B modeling
==============

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


.. image:: images/10000000000002BC00000085A4EBE30540B47A7B.png
    :width: 4.6909in
    :height: 0.9362in


.. _RefImage_10000000000002BC00000085A4EBE30540B47A7B.png:

The mesh is composed of:


.. _DdeLink__2418_720418832:

• 7 QUAD4 meshes on which the DKT, DST, Q4G, Q4G, DKTG, Q4GG, GRILLE_EXCENTRE, GRILLE_MEMBRANE and MEMBRANE models are assigned.

• 7 TRIA3 meshes on which the DKT, DST, Q4G, Q4G, DKTG, Q4GG, GRILLE_EXCENTRE and GRILLE_MEMBRANE models are assigned.


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 [:ref:`U4.42.01 <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
-------------------------

The 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**"
    "DKT4 "," :math:`x` "," :math:`X` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "DKT3 "," :math:`x` "," :math:`Y` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "DST4 "," :math:`x` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DST3 "," :math:`x` "," :math:`X` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "Q4G4"," :math:`x` "," :math:`Y` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "DKTG4 "," :math:`x` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "GRME3 "," :math:`x` "," :math:`X` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "Q4 GG3 "," :math:`x` "," :math:`Y` "," :math:`0.5` "," :math:`1.E-8`"
    "GREX4 "," :math:`x` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "MEMB4 "," :math:`x` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DKT4 "," :math:`z` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DKT3 "," :math:`z` "," :math:`Y` "," "," :math:`-0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DST3 "," :math:`z` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "Q4G4"," :math:`z` "," :math:`Y` "," "," :math:`-0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "GRME3 "," :math:`z` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "Q4 GG3 "," :math:`z` "," :math:`Y` "," :math:`-0.707106781186E0` "," :math:`1.E\mathrm{-}8`"