C modeling
==============


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

Meshing with incompressible 2D elements like QUAD8 and TRIA6.


.. image:: images/10005A2E00002957000015E96F33A1848BC62479.svg
    :width: 533
    :height: 282


.. _RefImage_10005A2E00002957000015E96F33A1848BC62479.svg:

Boundary conditions:

DDL_IMPO = GROUP_NO =' GRNM11 ', DX = 0 side :math:`\mathrm{AB}`

FACE_IMPO = GROUP_MA =' GRMA12 ', DNOR = 0 side :math:`\mathrm{EF}`

PRES_REP = GROUP_MA =' GRMA13 ', PRES = 60 sided :math:`\mathrm{AE}`

**Node name:**

:math:`A=\mathrm{N2}`, :math:`B=\mathrm{N361}`, :math:`C=\mathrm{N121}`, :math:`D=\mathrm{N584}`,, :math:`E=\mathrm{N155}`, :math:`F=\mathrm{N503}`


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

Number of knots: 591

Number of meshes: 200 TRIA6, 50 QUAD8.


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

Results at point :math:`A`:


* first column D_ PLAN_INCO_UPG without imposing :math:`\mathrm{GONF}=0`


* second column D_ PLAN_INCO_UPG by imposing :math:`\mathrm{GONF}=0`


* third column D_ PLAN_INCO_UP with quadratic mesh


* fourth columnD_ PLAN_INCO_UP with linear mesh


* fifth columnD_ PLAN_INCO_UPO with linear elements


+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|**Identification**                           |**Reference type**|**Reference value**|**Tolerance**                        |
+                                             +                  +                   +-------------+-----+-----+-----+-----+
|                                             |                  |                   |**1**        |**2**|**3**|**4**|**5**|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`u`                                    |'ANALYTIQUE'      |                   |10-5         |10-5 |10-5 |10-5 |10-5 |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`v`                                    |'ANALYTIQUE'      | #. 10-5           |0.50%        |0.50%|0.50%|0.50%|0.50%|
+                                             +                  +                   +             +     +     +     +     +
|                                             |                  |                   |             |     |     |     |     |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{xx}}`              |'ANALYTIQUE'      |                   |0.50%        |0.50%|0.50%|0.60%|0.50%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{yy}}`              |'ANALYTIQUE'      |—60.               |0.50%        |0.50%|0.50%|2.50%|2.10%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{zz}}`              |'ANALYTIQUE'      |                   |0.50%        |0.50%|0.50%|5.00%|1.60%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{xy}}`              |'ANALYTIQUE'      |                   |0.3          |0.3  |0.3  |1.5  |0.9  |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{xx}}`         |'ANALYTIQUE'      | #. 10-4           |0.50%        |0.50%|0.50%|0.50%|0.50%|
+                                             +                  +                   +             +     +     +     +     +
|                                             |                  |                   |             |     |     |     |     |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{yy}}`         |'ANALYTIQUE'      |—6. 10-4           |0.50%        |0.50%|0.50%|1.50%|1.50%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{xy}}`         |'ANALYTIQUE'      |                   |10-5         |10-5 |10-5 |10-5 |10-5 |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{eq}}` - INVA_2|'ANALYTIQUE'      |6.92 10-4          |0.50%        |0.50%|0.50%|1.00%|1.00%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{eq}}` - PRIN_1|'ANALYTIQUE'      |—6. 10-4           |0.50%        |0.50%|0.50%|1.50%|1.50%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{eq}}` - PRIN_2|'ANALYTIQUE'      |                   |10-5         |10-5 |10-5 |10-5 |10-5 |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{eq}}` - PRIN_3|'ANALYTIQUE'      | #. 10-4           |0.50%        |0.50%|0.50%|0.50%|0.50%|
+                                             +                  +                   +             +     +     +     +     +
|                                             |                  |                   |             |     |     |     |     |
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{eq}}` - VMIS       |'ANALYTIQUE'      |138.56             |1.00%        |1.00%|1.00%|1.00%|1.00%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{eq}}` - TRESCA     |'ANALYTIQUE'      |                   |1.00%        |1.00%|1.00%|1.00%|1.00%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{eq}}` - PRIN_1     |'ANALYTIQUE'      |-60.               |1.00%        |1.00%|1.00%|2.50%|2.10%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{eq}}` - PRIN_2     |'ANALYTIQUE'      |                   |1.00%        |1.00%|1.00%|5.00%|1.60%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{eq}}` - PRIN_3     |'ANALYTIQUE'      |                   |1.00%        |1.00%|1.00%|1.00%|1.00%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{eq}}` - VMIS       |'ANALYTIQUE'      |138.56             |1.00%        |1.00%|1.00%|1.00%|1.00%|
+---------------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+

Results at point :math:`F`:


* first column D_ PLAN_INCO_UPG without imposing :math:`\mathrm{GONF}=0`


* second column D_ PLAN_INCO_UPG by imposing :math:`\mathrm{GONF}=0`


* third column D_ PLAN_INCO_UP with quadratic mesh


* fourth columnD_ PLAN_INCO_UP with linear mesh


* fifth columnD_ PLAN_INCO_UPO with linear elements


+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|**Identification**                  |**Reference type**|**Reference value**|**Tolerance**                        |
+                                    +                  +                   +-------------+-----+-----+-----+-----+
|                                    |                  |                   |**1**        |**2**|**3**|**4**|**5**|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`u`                           |'ANALYTIQUE'      |—2.12 10-5         |0.50%        |0.50%|0.50%|0.50%|0.50%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`v`                           |'ANALYTIQUE'      |2.12 10-5          |0.50%        |0.50%|0.50%|0.50%|0.50%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{xx}}`     |'ANALYTIQUE'      |                   |0.50%        |0.50%|0.50%|1.00%|1.00%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{yy}}`     |'ANALYTIQUE'      |                   |0.50%        |0.50%|0.50%|2.00%|1.50%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{zz}}`     |'ANALYTIQUE'      |                   |0.50%        |0.50%|0.50%|0.50%|0.50%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\sigma }_{\mathrm{xy}}`     |'ANALYTIQUE'      |                   |0.50%        |0.50%|0.50%|0.50%|0.50%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{xx}}`|'ANALYTIQUE'      |                   |10-5         |10-5 |10-5 |10-5 |10-5 |
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{yy}}`|'ANALYTIQUE'      |                   |10-5         |10-5 |10-5 |10-5 |10-5 |
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+
|:math:`{\varepsilon }_{\mathrm{xy}}`|'ANALYTIQUE'      |1.5 10-4           |0.50%        |0.50%|0.50%|0.50%|0.50%|
+------------------------------------+------------------+-------------------+-------------+-----+-----+-----+-----+


notes
---------

As for 3D modeling, the results obtained are completely satisfactory.