G modeling
==============

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

Solid rectangular section, width :math:`\mathrm{0.02m}` and height :math:`\mathrm{0.05m}`. It is divided into two rectangles of respective heights :math:`\mathrm{0.025m}`, in order to test the calculation of the characteristics on groups of cells for a network consisting here of two parallel beams, between two floors distant from :math:`L=\mathrm{0.0002m}` (which makes it possible to obtain characteristics (shear coefficient) very close to that of the complete section).


.. image:: images/100000000000022F00000284A76167CEDA12D86E.png
    :width: 2.3035in
    :height: 2.6543in


.. _RefImage_100000000000022F00000284A76167CEDA12D86E.png:

with b = 0.01, h=0.025


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

Number of stitches: 32 QUAD8


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

Geometric characteristics for the complete section and for each half-section:

LIEU A CDG_Y CDG_Z IY_G IZ_G IYZ_G

All 1.00E-03 0.0 0.0 2.08E-07 3.33E-08 0.0

GR1 5.00E-04 0.0 -1.25E-02 2.60E-08 1.67E-08 0.0

GR2 5.00E-04 0.0 1.25E-02 2.60E-08 1.67E-08 0.0

LIEU Y_P Z_P IY_P IZ_P IYZ_P IY IZ

All 0.00E+00 0.00E+00 2.08E-07 3.33E-08 0.0 3.33E-08 2.08E-07

GR1 0.00E+00 0.00E+00 1.04E-07 1.67E-07 1.67E-08 0.0 1.67E-08 1.04E-07

GR2 0.00E+00 0.00E+00 1.04E-07 1.67E-07 1.67E-08 0.0 1.67E-08 1.04E-07

Shear coefficients: for each rectangular section: :math:`{A}_{y}={A}_{z}=1.2`


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

For the complete section, the geometric and mechanical characteristics are:

.. csv-table::

    "**Identification**", "**Reference**", "**% difference**"
    ":math:`A` ", "1.0000000E—03", "0.00E+00"
    ":math:`\mathit{ALPHA}` ", "9.0000000E+01", "0.00E+00"
    ":math:`\mathit{AY}` ", "1.2000000E+00", "—0.004"
    ":math:`\mathit{AZ}` ", "1.2000000E+00", "—0.065"
    ":math:`{\mathit{CDG}}_{Y}` ", "0.0000000E+00", "—1.03E—19"
    ":math:`{\mathit{CDG}}_{Z}` ", "0.0000000E+00", "—2.67E—19"
    ":math:`\mathit{JX}` ", "9.9805000E—08", "—0.124"
    ":math:`\mathit{EY}` ", "0.0000000E+00", "1.55E—18"
    ":math:`\mathit{EZ}` ", "0.0000000E+00", "—4.79E—18"
    ":math:`{\mathit{IY}}_{G}` ", "2.0833333E—07", "1.60E—06"
    ":math:`{\mathit{IYZ}}_{G}` ", "0.0000000E+00", "—1.40E—24"
    ":math:`{\mathit{IZ}}_{G}` ", "3.3333330E—08", "1.00E—05"
    ":math:`\mathit{PCTY}` ", "0.0000000E+00", "4.90E—18"
    ":math:`\mathit{PCTZ}` ", "0.0000000E+00", "1.82E—18"
    ":math:`{Y}_{\mathit{MAX}}` ", "2.5000000E—02", "0.00E+00"
    ":math:`{Y}_{\mathit{MIN}}` ", "—2.5000000E—02", "0.00E+00"
    ":math:`{Z}_{\mathit{MAX}}` ", "1.0000000E—02", "1.73E—14"
    ":math:`{Z}_{\mathit{MIN}}` ", "—1.0000000E—02", "1.73E—14"


For the two disjoint groups, we obtain:

.. csv-table::

    "**Location**", "**Identification**", "**Reference**", "**% difference**"
    ":math:`\mathit{GR2}` "," :math:`A` ", "5.00000E—04", "2.17E—14"
    ":math:`\mathit{GR1}` "," :math:`A` ", "5.00000E—04", "4.34E—14"
    ":math:`\mathit{TOUT}` "," :math:`\mathit{AY}` ", "1.20000E+00", "—0.064"
    ":math:`\mathit{GR1}` "," :math:`\mathit{AY}` ", "1.20000E+00", "—0.065"
    ":math:`\mathit{GR2}` "," :math:`\mathit{AY}` ", "1.20000E+00", "—0.065"
    ":math:`\mathit{GR1}` "," :math:`\mathit{AZ}` ", "1.20000E+00", "—0.065"
    ":math:`\mathit{GR2}` "," :math:`\mathit{AZ}` ", "1.20000E+00", "—0.065"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{CDG}}_{Y}` ", "0.00000E+00", "1.59E—19"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{CDG}}_{Y}` ", "0.00000E+00", "2.11E—19"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{CDG}}_{Z}` ", "1.25000E—02", "—1.39E—14"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{CDG}}_{Z}` ", "—1.25000E—02", "—4.16E—14"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{IY}}_{G}` ", "2.60417E—08", "—1.28E—04"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{IY}}_{G}` ", "2.60417E—08", "—1.28E—04"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{IYZ}}_{G}` ", "0.00000E+00", "—1.58E—24"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{IYZ}}_{G}` ", "0.00000E+00", "1.98E—24"
    ":math:`\mathit{GR1}` "," :math:`{\mathit{IZ}}_{G}` ", "1.66667E—08", "—2.00E—04"
    ":math:`\mathit{GR2}` "," :math:`{\mathit{IZ}}_{G}` ", "1.66667E—08", "—2.00E—04"