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


Geometry
---------

It is a rectangular plate with cracks:


.. image:: images/10000FF400001C5200001C6C0A2312F6CCECCA50.svg
    :width: 365
    :height: 366


.. _RefImage_10000FF400001C5200001C6C0A2312F6CCECCA50.svg:

**Figure 1.1-a: Cracked rectangular plate**

The dimensions of this plate are as follows:


.. csv-table::

    "Half plate height:", ":math:`h=200.0\mathrm{mm}`"
    "Half-width of the plate:", ":math:`I=100.0\mathrm{mm}`"
    "Half-length of crack:", ":math:`a=50.0\mathrm{mm}`"


 In modeling A, a quarter of the plate is modelled, as in FIG. 1.1-a.

 In modeling B, the entire height of the plate is modelled.


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


.. csv-table::

    "Thermal properties:", ":math:`\mathit{Cp}\mathrm{=}0.`"
    "", ":math:`\lambda =1.0W/m°C`"
    "Mechanical properties:", ":math:`E=200000\mathrm{MPa}`"
    "", ":math:`\nu =0.3`"
    "", ":math:`\alpha ={5.10}^{-6}/°C`"


We are under the hypothesis of plane deformations.


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


Modeling A
~~~~~~~~~~~~~~~


* Temperature imposed in :math:`X=0.`: :math:`T=-100.0°C`


* Temperature imposed in :math:`X=100`: :math:`T=+100.0°C`


* Travel to :math:`a<X<I`, :math:`Y=0.`: :math:`v=0.`


* Travel to :math:`0<X<I`, :math:`Y=H`: :math:`v=0.`


* Travel to :math:`X=0.`, :math:`Y=H`: :math:`u=0.`


B modeling
~~~~~~~~~~~~~~~


* Rigid body rotation at a 45° angle


* Then pressure imposed in :math:`X=100` and :math:`X=-100`: :math:`P=-10\mathit{MPa}`