Modélisation A
==============


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

On utilise une modélisation DKT avec 3 couches dans l'épaisseur.


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

Le maillage contient 5000 éléments de type TRIA3.


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

On teste le déplacement suivant l'axe :math:`Z` et le moment :math:`\mathit{MXX}` le long de :math:`\mathit{AB}` .


+----------------------------------------------+-----------------------+-------------------------+--------------------+
| **Identification**                           | **Type de référence** | **Valeur de référence** | **Tolérance**      |
|                                              |                       |                         | **%**              |
+---------------------+------------------------+                       |                         |                    |
| DEPL                | :math:`X(\mathit{cm})` |                       |                         |                    |
+---------------------+------------------------+-----------------------+-------------------------+--------------------+
|                     | :math:`0.0`            | 'SOURCE_EXTERNE'      | :math:`0.1033`          | :math:`4.0\text{}` |
| :math:`\mathit{DZ}` |                        |                       |                         |                    |
|                     +------------------------+-----------------------+-------------------------+--------------------+
|                     | :math:`2.0`            | 'SOURCE_EXTERNE'      | :math:`0.0992`          | :math:`3.5\text{}` |
|                     +------------------------+-----------------------+-------------------------+--------------------+
|                     | :math:`4.0`            | 'SOURCE_EXTERNE'      | :math:`0.0883`          | :math:`3.\text{}`  |
|                     +------------------------+-----------------------+-------------------------+--------------------+
|                     | :math:`6.0`            | 'SOURCE_EXTERNE'      | :math:`0.0692`          | :math:`3.\text{}`  |
|                     +------------------------+-----------------------+-------------------------+--------------------+
|                     | :math:`8.0`            | 'SOURCE_EXTERNE'      | :math:`0.0400`          | :math:`2.\text{}`  |
+---------------------+------------------------+-----------------------+-------------------------+--------------------+


+-----------------------------------------------+-----------------------+-------------------------+--------------------+
| **Identification**                            | **Type de référence** | **Valeur de référence** | **Tolérance**      |
|                                               |                       |                         | **%**              |
+----------------------+------------------------+                       |                         |                    |
| EFGE_NOEU            | :math:`X(\mathit{cm})` |                       |                         |                    |
+----------------------+------------------------+-----------------------+-------------------------+--------------------+
| :math:`\mathit{MXX}` | :math:`1.0`            | 'SOURCE_EXTERNE'      | :math:`-50.0`           | :math:`0.5\text{}` |
|                      +------------------------+-----------------------+-------------------------+--------------------+
|                      | :math:`3.0`            | 'SOURCE_EXTERNE'      | :math:`-45.6`           | :math:`0.2\text{}` |
|                      +------------------------+-----------------------+-------------------------+--------------------+
|                      | :math:`5.0`            | 'SOURCE_EXTERNE'      | :math:`-36.4`           | :math:`1.0\text{}` |
|                      +------------------------+-----------------------+-------------------------+--------------------+
|                      | :math:`7.0`            | 'SOURCE_EXTERNE'      | :math:`-23.2`           | :math:`3.0\text{}` |
|                      +------------------------+-----------------------+-------------------------+--------------------+
|                      | :math:`9.0`            | 'SOURCE_EXTERNE'      | :math:`-8.0`            | :math:`0.5\text{}` |
+----------------------+------------------------+-----------------------+-------------------------+--------------------+

On teste les contraintes sur la peau inférieure, moyenne et supérieure dans 2 couches.


*   Couche n°1 : :math:`-\mathrm{0.125cm}<Z<-\mathrm{0.0417cm}`


+---------------------------+----------------------+-----------------------+-----------------------+-------------------------+-------------------------------------+
| **Point / Maille**        | **Couche**           | **Grandeur**          | **Type de référence** | **Valeur de référence** | **Tolérance**                       |
+---------------------------+----------------------+-----------------------+-----------------------+-------------------------+-------------------------------------+
| :math:`A(\mathit{M5200})` | :math:`\mathit{INF}` | :math:`\mathit{SIXX}` | 'NON_DEFINI'          | :math:`4880.375`        | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIYY}` | 'NON_DEFINI'          | :math:`4880.125`        | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIXY}` | 'NON_DEFINI'          | :math:`-0.125`          | :math:`{10}^{-6}`                   |
|                           +----------------------+-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           | :math:`\mathit{MOY}` | :math:`\mathit{SIXX}` | 'NON_DEFINI'          | :math:`3225.583`        | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIYY}` | 'NON_DEFINI'          | :math:`3253.417`        | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIXY}` | 'NON_DEFINI'          | :math:`-0.083`          | :math:`{10}^{-6}`                   |
|                           +----------------------+-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           | :math:`\text{SUP}`   | :math:`\mathit{SIXX}` | 'NON_DEFINI'          | :math:`1626.712`        | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIYY}` | 'NON_DEFINI'          | :math:`1626.708`        | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+-------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIXY}` | 'NON_DEFINI'          | :math:`-0.042`          | :math:`{10}^{-6}`                   |
+---------------------------+----------------------+-----------------------+-----------------------+-------------------------+-------------------------------------+


*   Couche n°3 : :math:`\mathrm{0.0417cm}<Z<\mathrm{0.125cm}`


+---------------------------+----------------------+-----------------------+-----------------------+----------------------------+-------------------------------------+
| **Point / Maille**        | **Couche**           | **Grandeur**          | **Type de référence** | **Valeur de référence**    | **Tolérance**                       |
+---------------------------+----------------------+-----------------------+-----------------------+----------------------------+-------------------------------------+
| :math:`A(\mathit{M5200})` | :math:`\mathit{INF}` | :math:`\mathit{SIXX}` | 'NON_DEFINI'          | :math:`-1626.792`          | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIYY}` | 'NON_DEFINI'          | :math:`-1626.708`          | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIXY}` | 'NON_DEFINI'          | :math:`0.042`              | :math:`{10}^{-6}`                   |
|                           +----------------------+-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           | :math:`\mathit{MOY}` | :math:`\mathit{SIXX}` | 'NON_DEFINI'          | :math:`-3252.583`          | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIYY}` | 'NON_DEFINI'          | :math:`-3252.416`          | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIXY}` | 'NON_DEFINI'          | :math:`0.083`              | :math:`{10}^{-6}`                   |
|                           +----------------------+-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           | :math:`\text{SUP}`   | :math:`\mathit{SIXX}` | 'NON_DEFINI'          | :math:`-4880.375`          | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIYY}` | 'NON_DEFINI'          | :math:`-4880.125`          | :math:`{10}^{-4}\text{%}`           |
|                           |                      +-----------------------+-----------------------+----------------------------+-------------------------------------+
|                           |                      | :math:`\mathit{SIXY}` | 'NON_DEFINI'          | :math:`0.125`              | :math:`{10}^{-6}`                   |
+---------------------------+----------------------+-----------------------+-----------------------+----------------------------+-------------------------------------+