Modélisation A
==============


Caractéristiques de la modélisation
-----------------------------------

2 éléments POU_D_E :math:`{k}_{y}={k}_{z}=1` :math:`\phi =0` par type de section

:math:`\mathrm{S1}` : Section rectangulaire modélisée par 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}` : Section cornière

: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}` : Section rectangulaire modélisée par 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}`


Caractéristiques du maillage
----------------------------

:math:`4\times 2` maillesSEG_2. La poutre est orientée selon le vecteur :math:`(1,1,1)` .


Grandeurs testées et résultats
------------------------------

.. csv-table::

    "**Cas de charge**", "**Poutre**", "**Identification**", "**Référence**"
    ":math:`{F}_{x}=1`", ":math:`\mathrm{S1}=\mathrm{S3}`", ":math:`{u}_{x}(B)`", "2.887E-10"
    "", "", ":math:`{\theta}_{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}_{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}_{xx}(0)`", "3000"
    "", ":math:`\mathrm{S2}`", ":math:`{u}_{y}(B)`", "9.017E-8"
    "", ":math:`\mathrm{S4}`", ":math:`{\sigma}_{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}_{xx}(0)`", "6000"
    "", "", ":math:`{\sigma}_{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}_{xx}(0)`", "2546.479"
    "", "", ":math:`{\sigma}_{xz}(0)`", "31.831"
    ":math:`{M}_{x}=1`", ":math:`\mathrm{S1}=\mathrm{S3}`", ":math:`{\theta}_{x}(B)`", "3.279E-7"
    "", "", ":math:`{\sigma}_{xy}={\sigma}_{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}_{xy}={\sigma}_{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}_{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}_{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}_{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}_{xx}(0)`", "1273.2395"
    ":math:`{M}_{y}=1`", ":math:`\mathrm{S1}=\mathrm{S3}`", ":math:`{\sigma}_{xx}\max(0)`", "4550.0"
    ":math:`{M}_{z}=1`
    :math:`{F}_{x}=1`", "", ":math:`{\sigma}_{xx}(\frac{a}{2,}\frac{b}{2})`", "1550.0"
    "", ":math:`\mathrm{S4}`", ":math:`{\sigma}_{xx}\max(0)`", "1832.4636"
    ":math:`{F}_{y}=1`", ":math:`\mathit{S1},\mathit{S3}`", ":math:`{\sigma}_{xy}(0)`", "2000.0"
    ":math:`{F}_{z}=1`", "", ":math:`{\sigma}_{xz}(0)`", "2000.0"
    ":math:`{M}_{x}=1`", "", ":math:`{\sigma}_{xx}max(0)`", "9000.0"
    "", ":math:`\mathit{S1},\mathit{S3}`", ":math:`{\sigma}_{xx}\left(\frac{a}{2,}\frac{b}{2}\right)`", "-9000.0"
    "", ":math:`\mathit{S4}`", ":math:`{\sigma}_{xx}max(0)`", "3601.27"
    "", "", ":math:`{\sigma}_{xy}(0)`", "668.451"