H modeling
==============


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

Q4G shell element (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                                         |0.2%         |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_49.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|D                                                                                                       |'ANALYTIQUE'      |—495.56                                         |0.3%         |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_59.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|E                                                                                                       |'ANALYTIQUE'      |—495.56                                         |0.3%         |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_60.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+
|F                                                                                                       |'ANALYTIQUE'      |—441.18                                         |0.3%         |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+ .. image:: images/Object_61.svg                                                                        +                  +                                                +             +
|    :width: 33                                                                                          |                  |                                                |             |
+    :height: 21                                                                                         +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+                                                                                                        +                  +                                                +             +
|                                                                                                        |                  |                                                |             |
+--------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------+-------------+



+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|**Identification**                                                                                    |**Reference type**|**Reference values**|**Tolerance**|
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|O                 |                                                                                   |'ANALYTIQUE'      |—0.20625            |0.2%         |
+                  + .. image:: images/Object_76.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.20625            |0.2%         |
+                  + .. image:: images/Object_77.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|A                 |                                                                                   |'ANALYTIQUE'      |                    |0.02         |
+                  + .. image:: images/Object_392.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.0875             |4.5%         |
+                  + .. image:: images/Object_393.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|B                 |                                                                                   |'ANALYTIQUE'      |-0.04375            |20%          |
+                  + .. image:: images/Object_395.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |-0.04375            |20%          |
+                  + .. image:: images/Object_396.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|C                 |                                                                                   |'ANALYTIQUE'      |—0.0875             |0.02         |
+                  + .. image:: images/Object_398.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |                    |4.5%         |
+                  + .. image:: images/Object_399.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|D                 |                                                                                   |'ANALYTIQUE'      |—0.15469            |0.25%        |
+                  + .. image:: images/Object_78.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.17656            |0.25%        |
+                  + .. image:: images/Object_128.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|E                 |                                                                                   |'ANALYTIQUE'      |—0.15469            |0.25%        |
+                  + .. image:: images/Object_145.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.17656            |0.25%        |
+                  + .. image:: images/Object_148.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|F                 |                                                                                   |'ANALYTIQUE'      |—0.14025            |0.35%        |
+                  + .. image:: images/Object_155.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.16825            |0.35%        |
+                  + .. image:: images/Object_163.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+