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


Geometry
---------


.. image:: images/10000201000002F9000005E201E5004F5AA5432B.png
    :width: 1.8102in
    :height: 3.5827in


.. _RefImage_10000201000002F9000005E201E5004F5AA5432B.png:

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

Geometric dimensions of the cracked plate:


.. csv-table::

    "width", ":math:`L=\mathrm{8m}`"
    "thickness", ":math:`E\mathrm{=}\mathrm{1m}`"
    "height", ":math:`H=\mathrm{18m}`"


Initial plane crack length: :math:`{a}_{0}=\mathrm{2m}`

The crack is positioned in the middle of the height of the plate (:math:`H/2`).


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

Young's module :math:`E=205000\mathrm{MPa}`

Poisson's ratio :math:`\nu =0.3`


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


.. image:: images/100002010000032A000005E65ABF88483B3279A7.png
    :width: 1.778in
    :height: 3.3138in


.. _RefImage_100002010000032A000005E65ABF88483B3279A7.png:

**Figure** 1.3-a **: boundary conditions and loads**

Boundary conditions:

 Point :math:`P`: :math:`\Delta X=\Delta Y=\Delta Z=0`

 Points on segment :math:`\mathrm{AB}`: :math:`\Delta X=\Delta Z=0`

 Points on the surface :math:`\text{INF}`: :math:`\Delta Z=0`

Charging:

 Surface pressure :math:`\text{SUP}`: :math:`P=-1\mathrm{MPa}`

Charging is constant during propagation. Three calls to operator PROPA_FISS are made to simulate the propagation of the initial crack already present in the structure. At each call the advance and the direction of propagation of **each point** of the crack bottom are imposed:

 Advance from the bottom point: :math:`\Delta a=0.4m`

 Propagation angle: :math:`\beta =30°`

The positive direction of angle :math:`\beta` is visible on the.

The bottom of the crack stays **always right** throughout the propagation. The motivation for this choice will be explained in paragraph :ref:`4 <RefNumPara__34332428>`.