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


Geometry
---------

The 2D structure is a rectangular plate (:math:`\mathrm{LX}=10m`, :math:`\mathrm{LY}=30m`), with an through crack [:ref:`Figure 1.1-a <Ref94087906>`]. The length of the initial crack is :math:`a=5m`.

We call the "bottom line" the line in :math:`y=0` and "top line" the line in :math:`y=\mathrm{Ly}`.


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


.. _Ref94087906:

Figure 1.1-a: geometry of the cracked plate

The nodes marked :math:`\mathrm{P1}` and :math:`\mathrm{P4}` on the :ref:`Figure 1.1-a <Ref94087906>` are used to impose boundary conditions, which are explained in paragraph [§ :ref:`1.3 <Ref193800026>`].


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

Young's module: :math:`E=205{10}^{9}\mathrm{Pa}`

Poisson's ratio: :math:`\nu =0`


.. _Ref193800026:


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

Charging consists of applying a force distributed over the lower and upper lines :math:`p=106\mathrm{Pa}` and in the direction of the external normal to the surface.

In order to block rigid modes, we block the movements of the nodes :math:`{P}_{1}`, :math:`{P}_{2}`, :math:`{P}_{3}` and :math:`{P}_{4}` as follows:


* :math:`{\mathrm{DY}}^{\mathrm{P4}}={\mathrm{DY}}^{\mathrm{P1}}=0`;


* :math:`{\mathrm{DX}}^{\mathrm{P4}}=0`.