E modeling
==============

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


.. image:: images/10000000000001EC000000BEED9138FE202330B0.png
    :width: 3.7339in
    :height: 1.3102in


.. _RefImage_10000000000001EC000000BEED9138FE202330B0.png:

The mesh is composed of:

• 3 QUAD4sur meshes that affect the C_ PLAN, D_ PLANet AXIS models.

• 3 TRIA3sur meshes that affect the C_ PLAN, D_ PLANet AXIS models.


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).

In the 2D case, the orientation of the coordinate system is taken into account by the ANGL_REP keyword, which only has one component left.

The table above gives the orientations chosen for each element:

.. csv-table::

    "QUAD4 "," ANGL_REP "," :math:`90`"
    "TRIA3 "," ANGL_REP "," :math:`45`"



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

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

The values given in ANGL_REP define the following guidelines:


* :math:`x\mathrm{=}(\mathrm{0,1})` and :math:`y\mathrm{=}(\mathrm{-}\mathrm{1,0})` for the QUAD4


* :math:`x=\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)` and :math:`y=\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)` for the TRIA3


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

The tested results are shown in the following table:

.. csv-table::

    "MAILLE ", "Vector", "Component", "**Reference Value**", "**Tolerance**"
    "CPL4 "," :math:`x` "," :math:`X` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "CPL4 "," :math:`x` "," :math:`Y` "," "," :math:`1` "," :math:`1.E\mathrm{-}8`"
    "DPL4 "," :math:`x` "," :math:`X` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "DPL4 "," :math:`x` "," :math:`Y` "," "," :math:`1` "," :math:`1.E\mathrm{-}8`"
    "AXI4 "," :math:`x` "," :math:`X` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "AXI4 "," :math:`x` "," :math:`Y` "," "," :math:`1` "," :math:`1.E\mathrm{-}8`"
    "CPL3 "," :math:`x` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "CPL3 "," :math:`x` "," :math:`Y` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DPL3 "," :math:`x` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DPL3 "," :math:`x` "," :math:`Y` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "AXI3 "," :math:`x` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "AXI3 "," :math:`x` "," :math:`Y` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "CPL4 "," :math:`y` "," :math:`X` "," "," :math:`\mathrm{-}1` "," :math:`1.E\mathrm{-}8`"
    "CPL4 "," :math:`y` "," :math:`X` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "DPL4 "," :math:`y` "," :math:`Y` "," "," :math:`\mathrm{-}1` "," :math:`1.E\mathrm{-}8`"
    "DPL4 "," :math:`y` "," :math:`X` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "AXI4 "," :math:`y` "," :math:`Y` "," "," :math:`\mathrm{-}1` "," :math:`1.E\mathrm{-}8`"
    "AXI4 "," :math:`y` "," :math:`X` "," "," :math:`0` "," :math:`1.E\mathrm{-}8`"
    "CPL3 "," :math:`y` "," :math:`Y` "," "," :math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "CPL3 "," :math:`y` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DPL3 "," :math:`y` "," :math:`Y` "," "," :math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "DPL3 "," :math:`y` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "AXI3 "," :math:`y` "," :math:`Y` "," "," :math:`\mathrm{-}0.707106781186E0` "," :math:`1.E\mathrm{-}8`"
    "AXI3 "," :math:`y` "," :math:`X` "," "," :math:`0.707106781186E0` "," :math:`1.E\mathrm{-}8`"