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

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

This is the section of a circle with an outer radius :math:`R\mathrm{=}\mathrm{0.025m}` and a thickness of :math:`\mathrm{0.005m}`. We represent only a quarter of the section. 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.


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

30 QUAD8 stitches.


.. image:: images/10000000000002BC0000028B4CAF4AEB00AE86BA.png
    :width: 3.4689in
    :height: 3.2283in


.. _RefImage_10000000000002BC0000028B4CAF4AEB00AE86BA.png:


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

For the full section:

:math:`A=\pi \left[{R}^{2}-{(R-\mathrm{ep})}^{2}\right]=1.76714E\text{-}04{m}^{2}`

:math:`{I}_{y}={I}_{z}=\frac{\pi }{4}\left[{R}^{4}-{(R-\mathrm{ep})}^{4}\right]=1.81132E\text{-}7{m}^{4}`

:math:`{I}_{p}=2{I}_{y}=2{I}_{z}`


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

.. csv-table::

    "**Identification**", "**Reference**", "**% difference**"
    ":math:`{A}_{M}` ", "1.76714E—04", "—7.76E—05"
    ":math:`{\mathit{CDG}}_{\text{Y-M}}` ", "1.438288E—02", "—1.25E—04"
    ":math:`{\mathit{CDG}}_{\text{Z-M}}` ", "1.438288E—02", "—1.25E—04"
    ":math:`{\mathit{IY}}_{\text{G-M}}` ", "8.7265757E—09", "—2.78E—04"
    ":math:`{\mathit{IZ}}_{\text{G-M}}` ", "8.7265757E—09", "—2.78E—04"
    ":math:`{\mathit{IYZ}}_{\text{G-M}}` ", "—7.72837E—09", "—3.83E—04"
    ":math:`A` ", "7.0685745E—04", "—7.76E—05"
    ":math:`{\mathit{CDG}}_{Y}` ", "0.00000E+00", "0"
    ":math:`{\mathit{CDG}}_{Z}` ", "0.00000E+00", "0"
    ":math:`{\mathit{IY}}_{G}` ", "1.81132E—07", "—4.19E—06"
    ":math:`{\mathit{IZ}}_{G}` ", "1.81132E—07", "—4.19E—06"
    ":math:`{\mathit{IYZ}}_{G}` ", "0.00000E+00", ""
    ":math:`\mathit{IY}` ", "1.81132E—07", "—4.19E—06"
    ":math:`\mathit{IZ}` ", "1.81132E—07", "—4.19E—06"
    ":math:`{Y}_{\mathit{MIN}}` ", "—2.50000E—02", "0.00E+00"
    ":math:`{Y}_{\mathit{MAX}}` ", "2.50000E—02", "0.00E+00"
    ":math:`{Z}_{\mathit{MIN}}` ", "—2.50000E—02", "0.00E+00"
    ":math:`{Z}_{\mathit{MAX}}` ", "2.50000E—02", "0.00E+00"