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


Geometry
---------

The geometry, dimensions, and materials are taken to be identical to those of Mariani et al. [:ref:`1 <1>`].

Structure :math:`\mathrm{2D}` is a rectangular plate (:math:`230\mathrm{mm}\times 75\mathrm{mm}`), with a through crack []. The length of the initial crack is :math:`a=19\mathrm{mm}`.

The nodes noted :math:`\mathrm{P1}`, :math:`\mathrm{P2}`, and :math:`\mathrm{P3}` are used to impose boundary conditions, which are explained in paragraph [§ :ref:`1.3 <Ref193800026>`].


.. image:: images/100000000000036C000001F4204637ECE470175F.jpg
    :width: 3.9173in
    :height: 2.4098in


.. _RefImage_100000000000036C000001F4204637ECE470175F.jpg:

**Figure** 1.1-a **: geometry of the cracked plate**

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

Young's module: :math:`E=\mathrm{31,37}{10}^{9}\mathrm{Pa}`

Poisson's ratio: :math:`\nu =0.2`


.. _Ref193800026:


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

Charging consists of applying a unit nodal force in :math:`\mathrm{P3}`.

In order to block rigid modes, we block the movements of nodes :math:`\mathrm{P1}` and :math:`\mathrm{P2}` as follows:


* :math:`{\mathrm{DY}}^{\mathrm{P1}}={\mathrm{DY}}^{\mathrm{P2}}=0`;


* :math:`{\mathrm{DX}}^{\mathrm{P1}}=0`.