Modeling A
==============


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

Shell element DKT (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{M30}\mathrm{M33}`"
    "Point :math:`A` ", "stitches: :math:`\mathrm{M76}`"
    "Point :math:`B` ", "stitches: :math:`\mathrm{M39}\mathrm{M40}\mathrm{M51}`"
    "Point :math:`C` ", "stitches: :math:`\mathrm{M1}`"
    "Point :math:`D` ", "stitches: :math:`\mathrm{M55}\mathrm{M56}\mathrm{M65}`"
    "Point :math:`E` ", "stitches: :math:`\mathrm{M8}\mathrm{M17}\mathrm{M18}`"
    "Point :math:`F` ", "stitches: :math:`\mathit{M34}\mathit{M35}\mathit{M37}\mathit{M41}\mathit{M46}\mathit{M47}\mathit{M48}`"



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

Number of knots: 50

Number of meshes and types: 76 TRIA3


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

The parameters of the result data structure are tested:


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference Value**"
    "INSTpour NUME_ORDRE =3", "'ANALYTIQUE'", "0.6"
    "INSTpour NUME_ORDRE =4"," ANALYTIQUE ", "1"



+---------------------------------------------------------------------------------------------------------+------------------+--------------------+
|**Identification**                                                                                       |**Reference type**|**Reference values**|
+---------------------------------------------------------------------------------------------------------+------------------+--------------------+
|O                                                                                                        |'ANALYTIQUE'      |— 695.6256          |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+ .. image:: images/Object_362.svg                                                                        +                  +                    +
|    :width: 33                                                                                           |                  |                    |
+    :height: 21                                                                                          +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+---------------------------------------------------------------------------------------------------------+------------------+--------------------+
|D                                                                                                        |'ANALYTIQUE'      |—489,727            |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+ .. image:: images/Object_363.svg                                                                        +                  +                    +
|    :width: 33                                                                                           |                  |                    |
+    :height: 21                                                                                          +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+---------------------------------------------------------------------------------------------------------+------------------+--------------------+
|E                                                                                                        |'ANALYTIQUE'      |—489,727            |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+ .. image:: images/Object_364.svg                                                                        +                  +                    +
|    :width: 33                                                                                           |                  |                    |
+    :height: 21                                                                                          +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+---------------------------------------------------------------------------------------------------------+------------------+--------------------+
|F                                                                                                        |'ANALYTIQUE'      |— 435.8974          |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+ .. image:: images/Object_365.svg                                                                        +                  +                    +
|    :width: 33                                                                                           |                  |                    |
+    :height: 21                                                                                          +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+                                                                                                         +                  +                    +
|                                                                                                         |                  |                    |
+---------------------------------------------------------------------------------------------------------+------------------+--------------------+



+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|**Identification**                                                                                    |**Reference type**|**Reference values**|**Tolerance**|
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|O                 |                                                                                   |'ANALYTIQUE'      |—0.20625            |1.5%         |
+                  + .. image:: images/Object_9.svg                                                    +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.20625            |1.5%         |
+                  + .. image:: images/Object_12.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|A                 |                                                                                   |'ANALYTIQUE'      |                    |0.01         |
+                  + .. image:: images/Object_15.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.0875             |6%           |
+                  + .. image:: images/Object_366.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|B                 |                                                                                   |'ANALYTIQUE'      |—0.04375            |13%          |
+                  + .. image:: images/Object_102.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.04375            |14%          |
+                  + .. image:: images/Object_13.svg                                                   +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|C                 |                                                                                   |'ANALYTIQUE'      |—0.0875             |6%           |
+                  + .. image:: images/Object_371.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |                    |0.01         |
+                  + .. image:: images/Object_372.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|D                 |                                                                                   |'ANALYTIQUE'      |—0.15469            |0.5%         |
+                  + .. image:: images/Object_374.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.17656            |0.5%         |
+                  + .. image:: images/Object_375.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|E                 |                                                                                   |'ANALYTIQUE'      |—0.15469            |0.3%         |
+                  + .. image:: images/Object_377.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.17656            |0.3%         |
+                  + .. image:: images/Object_378.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|F                 |                                                                                   |'ANALYTIQUE'      |—0.14025            |10%          |
+                  + .. image:: images/Object_380.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +-----------------------------------------------------------------------------------+------------------+--------------------+-------------+
|                  |                                                                                   |'ANALYTIQUE'      |—0.16825            |10%          |
+                  + .. image:: images/Object_381.svg                                                  +                  +                    +             +
|                  |    :width: 33                                                                     |                  |                    |             |
+                  +    :height: 21                                                                    +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+                  +                                                                                   +                  +                    +             +
|                  |                                                                                   |                  |                    |             |
+------------------+-----------------------------------------------------------------------------------+------------------+--------------------+-------------+



