G modeling
==============


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

Shell element DSQ (quarter plate modeling)


Boundary conditions
~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "in all the nodes of the arc :math:`\mathrm{ABC}` ", ":", "DX: 0. , BY: 0. , Z: 0."
    "in all the nodes in segment :math:`\left]\mathrm{OA}\right[` ", ":", "DY: 0. , DRX :0. , DRZ :0."
    "in all the nodes in segment :math:`\left]\mathrm{OC}\right[` ", ":", "DX: 0. , DRY :0. , DRZ :0."
    "to node :math:`O` ", ":", "DX: 0. , BY: 0. , DRX :0. , DRY :0. , DRZ :0."



.. csv-table::

    "Point :math:`O` ", "stitches: :math:`\mathrm{M1}`"
    "Point :math:`A` ", "stitches: :math:`\mathrm{M147}`"
    "Point :math:`B` ", "stitches: :math:`\mathrm{M98}\mathrm{M111}`"
    "Point :math:`C` ", "stitches: :math:`\mathrm{M14}`"
    "Point :math:`D` ", "stitches: :math:`\mathrm{M85}\mathrm{M99}`"
    "Point :math:`E` ", "stitches: :math:`\mathrm{M7}\mathrm{M8}`"
    "Point :math:`F` ", "stitches: :math:`\mathrm{M91}\mathrm{M92}\mathrm{M105}`"



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

Number of knots: 169

Number of meshes and types: 147 QUAD4


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


+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|**Identification**                                                                                      |**Reference type**|**Reference values**                            |**Tolerance**|
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  | **Reissner**                                   |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|O                                                                                                       |'ANALYTIQUE'      |—703.40                                         |0.15%        |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_45.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|D                                                                                                       |'ANALYTIQUE'      |—495.56                                         |0.15%        |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_46.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|E                                                                                                       |'ANALYTIQUE'      |—495.56                                         |0.15%        |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_47.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|F                                                                                                       |'ANALYTIQUE'      |—441.18                                         |0.2%         |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_48.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+



+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|**Identification**                                                                                    |**Reference type**|**Reference values**|**Tolerance**|
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|O                 |                                                                                   |'ANALYTIQUE'      |—0.20625            |1%           |
+                  + .. image:: images/Object_63.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.20625            |1%           |
+                  + .. image:: images/Object_64.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|A                 |                                                                                   |'ANALYTIQUE'      |                    |0.01         |
+                  + .. image:: images/Object_179.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.0875             |2.5%         |
+                  + .. image:: images/Object_180.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|B                 |                                                                                   |'ANALYTIQUE'      |-0.04375            |7.5%         |
+                  + .. image:: images/Object_182.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |-0.04375            |7.5%         |
+                  + .. image:: images/Object_183.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|C                 |                                                                                   |'ANALYTIQUE'      |—0.0875             |2.5%         |
+                  + .. image:: images/Object_231.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |                    |0.01         |
+                  + .. image:: images/Object_232.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|D                 |                                                                                   |'ANALYTIQUE'      |—0.15469            |0.6%         |
+                  + .. image:: images/Object_65.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.17656            |0.6%         |
+                  + .. image:: images/Object_103.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|E                 |                                                                                   |'ANALYTIQUE'      |—0.15469            |0.7%         |
+                  + .. image:: images/Object_112.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.17656            |0.7%         |
+                  + .. image:: images/Object_113.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|F                 |                                                                                   |'ANALYTIQUE'      |—0.14025            |19%          |
+                  + .. image:: images/Object_114.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.16825            |19%          |
+                  + .. image:: images/Object_115.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+


+------------------+------------------------------------------+---------+--------+------------------+--------------------+-------------+
|**Identification**                                                              |**Reference type**|**Reference values**|**Tolerance**|
+------------------+------------------------------------------+---------+--------+                  +                    +             +
|**Size**                                                     |**Point**|**Mesh**|                  |                    |             |
+------------------+------------------------------------------+---------+--------+------------------+--------------------+-------------+
|ENEL_ELNO         |:math:`\mathit{TOTALE}`                   |C        |M14     |'NON_REGRESSION'  |45.79374            |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{MEMBRANE}`                 |         |        |'NON_REGRESSION'  |0.0                 |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{FLEXION}`                  |         |        |'NON_REGRESSION'  |44.78267            |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{CISAILLE}`                 |         |        |'NON_REGRESSION'  |1.01107             |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{COUPL}\text{\_}\mathit{MF}`|         |        |'NON_REGRESSION'  |0.0                 |0.1%         |
+------------------+------------------------------------------+---------+--------+------------------+--------------------+-------------+


+------------------+------------------------------------------+---------+--------+------------------+--------------------+-------------+
|**Identification**                                                              |**Reference type**|**Reference values**|**Tolerance**|
+------------------+------------------------------------------+---------+--------+                  +                    +             +
|**Size**                                                     |**Point**|**Mesh**|                  |                    |             |
+------------------+------------------------------------------+---------+--------+------------------+--------------------+-------------+
|ENEL_ELGA         |:math:`\mathit{TOTALE}`                   |1        |M14     |'NON_REGRESSION'  |57.36959            |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{MEMBRANE}`                 |         |        |'NON_REGRESSION'  |0.0                 |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{FLEXION}`                  |         |        |'NON_REGRESSION'  |56.47085            |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{CISAILLE}`                 |         |        |'NON_REGRESSION'  |0.89874             |0.1%         |
+                  +------------------------------------------+         +        +------------------+--------------------+-------------+
|                  |:math:`\mathit{COUPL}\text{\_}\mathit{MF}`|         |        |'NON_REGRESSION'  |0.0                 |0.1%         |
+------------------+------------------------------------------+---------+--------+------------------+--------------------+-------------+


+------------------+------------------------------------------+--------+------------------+--------------------+-------------+
|**Identification**                                                    |**Reference type**|**Reference values**|**Tolerance**|
+------------------+------------------------------------------+--------+                  +                    +             +
|**Size**                                                     |**Mesh**|                  |                    |             |
+------------------+------------------------------------------+--------+------------------+--------------------+-------------+
|ENEL_ELEM         |:math:`\mathit{TOTALE}`                   |M14     |'NON_REGRESSION'  |0.42940             |0.1%         |
+                  +------------------------------------------+        +------------------+--------------------+-------------+
|                  |:math:`\mathit{MEMBRANE}`                 |        |'NON_REGRESSION'  |0.0                 |0.1%         |
+                  +------------------------------------------+        +------------------+--------------------+-------------+
|                  |:math:`\mathit{FLEXION}`                  |        |'NON_REGRESSION'  |0.42229             |0.1%         |
+                  +------------------------------------------+        +------------------+--------------------+-------------+
|                  |:math:`\mathit{CISAILLE}`                 |        |'NON_REGRESSION'  |7.11225E-03         |0.1%         |
+                  +------------------------------------------+        +------------------+--------------------+-------------+
|                  |:math:`\mathit{COUPL}\text{\_}\mathit{MF}`|        |'NON_REGRESSION'  |0.0                 |0.1%         |
+------------------+------------------------------------------+--------+------------------+--------------------+-------------+