J modeling
==============


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

Axisymmetric shell element SEG3, in Mindlin-Reissner theory: we do not consider any metric modification, the coefficient A_ CIS is equal to :math:`5\mathrm{/}6`.


.. image:: images/100005380000175C00000D20B37F2DCC90A00C38.svg
    :width: 301
    :height: 169


.. _RefImage_100005380000175C00000D20B37F2DCC90A00C38.svg:

Boundary conditions:


.. code-block:: text
 DDL_IMPO =( _F
(NOEUD = 'A', DX= 0. , DY= 0. , DRZ = 0.)
(NOEUD = 'O', DRZ = 0.))


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

Number of knots: 21

Number of meshes and types: 10 SEG3


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


+-----------------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------------+---------------------------------+
|**Identification**                                                                                               |**Reference type**|**Reference values**                                  |**Tolerance** :math:`(\text{\%})`|
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  | **Love-Kirchhoff**                                   |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+-----------------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------------+---------------------------------+
|Arrow                                                                                                            |'ANALYTIQUE'      |—178.424                                              |0.5                              |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+ .. image:: images/Object_21.svg                                                                                 +                  +                                                      +                                 +
|    :width: 301                                                                                                  |                  |                                                      |                                 |
+    :height: 169                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+-----------------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------------+---------------------------------+
|Arrow                                                                                                            |'ANALYTIQUE'      |—101.827                                              |0.5                              |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+ .. image:: images/Object_22.svg                                                                                 +                  +                                                      +                                 +
|    :width: 301                                                                                                  |                  |                                                      |                                 |
+    :height: 169                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+-----------------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------------+---------------------------------+
|Rotation                                                                                                         |'ANALYTIQUE'      |255.940                                               |0.5                              |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+ .. image:: images/Object_23.svg                                                                                 +                  +                                                      +                                 +
|    :width: 301                                                                                                  |                  |                                                      |                                 |
+    :height: 169                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+                                                                                                                 +                  +                                                      +                                 +
|                                                                                                                 |                  |                                                      |                                 |
+-----------------------------------------------------------------------------------------------------------------+------------------+------------------------------------------------------+---------------------------------+



+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|**Identification**                                                                                             |**Reference type**|**Reference values**|**Tolerance** :math:`(\text{\%})`|
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|Point             |Maille|Component                                                                            |                  |                    |                                 |
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|D                 |IJK   |                                                                                     |'ANALYTIQUE'      |170.625             |                                 |
+                  +      + .. image:: images/Object_90.svg                                                     +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |      |                                                                                     |'ANALYTIQUE'      |511.875             |0.5                              |
+                  +      + .. image:: images/Object_253.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |KLM   |                                                                                     |'ANALYTIQUE'      |170.625             |                                 |
+                  +      + .. image:: images/Object_269.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |      |                                                                                     |'ANALYTIQUE'      |511.875             |0.5                              |
+                  +      + .. image:: images/Object_270.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+


+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|**Identification**                                                                                             |**Reference type**|**Reference values**|**Tolerance** :math:`(\text{\%})`|
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|Point             |Maille|Component                                                                            |                  |                    |                                 |
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|O                 |STU   |                                                                                     |'ANALYTIQUE'      |—0.08125            |                                 |
+                  +      + .. image:: images/Object_272.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |      |                                                                                     |'ANALYTIQUE'      |—0.08125            |                                 |
+                  +      + .. image:: images/Object_273.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|A                 |ABC   |                                                                                     |'ANALYTIQUE'      |0.125               |                                 |
+                  +      + .. image:: images/Object_274.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |      |                                                                                     |'ANALYTIQUE'      |0.0375              |                                 |
+                  +      + .. image:: images/Object_275.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|A                 |IJK   |                                                                                     |'ANALYTIQUE'      |—0.05156            |0.5                              |
+                  +      + .. image:: images/Object_277.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+
|                  |KLM   |                                                                                     |'ANALYTIQUE'      |—0.05156            |0.7                              |
+                  +      + .. image:: images/Object_279.svg                                                    +                  +                    +                                 +
|                  |      |    :width: 301                                                                      |                  |                    |                                 |
+                  +      +    :height: 169                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+                  +      +                                                                                     +                  +                    +                                 +
|                  |      |                                                                                     |                  |                    |                                 |
+------------------+------+-------------------------------------------------------------------------------------+------------------+--------------------+---------------------------------+

**Notes:**

*We note the good results obtained, except on*

.. image:: images/Object_121.svg
    :width: 301
    :height: 169


.. _RefImage_Object_121.svg:

*and*

.. image:: images/Object_122.svg
    :width: 301
    :height: 169


.. _RefImage_Object_122.svg:

*, which involve higher-order derivatives that are less well calculated by the element.*


Contents of the results file
----------------------------

Generalized movements, deformations and forces and stresses at the nodes.