D modeling
==============


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

Meshing with elements "AXIS_INCO_UPG" and "DEFORMATION =' SIMO_MIEHE '``
incompressible types TRIA6 and QUAD8.


.. image:: images/1000125A00002D7A00000E0E17035B052F36D7EF.svg
    :width: 586
    :height: 181


.. _RefImage_1000125A00002D7A00000E0E17035B052F36D7EF.svg:

The boundary conditions are:

* Zero vertical displacement on 'FACSUP' faces (side :math:`\mathit{EF}`)
  and 'FACINF' (side :math:`\mathit{AB}`): DY = 0.
* Radial displacement imposed on the inside 'FACEAE'
  (side :math:`\mathit{AE}`): DX = 6. 10-5

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

Number of knots: 175.

Number of meshes and types: 20 QUAD8, 40 TRIA6.


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

Displacements and constraints SIGM_NOEU are evaluated at points :math:`A`
and :math:`F`. The components of field SIEQ_NOEU are tested to the point
:math:`A` only.


+------------------+----------------------------+------------------+-------------+-------------+
|**Identification**                             |**Reference type**|**Reference**|**Tolerance**|
+------------------+----------------------------+------------------+-------------+-------------+
|:math:`A`         |:math:`\mathit{u}` (X)      |ANALYTIQUE        | #. 10-5     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{v}` (DY)     |ANALYTIQUE        |             | #. 10-5     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xx}}`|ANALYTIQUE        |-59.9955     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{yy}}`|ANALYTIQUE        |19.9326      | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{zz}}`|ANALYTIQUE        |99.9566      | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xy}}`|ANALYTIQUE        |             | #. 10-5     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |VMIS                        |ANALYTIQUE        |138.5226     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |TRESCA                      |ANALYTIQUE        |159.9521     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_1                      |ANALYTIQUE        |-59.9955     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_2                      |ANALYTIQUE        |19.9326      | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_3                      |ANALYTIQUE        |99.9566      | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |VMIS_SG                     |ANALYTIQUE        |138.5226     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+


+------------------+----------------------------+------------------+-------------+-------------+
|**Identification**                             |**Reference type**|**Reference**|**Tolerance**|
+------------------+----------------------------+------------------+-------------+-------------+
|:math:`F`         |:math:`\mathit{u}` (X)      |ANALYTIQUE        | #. 10-5     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{v}` (DY)     |ANALYTIQUE        |             | #. 10-5     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xx}}`|ANALYTIQUE        |             |0.03         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{yy}}`|ANALYTIQUE        |20.0         | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{zz}}`|ANALYTIQUE        |40.006       | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xy}}`|ANALYTIQUE        |             | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+

For Green-Lagrange deformations:


+------------------+-------------------------+------------------+------------------+-------------+
|**Identification**                          |**Reference type**|**Reference**     |**Tolerance**|
+------------------+-------------------------+------------------+------------------+-------------+
|:math:`A`         |:math:`{E}_{\mathit{xx}}`|ANALYTIQUE        |-0.000598704996172|2E-3         |
+------------------+-------------------------+------------------+------------------+-------------+


notes
---------

The precision obtained is very good since all the constraints are obtained.
with an accuracy of less than :math:`\text{0.5%}`.