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

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

Hollow rectangular section. This modeling makes it possible to test MACR_CARA_POUTRE to calculate the geometric and mechanical characteristics of a flat area.

Two calculations are carried out:

• the first is performed with the keyword SYME_Z = 'OUI', i.e. the section in question is obtained by symmetry around the :math:`Z` axis (honeycomb section). In addition, the inertias are calculated with respect to the coordinate point :math:`(\mathrm{0,}–0.025)` (keyword ORIG_INER),

• the second is performed without symmetry, on the mesh section, with a calculation of the inertias at the center of the mesh, :math:`C` of coordinates :math:`(0.005\mathrm{,0})`, and 2 different groups of cells, which each correspond to the vertical half of the mesh (on either side of the axis :math:`\mathit{Cz}`).


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

+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------+
|40 QUAD4 stitches.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |                                                                                                                            |
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        + .. image:: images/10000000000002BC0000028B609A77C24DAEB77E.png                                                             +
| The coordinates of the node vertices of the rectangle are: :math:`\mathrm{N1}` 0.00E+00 —2.50E—02 :math:`\mathrm{N2}` 0.00E—02 0.00E—02 :math:`\mathrm{N3}` 1.00E—02 2.50E—02 :math:`\mathrm{N4}` 1.00E—02 —2.50E—02 :math:`\mathrm{N5}` 2.50E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00E—02 2.00 :math:`\mathrm{N6}` :math:`\mathrm{N7}` :math:`\mathrm{N8}` —2.00E—02 :math:`\mathrm{N9}` 0.00E+00 0.00E+00                                 |    :width: 1.7083in                                                                                                        |
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        +    :height: 3.602in                                                                                                        +
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |                                                                                                                            |
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        +                                                                                                                            +
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |                                                                                                                            |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------------------+



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

For the symmetrized section following :math:`\mathit{OY}`, the geometric characteristics are:

.. csv-table::

    "**Identification**", "**Reference**", "**% difference**"
    ":math:`{A}_{M}` ", "2.600E—04", "—1.25E—13"
    ":math:`A` ", "5.200E—04", "—1.25E—13"
    ":math:`\mathit{ALPHA}` ", "9.000E+01", "0.00E+00"
    ":math:`{\mathit{CDG}}_{\text{Y-M}}` ", "5.000E—03", "—5.20E—14"
    ":math:`{\mathit{CDG}}_{Y}` ", "0.000E+00", "0.00E+00"
    ":math:`{\mathit{CDG}}_{\text{Z-M}}` ", "0.000E+00", "1.40E—18"
    ":math:`{\mathit{CDG}}_{Z}` ", "0.000E+00", "1.40E—18"
    ":math:`{\mathit{IY}}_{\text{G-M}}` ", "7.21667E—08", "—4.62E—05"
    ":math:`{\mathit{IY}}_{G}` ", "1.44333E—07", "2.31E—04"
    ":math:`{\mathit{IY}}_{P}` ", "4.69333E—07", "7.10E—05"
    ":math:`{\mathit{IYZ}}_{\text{G-M}}` ", "0.000E+00", "—4.33E—26"
    ":math:`{\mathit{IYZ}}_{G}` ", "0.000E+00", "—4.33E—26"
    ":math:`{\mathit{IZ}}_{\text{G-M}}` ", "3.44667E—09", "—9.67E—05"
    ":math:`{\mathit{IZ}}_{G}` ", "1.98933E—08", "1.68E—04"
    ":math:`\mathit{IY}` ", "1.98933E—08", "1.68E—04"
    ":math:`{\mathit{IY}}_{P}` ", "1.98933E—08", "1.68E—04"
    ":math:`\mathit{IZ}` ", "1.44333E—07", "2.31E—04"
    ":math:`{R}_{\mathit{MAX}}` ", "2.69260E—02", "—6.54E—04"
    ":math:`{Y}_{\mathit{MAX}}` ", "2.500E—02", "0.00E+00"
    ":math:`{Y}_{\mathit{MIN}}` ", "—2.500E—02", "0.00E+00"
    ":math:`{Z}_{\mathit{MAX}}` ", "1.000E—02", "1.73E—14"
    ":math:`{Z}_{\mathit{MIN}}` ", "—1.000E—02", "1.73E—14"


For the non-symmetrized section, the geometric characteristics are:

.. csv-table::

    "Location", "**Identification**", "**Reference**", "**% difference**"
    ":math:`\mathit{TOUT}` "," :math:`{\mathit{IY}}_{P}` ", "3.60833E—08", "9.24E—05"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{IY}}_{P}` ", "3.60833E—08", "9.24E—05"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{IY}}_{P}` ", "7.21667E—08", "—4.62E—05"
    ":math:`\mathit{TOUT}` "," :math:`{\mathit{IZ}}_{P}` ", "1.72333E—09", "1.93E—04"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{IZ}}_{P}` ", "1.72333E—09", "1.93E—04"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{IZ}}_{P}` ", "3.44667E—09", "—9.67E—05"