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


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

2D axisymmetric finite elements



.. image:: images/Object_12.svg
    :width: 245
    :height: 361


.. _RefImage_Object_12.svg:

The discretized geometry is shown above:


.. csv-table::

    ":math:`\mathrm{Bord}` "," :math:`\mathrm{group}\text{\_}\mathrm{no}`"
    ":math:`\mathrm{BC}` "," :math:`\mathrm{BC}`"
    ":math:`\mathrm{DA}` "," :math:`\mathrm{DA}`"
    ":math:`\mathrm{AB}` "," :math:`\mathrm{BAS}`"
    ":math:`\mathrm{CD}` "," :math:`\mathrm{HAUT}`"



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

The mesh is regular: 4 elements in the height, 8 in the thickness.

Number of knots: 121

Number of meshes and type: 32 QUAD8


Boundary conditions while on the go
-------------------------------------


Gravity
~~~~~~~~

Move :math:`\mathrm{DY}` is stuck at point :math:`F` alone.


Rotation
~~~~~~~

Move :math:`\mathrm{DY}` is stuck on sides :math:`[\mathrm{AB}]` (GROUP_NO = 'BAS') and on :math:`[\mathrm{CD}]` (GROUP_NO = 'HAUT').


Thermal expansion case no. 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Move :math:`\mathrm{DY}` is stuck all over the structure.


Thermal expansion case no. 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Move :math:`\mathrm{DY}` is stuck on sides :math:`[\mathrm{AB}]` (GROUP_NO = 'BAS') and :math:`[\mathrm{CD}]` (GROUP_NO = 'HAUT').


Model A results
------------------------------


+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|**Identification**                  |**Knot (Knit)**                   |**Value tested**                            |**Reference**|
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|Gravity                             |:math:`\mathrm{N78}`              |:math:`\mathrm{DX}` :math:`(\mathrm{mm})`   |—2.34000 10—8|
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N120}`             |:math:`\mathrm{DY}` :math:`(\mathrm{mm})`   |—1.185 10—9  |
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N13}`              |:math:`\mathrm{DY}` :math:`(\mathrm{mm})`   |1.2150 10—9  |
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N78}(\mathrm{M13})`|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|8.0000 10—4  |
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|                                    |                                  |                                            |             |
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|Uniform rotation - centrifugal force|:math:`\mathrm{N120}`             |:math:`\mathrm{DX}` :math:`(\mathrm{mm})`   |—2.94240 10—7|
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N13}`              |:math:`\mathrm{DX}` :math:`(\mathrm{mm})`   |2.88010 10—7 |
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N120}(\mathrm{M1})`|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|9.94880 10—4 |
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N13}(\mathrm{M32})`|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|9.26310 10—4 |
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|                                    |                                  |                                            |             |
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|Dilation case 1                     |:math:`\mathrm{N120}`             |:math:`\mathrm{DX}` :math:`(\mathrm{mm})`   |1.056145 10—6|
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N13}`              |:math:`\mathrm{DX}` :math:`(\mathrm{mm})`   |1.110317 10—6|
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N120}(\mathrm{M1})`|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|1.4321427    |
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|                                    |                                  |                                            |             |
+------------------------------------+----------------------------------+--------------------------------------------+-------------+
|Dilation case 2                     |:math:`\mathrm{N120}`             |:math:`\mathrm{DX}` :math:`(\mathrm{mm})`   |2.53500 10—5 |
+                                    +----------------------------------+--------------------------------------------+-------------+
|                                    |:math:`\mathrm{N120}(\mathrm{M1})`|:math:`\mathrm{SIYY}` :math:`(\mathrm{MPa})`|—2.00000 10—1|
+------------------------------------+----------------------------------+--------------------------------------------+-------------+