Modeling A
==============


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

2 elements POU_D_E :math:`{k}_{y}={k}_{z}=1` :math:`\phi =0` by section type

:math:`\mathrm{S1}`: Rectangular section modelled by SECTION: 'GENERALE'

:math:`\begin{array}{}\begin{array}{cccc}A=0.02& \mathrm{Iy}=0.1666E-4& \mathrm{Iz}=0.6666E-4& {J}_{x}=0.45776E-4\\ & \mathrm{Ry}=0.1& \mathrm{Rz}=0.05& {R}_{T}=0.0892632\end{array}\\ \mathrm{Point}\mathrm{de}\mathrm{calcul}\mathrm{des}\mathrm{contraintes}\end{array}`

:math:`\mathrm{S2}`: Corner section

:math:`\begin{array}{ccc}A=1.856E-3& {I}_{y}=4.167339E-4& {I}_{z}=1.045547E-4\\ {J}_{x}=03.9595E-8& {e}_{y}=41.012E-3& {e}_{z}=0.0\end{array}`

:math:`\mathrm{S3}`: Rectangular section modelled by SECTION: RECTANGLE

:math:`\mathrm{Hy}=0.2` :math:`\mathrm{Hz}=0.1`

:math:`\mathrm{S4}`: Section CERCLE :math:`R=0.1`

:math:`{I}_{Y}={I}_{Z}=\frac{\pi {R}^{4}}{4}=\frac{\pi }{4}{10}^{-4}`


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

:math:`4\times 2` mesh SEG_2. The beam is oriented according to the vector :math:`(\mathrm{1,}\mathrm{1,}1)`.


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

.. csv-table::

    "**Load case**", "**Beam**", "**Identification**", "**Reference**"
    ":math:`{F}_{x}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{u}_{x}(B)` ", "2.887E-10"
    "", "", ":math:`{\theta }_{\mathrm{xx}}(0)` ", "50."
    "", ":math:`\mathrm{S2}` "," :math:`{u}_{x}(B)` ", "3.11E-9"
    "", ":math:`\mathrm{S4}` "," :math:`{u}_{x}(B)` ", "1.838E-10"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}` ", "31.83"
    ":math:`{F}_{y}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{u}_{y}(B)` ", "+1.414E-7"
    "", "", ":math:`{\theta }_{z}(B)` ", "1.225E-7"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "3000"
    "", ":math:`\mathrm{S2}` "," :math:`{u}_{y}(B)` ", "9.017E-8"
    "", ":math:`\mathrm{S4}` "," :math:`{\sigma }_{\mathrm{xx}}(0)` ", "2546.479"
    ":math:`{F}_{z}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{u}_{z}(B)` ", "6.532E-7"
    "", "", ":math:`{\theta }_{y}(B)` ", "-4.243E-7"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "6000"
    "", "", ":math:`{\sigma }_{\mathrm{xz}}(0)` ", "50"
    "", ":math:`\mathrm{S2}` "," :math:`{u}_{z}(B)` ", "9.279E-7"
    "", "", ":math:`{\theta }_{y}(B)` ", "1.553E-5"
    "", "", ":math:`{\theta }_{x}(B)` ", "1.555E-5"
    "", ":math:`\mathrm{S4}` "," :math:`{u}_{z}(B)` ", "1.386E-7"
    "", "", ":math:`{\theta }_{y}(B)` ", "-9E-8"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "2546.479"
    "", "", ":math:`{\sigma }_{\mathrm{xz}}(0)` ", "31.831"
    ":math:`{M}_{x}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{\theta }_{x}(B)` ", "3.279E-7"
    "", "", ":math:`{\sigma }_{\mathrm{xy}}={\sigma }_{\mathrm{xz}}(0)` ", "1950.0"
    "", ":math:`\mathrm{S2}` "," :math:`{\theta }_{x}(B)` ", "3.791E-4"
    "", "", ":math:`{u}_{z}(B)` ", "2.199E-5"
    "", ":math:`\mathrm{S4}` "," :math:`{\theta }_{x}(B)` ", "9.556E-8"
    "", "", ":math:`{\sigma }_{\mathrm{xy}}={\sigma }_{\mathrm{xz}}(0)` ", "636.62"
    ":math:`{M}_{y}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{u}_{z}(B)` ", "-4.899E-7"
    "", "", ":math:`{\theta }_{y}(B)` ", "4.243E-7"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "3000"
    "", ":math:`\mathrm{S2}` "," :math:`{u}_{z}(B)` ", "-1.959E-8"
    "", "", ":math:`{\theta }_{y}(B)` ", "1.697E-8"
    "", ":math:`\mathrm{S4}` "," :math:`{u}_{z}(B)` ", "-1.04E-7"
    "", "", ":math:`{\theta }_{y}(B)` ", "9.0E-8"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "1273.2395"
    ":math:`{M}_{z}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{u}_{y}(B)` ", "1.061E-7"
    "", "", ":math:`{\theta }_{z}(B)` ", "1.225E-7"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "1500.0"
    "", ":math:`\mathrm{S2}` "," :math:`{u}_{y}(B)` ", "6.763E-8"
    "", "", ":math:`{\theta }_{z}(B)` ", "7.809E-8"
    "", ":math:`\mathrm{S4}` "," :math:`{u}_{y}(B)` ", "9.0E-7"
    "", "", ":math:`{\sigma }_{z}(B)` ", "1.04E-7"
    "", "", ":math:`{\sigma }_{\mathrm{xx}}(0)` ", "1273.2395"
    ":math:`{M}_{y}=1` "," :math:`\mathrm{S1}=\mathrm{S3}` "," :math:`{\sigma }_{\mathrm{xx}}\mathrm{max}(0)` ", "4550.0"
    ":math:`{M}_{z}=1`
    :math:`{F}_{x}=1` ", "", ":math:`{\sigma }_{\mathrm{xx}}(\frac{a}{\mathrm{2,}}\frac{b}{2})` ", "1550.0"
    "", ":math:`\mathrm{S4}` "," :math:`{\sigma }_{\mathrm{xx}}\mathrm{max}(0)` ", "1832.4636"
    ":math:`{F}_{y}=1` "," :math:`\mathit{S1},\mathit{S3}` "," :math:`{\sigma }_{\mathit{xy}}(0)` ", "2000.0"
    ":math:`{F}_{z}=1` ", "", ":math:`{\sigma }_{\mathit{xz}}(0)` ", "2000.0"
    ":math:`{M}_{x}=1` ", "", ":math:`{\sigma }_{\mathit{xx}}\mathit{max}(0)` ", "9000.0"
    "", ":math:`\mathit{S1},\mathit{S3}` "," :math:`{\sigma }_{\mathit{xx}}\left(\frac{a}{\mathrm{2,}}\frac{b}{2}\right)` ", "-9000.0"
    "", ":math:`\mathit{S4}` "," :math:`{\sigma }_{\mathit{xx}}\mathit{max}(0)` ", "3601.27"
    "", "", ":math:`{\sigma }_{\mathit{xy}}(0)` ", "668.451"