 Elastic energy


+------------------+------------------------------------------+--------+--------+------------------+--------------------+---------------+
|**Identification**                                                             |**Reference type**|**Reference values**|**Tolerance %**|
+------------------+------------------------------------------+--------+--------+                  +                    +               +
|**Size**                                                     |**Knot**|**Mesh**|                  |                    |               |
+------------------+------------------------------------------+--------+--------+------------------+--------------------+---------------+
|ENEL_ELNO         |:math:`\mathit{TOTALE}`                   |N2      |M1      |'NON_DEFINI'      |94.237              |0.1            |
+                  +------------------------------------------+        +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{MEMBRANE}`                 |        |        |'NON_DEFINI'      |0.0                 |0.1            |
+                  +------------------------------------------+        +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{FLEXION}`                  |        |        |'NON_DEFINI'      |93.112              |0.1            |
+                  +------------------------------------------+        +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{CISAILLE}`                 |        |        |'NON_DEFINI'      |1.125               |0.1            |
+                  +------------------------------------------+        +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{COUPL}\text{\_}\mathit{MF}`|        |        |'NON_DEFINI'      |0.0                 |0.1            |
+------------------+------------------------------------------+--------+--------+------------------+--------------------+---------------+


+------------------+------------------------------------------+---------+--------+------------------+--------------------+---------------+
|**Identification**                                                              |**Reference type**|**Reference values**|**Tolerance %**|
+------------------+------------------------------------------+---------+--------+                  +                    +               +
|**Size**                                                     |**Point**|**Mesh**|                  |                    |               |
+------------------+------------------------------------------+---------+--------+------------------+--------------------+---------------+
|ENEL_ELGA         |:math:`\mathit{TOTALE}`                   |1        |M1      |'NON_DEFINI'      |77.080              |0.1            |
+                  +------------------------------------------+         +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{MEMBRANE}`                 |         |        |'NON_DEFINI'      |0.0                 |0.1            |
+                  +------------------------------------------+         +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{FLEXION}`                  |         |        |'NON_DEFINI'      |75.955              |0.1            |
+                  +------------------------------------------+         +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{CISAILLE}`                 |         |        |'NON_DEFINI'      |1.1248              |0.1            |
+                  +------------------------------------------+         +        +------------------+--------------------+---------------+
|                  |:math:`\mathit{COUPL}\text{\_}\mathit{MF}`|         |        |'NON_DEFINI'      |0.0                 |0.1            |
+------------------+------------------------------------------+---------+--------+------------------+--------------------+---------------+


+------------------+------------------------------------------+--------+------------------+--------------------+---------------+
|**Identification**                                                    |**Reference type**|**Reference values**|**Tolerance %**|
+------------------+------------------------------------------+--------+                  +                    +               +
|**Size**                                                     |**Mesh**|                  |                    |               |
+------------------+------------------------------------------+--------+------------------+--------------------+---------------+
|ENEL_ELEM         |:math:`\mathit{TOTALE}`                   |M1      |'NON_DEFINI'      |0.781               |0.1            |
+                  +------------------------------------------+        +------------------+--------------------+---------------+
|                  |:math:`\mathit{MEMBRANE}`                 |        |'NON_DEFINI'      |0.0                 |0.1            |
+                  +------------------------------------------+        +------------------+--------------------+---------------+
|                  |:math:`\mathit{FLEXION}`                  |        |'NON_DEFINI'      |0.767               |0.1            |
+                  +------------------------------------------+        +------------------+--------------------+---------------+
|                  |:math:`\mathit{CISAILLE}`                 |        |'NON_DEFINI'      |0.015               |0.1            |
+                  +------------------------------------------+        +------------------+--------------------+---------------+
|                  |:math:`\mathit{COUPL}\text{\_}\mathit{MF}`|        |'NON_DEFINI'      |0.0                 |0.1            |
+------------------+------------------------------------------+--------+------------------+--------------------+---------------+

We also test in non-regression:


* the different components of elastic energy in the case of a calculation with MECA_STATIQUE,


* the VMIS component of SIEQ_ELNO.