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


Geometry
---------

We consider a hemisphere divided into 4 pieces (by symmetry around the equatorial planes).


.. image:: images/100002010000032D0000022BAD420090D7F3AB79.png
    :width: 2.7098in
    :height: 1.85in


.. _RefImage_100002010000032D0000022BAD420090D7F3AB79.png:

Radius of the sphere: :math:`R=10m`

Thickness of the sphere: :math:`t=\mathrm{0,04}m`

The hole is open: 18°


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

The sphere is made of aluminum. The material is linear isotropic elastic.

:math:`E\mathrm{=}6.825{10}^{7}\mathit{Pa}`, :math:`\nu \mathrm{=}0.3`


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

On a quarter of the hemisphere, symmetry conditions are applied on all three planes (which are therefore QUAD4):


* Plan :math:`(12)`: :math:`\mathit{DZ}=0`;


* Plan :math:`(13)`: :math:`\mathit{DY}=0`;


* Plan :math:`(23)`: :math:`\mathit{DX}=0`.

Moreover, a loading in the form of a point force is applied to points A and B such as:


* Point A: :math:`\mathit{FX}=\mathrm{0,5}N`;


* Point B: :math:`\mathit{FY}=-\mathrm{0,5}N`.