M modeling
==============


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

T3G shell element (quarter plate modeling)


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


.. csv-table::

    "Boundary conditions:", "DDL_IMPO"
    "at all the nodes of the arc ABC ", "(GROUP_NO = 'ABC', DX= 0. , DY= 0. , DZ= 0.)
    DRX =0. , DRY =0. , DRZ =0.)"
    "at all nodes in the segment] OA [", "(GROUP_NO = 'OA', DY= 0. , DRX =0. , DRZ =0.)"
    "at all the nodes in the segment] OC [", "(GROUP_NO = 'OC', DX= 0. , DRY =0. , DRZ =0.)"
    "to node O", "(GROUP_NO = 'O', DX= 0. , DY= 0. ,
    DRX =0. , DRY =0. , DRZ =0.)"



.. csv-table::

    "Point O", "meshes: M31"
    "Point A", "meshes: M19"
    "Point B", "meshes: M10 M100 M54"
    "Point C", "meshes: M1"
    "Point D", "meshes: M71 M113 M25"
    "Point E", "meshes: M37 M123 M86"



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

Number of knots: 561

Number of meshes and types: 1036 TRIA3


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


+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+---------------------------------+
|**Identification**                                                                                      |**Reference type**|**Reference values**                            |**Tolerance** :math:`(\text{\%})`|
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  | **Reissner**                                   |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+---------------------------------+
|O                                                                                                       |'ANALYTIQUE'      |—178.419                                        |0.5                              |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+ .. image:: images/Object_55.svg                                                                        +                  +                                                +                                 +
|    :width: 33                                                                                          |                  |                                                |                                 |
+    :height: 21                                                                                         +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+---------------------------------+
|D                                                                                                       |'ANALYTIQUE'      |—101.82                                         |1.0                              |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+ .. image:: images/Object_56.svg                                                                        +                  +                                                +                                 +
|    :width: 33                                                                                          |                  |                                                |                                 |
+    :height: 21                                                                                         +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+---------------------------------+
|E                                                                                                       |'ANALYTIQUE'      |—101.82                                         |1.0                              |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+ .. image:: images/Object_57.svg                                                                        +                  +                                                +                                 +
|    :width: 33                                                                                          |                  |                                                |                                 |
+    :height: 21                                                                                         +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+                                                                                                        +                  +                                                +                                 +
|                                                                                                        |                  |                                                |                                 |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+---------------------------------+



+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|**Identification**                                                                                    |**Reference type**|**Reference values**|**Tolerance** :math:`(\text{\%})`|
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|O                 |                                                                                   |'ANALYTIQUE'      |—0.08125            |1.0                              |
+                  + .. image:: images/Object_60.svg                                                   +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.08125            |1.0                              |
+                  + .. image:: images/Object_61.svg                                                   +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|A                 |                                                                                   |'ANALYTIQUE'      |0.125               |7.0                              |
+                  + .. image:: images/Object_62.svg                                                   +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |                                                                                   |'ANALYTIQUE'      |0.0375              |7.0                              |
+                  + .. image:: images/Object_106.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|B                 |                                                                                   |'ANALYTIQUE'      |0.08125             |8.0                              |
+                  + .. image:: images/Object_107.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |                                                                                   |'ANALYTIQUE'      |0.08125             |8.0                              |
+                  + .. image:: images/Object_254.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|C                 |                                                                                   |'ANALYTIQUE'      |0.125               |6.0                              |
+                  + .. image:: images/Object_255.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |                                                                                   |'ANALYTIQUE'      |0.0375              |6.5                              |
+                  + .. image:: images/Object_256.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|D                 |                                                                                   |'ANALYTIQUE'      |—0.02969            |1.0                              |
+                  + .. image:: images/Object_265.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.05156            |0.5                              |
+                  + .. image:: images/Object_267.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|E                 |                                                                                   |'ANALYTIQUE'      |—0.02969            |0.5                              |
+                  + .. image:: images/Object_276.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.05156            |                                 |
+                  + .. image:: images/Object_278.svg                                                  +                  +                    +                                 +
|                  |    :width: 33                                                                     |                  |                    |                                 |
+                  +    :height: 21                                                                    +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+                  +                                                                                   +                  +                    +                                 +
|                  |                                                                                   |                  |                    |                                 |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+