`\mathit{ABCD}` and :math:`\mathit{BEFC}`.

The solution is established with a mesh using 2 QUAD4 corresponding to the 2 squares.


.. image:: images/Object_1.svg
    :width: 364
    :height: 183


.. _RefImage_Object_1.svg:


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

elastic material:

:math:`E\mathrm{=}10.0` S.I. units

:math:`\nu \mathrm{=}0.0`

We take :math:`\nu \mathrm{=}0.0` so that we can deal with this plane problem with a layer of 3D elements by having the plane solution.


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

.. csv-table::

    "1)", "We apply a point force to point :math:`F`: :math:`\mathit{FY}\mathrm{=}4.0` u.s.i."
    "2)", "Blocks:
    Point :math:`A`: :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}0.`
    point :math:`D`: :math:`\mathit{DX}\mathrm{=}0.`"
    "3)", "Linear relationships between degrees of freedom:"


load case: cas1

:math:`1.0\mathit{DX}(E)\mathrm{-}0.5\mathit{DY}(D)\mathrm{-}0.5\mathit{DY}(C)\mathrm{=}0.0`

:math:`1.0\mathit{DY}(E)+0.5\mathit{DX}(D)+0.5\mathit{DX}(C)\mathrm{=}0.0`

load case: cas2

:math:`1.0\mathit{DY}(E)+0.5\mathit{DY}(D)+0.5\mathit{DY}(C)\mathrm{=}0.0`

:math:`1.0\mathit{DY}(B)+0.5\mathit{DY}(C)+0.5\mathit{DY}(F)\mathrm{=}0.0`

The initial conditions are not important here.