B modeling
==============


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

We use a AXIS model. Three calculations are performed with different matching options or contact algorithms.


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


.. image:: images/100000000000036A00000321F96CDE73DCFEB23F.png
    :width: 4.822in
    :height: 4.4465in


.. _RefImage_100000000000036A00000321F96CDE73DCFEB23F.png:

Knots: 376 knots.

Meshes: 30 TRIA3 and 324 QUAD4.


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

First calculation (algorithm 'PENALISATION', nodal matching, normal slave)


+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|**Identification**                                                                                                                       |**Reference type**|**Reference value**          |**Tolerance**|
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|                                                                                                                                         |'ANALYTIQUE'      |-2798.3 :math:`N`            |7.0%         |
+ .. image:: images/Object_9.svg                                                                                                          +                  +                             +             +
|    :width: 26                                                                                                                           |                  |                             |             |
+    :height: 24                                                                                                                          +                  +                             +             +
|                                                                                                                                         |                  |                             |             |
+ mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)`                                                                                 +                  +                             +             +
|                                                                                                                                         |                  |                             |             |
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)`                                                                                        |'ANALYTIQUE'      |0 :math:`\mathit{mm}`        |1.0E-10      |
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)`                                                                                        |'NON_REGRESSION'  |-0,111338 :math:`\mathit{mm}`|             |
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)`                                                                                        |'NON_REGRESSION'  |-0,161811 :math:`\mathit{mm}`|             |
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)`                                                                                        |'NON_REGRESSION'  |-0,168635 :math:`\mathit{mm}`|             |
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)`                                                                                        |'NON_REGRESSION'  |-0.628585 :math:`\mathit{mm}`|             |
+-----------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+


Second calculation (algorithm 'PENALISATION')


+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|**Identification**                                                                                                                        |**Reference type**|**Reference value**          |**Tolerance**|
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|                                                                                                                                          |'ANALYTIQUE'      |-2798.3 :math:`N`            |7.0%         |
+ .. image:: images/Object_94.svg                                                                                                          +                  +                             +             +
|    :width: 26                                                                                                                            |                  |                             |             |
+    :height: 24                                                                                                                           +                  +                             +             +
|                                                                                                                                          |                  |                             |             |
+ mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)`                                                                                  +                  +                             +             +
|                                                                                                                                          |                  |                             |             |
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)`                                                                                         |'ANALYTIQUE'      |0 :math:`\mathit{mm}`        |1.0E-10      |
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)`                                                                                         |'NON_REGRESSION'  |-0.108104 :math:`\mathit{mm}`|             |
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)`                                                                                         |'NON_REGRESSION'  |-0,164375 :math:`\mathit{mm}`|             |
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)`                                                                                         |'NON_REGRESSION'  |-0,160912 :math:`\mathit{mm}`|             |
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)`                                                                                         |'NON_REGRESSION'  |-0.631411 :math:`\mathit{mm}`|             |
+------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+


Third calculation (algorithm 'CONTRAINTE')


+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|**Identification**                                                                                                                         |**Reference type**|**Reference value**          |**Tolerance**|
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|                                                                                                                                           |'ANALYTIQUE'      |-2798.3 :math:`N`            |7.0%         |
+ .. image:: images/Object_117.svg                                                                                                          +                  +                             +             +
|    :width: 26                                                                                                                             |                  |                             |             |
+    :height: 24                                                                                                                            +                  +                             +             +
|                                                                                                                                           |                  |                             |             |
+ mesh :math:`\mathit{M31}` knot :math:`\mathit{N291}(G)`                                                                                   +                  +                             +             +
|                                                                                                                                           |                  |                             |             |
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N291}(G)`                                                                                          |'ANALYTIQUE'      |0 :math:`\mathit{mm}`        |1.0E-10      |
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N287}(H)`                                                                                          |'NON_REGRESSION'  |-0.108104 :math:`\mathit{mm}`|             |
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DY}` knot :math:`\mathit{N287}(H)`                                                                                          |'NON_REGRESSION'  |-0,164375 :math:`\mathit{mm}`|             |
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DX}` knot :math:`\mathit{N285}(I)`                                                                                          |'NON_REGRESSION'  |-0,160912 :math:`\mathit{mm}`|             |
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+
|:math:`\mathrm{DY}` knot :math:`\mathit{N285}(I)`                                                                                          |'NON_REGRESSION'  |-0.631409 :math:`\mathit{mm}`|             |
+-------------------------------------------------------------------------------------------------------------------------------------------+------------------+-----------------------------+-------------+



notes
---------

The difference between the contact pressure at point :math:`G` and the analytical solution is explained on the one hand by extrapolation (passage from Gauss points to nodes) and on the other hand by the poor refinement of the mesh.

We note that the contact algorithms' PENALISATION 'and' CONTRAINTE 'give exactly the same results and that the nodal matching makes it possible to maintain the symmetry of the problem while giving results that are very similar to the node-facet pairing.