D modeling
==============

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


.. image:: images/100000000000015500000097746E6448BBB0C0EC.png
    :width: 2.7in
    :height: 1.1283in


.. _RefImage_100000000000015500000097746E6448BBB0C0EC.png:

The mesh is composed of:

• 1 HEXA8sur mesh to which the 3D modeling is affected.

• 1 HEXA20sur mesh to which we assign the 3D modeling_ INTERFACE.


.. csv-table::

    "HEXA1 ", "3D"
    "HEXA2 ", "3D_ INTERFACE"



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

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

Several ways of defining a local coordinate system are proposed, here we are testing ANGL_REP and the ANGL_AXE/ORIG_AXE couple.

The table above gives the orientations chosen for each element:

.. csv-table::

    "HEXA1 "," ANGL_REP "," :math:`(\mathrm{45.0,45}\mathrm{.0,90}.0)`"
    "HEXA2 "," ORIG_AXE/ANGL_AXE "," :math:`(\mathrm{100.0,0}\mathrm{.5,0}.5)`/:math:`(\mathrm{0.0,}-45.0)`"



Calculating local landmarks
-------------------------

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

The values given in ANGL_REP define the following guidelines:

:math:`x=\left(\mathrm{0.5,0}\mathrm{.5,}-\frac{\sqrt{2}}{2}\right)`, :math:`y=\left(\mathrm{0.5,0}\mathrm{.5,}\frac{\sqrt{2}}{2}\right)`, and :math:`z=\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2},0\right)`.

The ANGL_AXE/ORIG_AXE pair is used in the case of a model with cylindrical geometry. They define an axis :math:`{e}_{z}` being the axis of the cylindrical coordinate system.

:math:`x` corresponds to the vector :math:`{e}_{z}` of this cylindrical coordinate system, the reference point being the barycenter of the cell here :math:`(1.5\mathrm{,0}.5\mathrm{,0}.5)`. :math:`y` corresponds to the vector :math:`\mathrm{-}{e}_{\theta }` and :math:`z` to the vector :math:`{e}_{r}`.

In this example :math:`x=\left(\frac{\sqrt{2}}{2},\mathrm{0,}\frac{\sqrt{2}}{2}\right)`, :math:`y\mathrm{=}(\mathrm{0,1}\mathrm{,0})`, and :math:`z=\left(\frac{-\sqrt{2}}{2},\mathrm{0,}\frac{\sqrt{2}}{2}\right)`.


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

The tested results are shown in the following table:

.. csv-table::

    "MAILLE ", "Vector", "Component", "**Reference Value**", "**Tolerance**"
    "HEXA1 "," :math:`x` "," :math:`X` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "HEXA1 "," :math:`x` "," :math:`Y` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "HEXA1 "," :math:`x` "," :math:`Z` "," "," :math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`x` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`x` "," :math:`Y` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`x` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "HEXA1 "," :math:`y` "," :math:`X` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "HEXA1 "," :math:`y` "," :math:`Y` "," "," :math:`0.5` "," :math:`1.E\mathrm{-}8`"
    "HEXA1 "," :math:`y` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`y` "," :math:`Y` "," "," :math:`1` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`z` "," :math:`X` "," "," :math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`z` "," :math:`Y` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "HEXA2 "," :math:`z` "," :math:`Z` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"