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

Characteristics of modeling
-----------------------------------

Hollow rectangular section of which a quarter is represented. This modeling makes it possible to test the CARA_GEOM keyword from POST_ELEM, which is also used by MACR_CARA_POUTRE to calculate the geometric characteristics of a flat area.


.. image:: images/100000000000030A000001BF728B656E5944631E.png
    :width: 3.9591in
    :height: 2.2736in


.. _RefImage_100000000000030A000001BF728B656E5944631E.png:

:math:`\mathit{Hx}\mathrm{=}\mathrm{0.02m}`, :math:`\mathit{Hy}\mathrm{=}\mathrm{0.05m}`, :math:`\mathit{epx}\mathrm{=}\mathrm{0.002m}`, :math:`\mathit{epy}\mathrm{=}\mathrm{0.005m}`.


Characteristics of the mesh
----------------------------

The coordinates of the nodes are:

+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+
|:math:`\mathit{N1}` 8.00E-03 0.00E+00 :math:`\mathit{N2}` 8.00E-03 2.00E-03 2.00E-02 :math:`\mathit{N3}` 0.00E-03 2.00E-02 :math:`\mathit{N4}` 0.00E-02 :math:`\mathit{N5}` 1.00E-02 2.50E-02 :math:`\mathit{N6}` 1.00E-02 2.50E-02 1.00E-02 0.00E+00 E-02 0.00E+00 :math:`\mathit{N7}` 8.00E-03 2.00E-03 6.6667E-03 6.6667E-03 6.6667E-03 6.6667E-03 :math:`\mathit{N8}` 8.00E-03 1.3333E-02 :math:`\mathit{N9}` 4.00E-03 2.00E-02 :math:`\mathit{N10}` 5.00E-03 2.50E-02 :math:`\mathit{N11}` 1.00E-02 1.66667E-02 :math:`\mathit{N12}` 1.00E-02 8.3333E-03|                                                                                                                             |
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             + .. image:: images/10000000000002BC0000028BE906D09C0EA4E01D.png                                                              +
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |    :width: 1.8898in                                                                                                         |
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             +    :height: 2.5043in                                                                                                        +
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                             |
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             +                                                                                                                             +
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                             |
+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+



Benchmark solution
---------------------

:math:`A={h}_{y}{h}_{z}-({h}_{y}-2{\mathrm{ep}}_{y})({h}_{z}-2{\mathrm{ep}}_{z})=3.6E\text{-}04{m}^{2}`

:math:`{I}_{x}=\frac{1}{12}\left[{h}_{y}{h}_{z}^{3}-({h}_{y}-2{\mathrm{ep}}_{y}){({h}_{z}-2{\mathrm{ep}}_{z})}^{3}\right]=1.23E\text{-}7{m}^{4}`

:math:`{I}_{y}=\frac{1}{12}\left[{h}_{z}{h}_{y}^{3}-({h}_{z}-2{\mathrm{ep}}_{z}){({h}_{y}-2{\mathrm{ep}}_{y})}^{3}\right]=1.968E\text{-}8{m}^{4}`


Tested sizes and results
------------------------------

.. csv-table::

    "**Identification**", "**Reference**", "**% difference**"
    ":math:`A` ", "3.60000E—04", "—2.26E—13"
    ":math:`\mathit{ALPHA}` ", "9.00000E+01", "0.00E+00"
    ":math:`{\mathit{CDG}}_{Y}` ", "0.00000E+00", "0"
    ":math:`{\mathit{CDG}}_{Z}` ", "0.00000E+00", "0.00E+00"
    ":math:`{\mathit{IY}}_{G}` ", "1.23000E—07", "—6.46E—14"
    ":math:`{\mathit{IYZ}}_{\text{G-M}}` ", "—1.11111E—09", "1.00E—04"
    ":math:`{\mathit{IZ}}_{G}` ", "1.96800E—08", "—2.52E—13"
    ":math:`\mathit{IY}` ", "1.96800E—08", "—2.52E—13"
    ":math:`\mathit{IZ}` ", "1.23000E—07", "—6.46E—14"
    ":math:`{R}_{\mathit{MAX}}` ", "2.69258E—02", "—6.54E—04"
    ":math:`{Y}_{\mathit{MAX}}` ", "2.50000E—02", "0.00E+00"
    ":math:`{Y}_{\mathit{MIN}}` ", "—2.50000E—02", "0.00E+00"
    ":math:`{Z}_{\mathit{MAX}}` ", "1.00000E—02", "0.00E+00"
    ":math:`{Z}_{\mathit{MIN}}` ", "—1.00000E—02", "0.00E+00"