C modeling
==============

Geometry and modeling
-------------------------


.. image:: images/1000000000000142000000AB45B84E3FE244AB2C.png
    :width: 2.6772in
    :height: 1.3362in


.. _RefImage_1000000000000142000000AB45B84E3FE244AB2C.png:

The mesh is composed of:

• 1 QUAD9sur mesh to which we assign the COQUE_3D modeling

• 1 QUAD8sur mesh to which models GRILLE_MEMBRANE and MEMBRANE are affected

• 1 TRIA7sur mesh to which we assign the COQUE_3D modeling

• 1 TRIA6sur mesh to which we assign the GRILLE_MEMBRANE modeling


Orientation of the local coordinate system
---------------------------

In order to define the local coordinate system for these elements, the ANGL_REP keyword from the AFFE_CARA_ELEM operator is used (see U4.42.01).

The table above gives the orientations chosen for each element:

.. csv-table::

    "Cases", "ANGL_REP "," :math:`(45.0,\mathrm{-}45.0)`"
    "Grids", "ANGL_REP "," :math:`(\mathrm{45.0,}-45.0)`"
    "Membranes", "ANGL_REP "," :math:`(45.0,\mathrm{-}45.0)`"



Calculation of local landmarks
-------------------------

Local landmarks are formed by the vectors :math:`x`, :math:`y`, and :math:`z`.

For shells and grids the vector :math:`z` is defined by the normal exiting to the shell. In our example we will have :math:`z=\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2},0\right)`.

The value given to ANGL_REP defines a vector whose projection on the tangential plane to the element gives the vector :math:`x`. So the values in the example are :math:`x=\left(\mathrm{0.5,0}\mathrm{.5,}\frac{\sqrt{2}}{2}\right)` and :math:`y=\left(-\mathrm{0.5,}-\mathrm{0.5,}\frac{\sqrt{2}}{2}\right)`.


Tested sizes
------------------

The tested results are shown in the following table:

.. csv-table::

    "MAILLE ", "Vector", "Component", "**Reference Value**", "**Tolerance**"
    "CQ3D4 "," :math:`x` ", "X", ":math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "CQ3D3 "," :math:`x` ", "Y", ":math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "CQ3D4 "," :math:`x` ", "Z", ":math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "GRME4 "," :math:`x` ", "X", ":math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "GRME3 "," :math:`x` ", "Y", ":math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "GRME4 "," :math:`x` ", "Z", ":math:`0.707106781186E0` "," :math:`1.E-8`"
    "MEMB4 "," :math:`x` ", "Z", ":math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "CQ3D4 "," :math:`z` ", "X", ":math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "CQ3D3 "," :math:`z` ", "Y", ":math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "GRME4 "," :math:`z` ", "X", ":math:`0.707106781186E0` "," :math:`1.E-8`"
    "GRME3 "," :math:`z` ", "Y", ":math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "MEMB4 "," :math:`z` ", "X", ":math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"