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


Geometry
---------

The geometry consists of two hemispheres of identical radius, a cross section of which is shown in the figure below.


.. image:: images/1000050000001C6C0000136EA235B717267D9113.svg
    :width: 366
    :height: 250


.. _RefImage_1000050000001C6C0000136EA235B717267D9113.svg:

Given the mesh differences, the positions of the nodes :math:`H` and :math:`I` shown here approximately are different in the 3 models.


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

:math:`E=20000.\mathrm{MPa}`

:math:`\nu =0.3`


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

Crush imposed on the spheres:


*
    *
        * :math:`\mathrm{DY}` imposed :math:`–2\mathrm{mm}` for the nodes of :math:`\mathrm{AB}`


        * :math:`\mathrm{DY}` imposed :math:`+2\mathit{mm}` for the nodes of :math:`\mathit{CD}`



For axisymmetric calculations:


*
    *
        * :math:`\mathrm{DX}` stuck on the :math:`\mathit{AC}` axis

For calculations :math:`\mathrm{3D}` (2 quarters of a sphere modelled):


*
    *
        * symmetry conditions on each quarter of a sphere