Modélisation C
==============


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

Maillage avec des éléments 2D incompressibles de type QUAD8 et TRIA6.


.. image:: images/10005A2E00002957000015E96F33A1848BC62479.svg
    :width: 533
    :height: 282


.. _RefImage_10005A2E00002957000015E96F33A1848BC62479.svg:

Conditions limites:

DDL_IMPO=    GROUP_NO=’GRNM11’,DX = 0            côté :math:`\mathrm{AB}`

FACE_IMPO    =GROUP_MA=’GRMA12’,DNOR = 0        coté :math:`\mathrm{EF}`

PRES_REP    =GROUP_MA=’GRMA13’,PRES =     60    face :math:`\mathrm{AE}`

**Nom des nœuds:**

:math:`A=\mathrm{N2}` , :math:`B=\mathrm{N361}` , :math:`C=\mathrm{N121}` , :math:`D=\mathrm{N584}` , :math:`E=\mathrm{N155}` , :math:`F=\mathrm{N503}`


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

Nombre de nœuds: 591

Nombre de mailles: 200 TRIA6, 50 QUAD8.


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

Résultats au point :math:`A` :


*   première colonne D_PLAN_INCO_UPG sans imposer :math:`\mathrm{GONF}=0`


*   deuxième colonne D_PLAN_INCO_UPG en imposant :math:`\mathrm{GONF}=0`


*   troisième colonne D_PLAN_INCO_UP avec maillage quadratique


*   quatrième colonneD_PLAN_INCO_UP avec maillage linéaire


*   cinquième colonneD_PLAN_INCO_UPO avec éléments linéaires


+----------------------------------------------+-----------------------+-------------------------+-----------------------------------------------+
| **Identification**                           | **Type de référence** | **Valeur de référence** | **Tolérance**                                 |
|                                              |                       |                         +---------------+-------+-------+-------+-------+
|                                              |                       |                         | **1**         | **2** | **3** | **4** | **5** |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`u`                                    | 'ANALYTIQUE'          | 0.                      | 10-5          | 10-5  | 10-5  | 10-5  | 10-5  |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`v`                                    | 'ANALYTIQUE'          | 6. 10-5                 | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{xx}`                        | 'ANALYTIQUE'          | 100.                    | 0.50%         | 0.50% | 0.50% | 0,60% | 0.50% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{yy}`                        | 'ANALYTIQUE'          | –60.                    | 0.50%         | 0.50% | 0.50% | 2,50% | 2,10% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{zz}`                        | 'ANALYTIQUE'          | 20.                     | 0.50%         | 0.50% | 0.50% | 5,00% | 1,60% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{xy}`                        | 'ANALYTIQUE'          | 0.                      | 0.3           | 0.3   | 0.3   | 1,5   | 0.9   |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{xx}`                   | 'ANALYTIQUE'          | 6. 10-4                 | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{yy}`                   | 'ANALYTIQUE'          | –6. 10-4                | 0.50%         | 0.50% | 0.50% | 1.50% | 1.50% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{xy}`                   | 'ANALYTIQUE'          | 0.                      | 10-5          | 10-5  | 10-5  | 10-5  | 10-5  |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{\mathrm{eq}}` -INVA_2  | 'ANALYTIQUE'          | 6.92 10-4               | 0.50%         | 0.50% | 0.50% | 1.00% | 1.00% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{\mathrm{eq}}` -PRIN_1  | 'ANALYTIQUE'          | –6. 10-4                | 0.50%         | 0.50% | 0.50% | 1.50% | 1.50% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{\mathrm{eq}}` -PRIN_2  | 'ANALYTIQUE'          | 0.                      | 10-5          | 10-5  | 10-5  | 10-5  | 10-5  |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{\mathrm{eq}}` -PRIN_3  | 'ANALYTIQUE'          | 6. 10-4                 | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{\mathrm{eq}}` -VMIS         | 'ANALYTIQUE'          | 138.56                  | 1.00%         | 1.00% | 1.00% | 1.00% | 1.00% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{\mathrm{eq}}` -TRESCA       | 'ANALYTIQUE'          | 160.                    | 1.00%         | 1.00% | 1.00% | 1.00% | 1.00% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{\mathrm{eq}}` -PRIN_1       | 'ANALYTIQUE'          | -60.                    | 1.00%         | 1.00% | 1.00% | 2,50% | 2,10% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{\mathrm{eq}}` -PRIN_2       | 'ANALYTIQUE'          | 20.                     | 1.00%         | 1.00% | 1.00% | 5,00% | 1,60% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{\mathrm{eq}}` -PRIN_3       | 'ANALYTIQUE'          | 100.                    | 1.00%         | 1.00% | 1.00% | 1.00% | 1.00% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{\mathrm{eq}}` -VMIS         | 'ANALYTIQUE'          | 138.56                  | 1.00%         | 1.00% | 1.00% | 1.00% | 1.00% |
+----------------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+

Résultats au point :math:`F` :


*   première colonne D_PLAN_INCO_UPG sans imposer :math:`\mathrm{GONF}=0`


*   deuxième colonne D_PLAN_INCO_UPG en imposant :math:`\mathrm{GONF}=0`


*   troisième colonne D_PLAN_INCO_UP avec maillage quadratique


*   quatrième colonneD_PLAN_INCO_UP avec maillage linéaire


*   cinquième colonneD_PLAN_INCO_UPO avec éléments linéaires


+--------------------------------------+-----------------------+-------------------------+-----------------------------------------------+
| **Identification**                   | **Type de référence** | **Valeur de référence** | **Tolérance**                                 |
|                                      |                       |                         +---------------+-------+-------+-------+-------+
|                                      |                       |                         | **1**         | **2** | **3** | **4** | **5** |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`u`                            | 'ANALYTIQUE'          | –2.12 10-5              | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`v`                            | 'ANALYTIQUE'          | 2.12 10-5               | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{xx}`                | 'ANALYTIQUE'          | 20.                     | 0.50%         | 0.50% | 0.50% | 1.00% | 1.00% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{yy}`                | 'ANALYTIQUE'          | 20.                     | 0.50%         | 0.50% | 0.50% | 2,00% | 1.50% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{zz}`                | 'ANALYTIQUE'          | 20.                     | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\sigma}_{xy}`                | 'ANALYTIQUE'          | 20.                     | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{xx}`           | 'ANALYTIQUE'          | 0.                      | 10-5          | 10-5  | 10-5  | 10-5  | 10-5  |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{yy}`           | 'ANALYTIQUE'          | 0.                      | 10-5          | 10-5  | 10-5  | 10-5  | 10-5  |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+
| :math:`{\varepsilon}_{xy}`           | 'ANALYTIQUE'          | 1.5 10-4                | 0.50%         | 0.50% | 0.50% | 0.50% | 0.50% |
+--------------------------------------+-----------------------+-------------------------+---------------+-------+-------+-------+-------+


Remarques
---------

Comme pour la modélisation 3D, les résultats obtenus sont tout à fait satisfaisants.