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


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

It is a modeling in plane deformations (D_ PLAN). The master and slave surfaces are not compliant.

Young's modulus :math:`{E}_{1}\mathrm{=}{E}_{2}` and Poisson's coefficients :math:`{\nu }_{1}\mathrm{=}{\nu }_{2}` are :math:`1.0E9\mathit{Pa}` and :math:`0.2` respectively. The pressure applied to the edge of the outer ring is :math:`1.0E7+\mathrm{10E5.cos}(2\theta )(\mathit{Pa})`, :math:`\theta` being the polar angle.

The outer ring defines the master surface.


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

The mesh (Figure 4.2-1) includes:


* 480 SEG2 meshes;


* 2640 QUAD4 meshes.


.. image:: images/10000000000002B8000002A0F4509587255710C3.png
    :width: 2.9925in
    :height: 2.889in


.. _RefImage_10000000000002B8000002A0F4509587255710C3.png:

**Figure** 4.2-a **: The B modeling mesh**

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

Note :math:`\lambda` the contact pressure calculated analytically, :math:`({U}_{x},{U}_{y})` the displacements calculated analytically.

In the case where the displacements are zero, an absolute tolerance equal to 2% of the value of the maximum radial displacement Urmax=5.5E-03 is defined.

The contact pressure (LAGS_C) and the components of the displacement in the plane (X, Y) (DX, DY) are calculated for the nodes with the following coordinates:


* N9 (5.98150400239877E-01, 4.70754574367070E-02)


* N10 (-4.70754574367070E-02, 5.98150400239877E-01)


* N11 (-5.98150400239877E-01, -4.70754574367070E-02)


* N12 (4.70754574367070E-02, -5.98150400239877E-01)


* N303 (3.89668829003112E-01, 4.56243579355747E-01)


* N371 (-4.562435793579355747E-01, 3.89668829003112E-01)


* N439 (-3.89668829003112E-01, -4.56243579355747E-01)


* N507 (4.562435793579355747E-01, -3.89668829003112E-01)


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**tolerance**"
    "LAGS_C at node 9"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at node 9"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 9"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 10"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at Node 10"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 10"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 11"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at Node 11"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 11"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 12"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at Node 12"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 12"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 303"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at node 303"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 303"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 371"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at node 371"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 371"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 439"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at node 439"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 439"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"
    "LAGS_C at node 507"," :math:`\lambda (x,y)` ", "Analytics", "2.10-2"
    "DX at node 507"," :math:`{U}_{x}(x,y)` ", "Analytics", "2.10-2"
    "DY at node 507"," :math:`{U}_{y}(x,y)` ", "Analytics", "2.10-2"


**Table** 4.3-1