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


Geometry
---------

A cylindrical shell (1/4 cylinder) of height :math:`h\mathrm{=}40` and radius :math:`R\mathrm{=}10` and thickness :math:`e\mathrm{=}0.2` is embedded on its center line and subjected to internal pressure :math:`p\mathrm{=}2`.

It is meshed twice:


.. csv-table::

    ":math:`\mathit{ma1}`: :math:`7\mathrm{\times }14` "," QUAD4"
    ":math:`\mathit{ma2}`: :math:`8\mathrm{\times }16\mathrm{\times }2` "," TRIA6"



+-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
|                                                                                                                             |                                                                                                                             |
+ .. image:: images/100000000000015D000001FF4344BADABB42C6E6.png                                                              + .. image:: images/100000000000015E0000020615E629ACDEA4FB02.png                                                              +
|    :width: 2.8138in                                                                                                         |    :width: 2.9717in                                                                                                         |
+    :height: 3.8992in                                                                                                        +    :height: 4.0311in                                                                                                        +
|                                                                                                                             |                                                                                                                             |
+                                                                                                                             +                                                                                                                             +
|                                                                                                                             |                                                                                                                             |
+-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
|:math:`\mathit{ma1}`                                                                                                         |:math:`\mathit{ma2}`                                                                                                         |
+-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+



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

:math:`E\mathrm{=}1.{10}^{6}`

:math:`\nu \mathrm{=}0.3`


Boundary conditions, loading
----------------------------------

The group of nodes :math:`\mathit{AB1}` is embedded (the three movements and the three rotations are blocked).


.. math::
: label: EQ-None

    \ mathit {DX}\ mathrm {=}\ mathit {DY}\ mathit {DY}\ mathrm {=}\ mathit {DZ}\ mathrm {=} 0.

The shell is subjected to an internal pressure :math:`p\mathrm{=}2`.


Validated functionalities
------------------------

The validation concerns the 'ELEM' method in the case of surface cells immersed in the :math:`\mathit{R3}` space. We also test the VIS_A_VIS keyword for the 'ELEM' method.