5. C modeling#

5.1. Characteristics of modeling#

It is a modeling in plane deformations (D_ PLAN). The master and slave surfaces are compliant.

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

The outer ring defines the master surface.

5.2. Characteristics of the mesh#

The mesh (Figure 4.2-1) includes:

  • 480 SEG3 meshes;

  • 2640 QUAD8 meshes.

_images/1000000000000377000003178AD7B902CE1F37F4.png

Figure 5.2-a : The C modeling mesh

5.3. Tested sizes and results#

Note \(\lambda\) the contact pressure calculated analytically, \(({U}_{x},{U}_{y})\) 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 (0.6, 0.0)

  • N10 (0.0, 0.6)

  • N11 (-0.6, 0.0)

  • N12 (0.0, -0.6)

  • N587 (4.24264068712436E-01, 4.24264068711421E-01)

  • N726 (-4.24264068711421E-01, 4.24264068712436E-01)

  • N865 (-4.24264068712436E-01, -4.24264068711421E-01)

  • N1004 (4.24264068711421E-01, -4.24264068712436E-01)

Identification

Reference

Aster

tolerance

LAGS_C at node 9

\(\lambda (x,y)\)

Analytics

2.10-2

DX at node 9

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 9

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 10

\(\lambda (x,y)\)

Analytics

2.10-2

DX at Node 10

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 10

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 11

\(\lambda (x,y)\)

Analytics

2.10-2

DX at Node 11

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 11

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 12

\(\lambda (x,y)\)

Analytics

2.10-2

DX at Node 12

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 12

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 587

\(\lambda (x,y)\)

Analytics

2.10-2

DX at node 587

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 587

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 726

\(\lambda (x,y)\)

Analytics

2.10-2

DX at node 726

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 726

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 865

\(\lambda (x,y)\)

Analytics

2.10-2

DX at node 865

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 865

\({U}_{y}(x,y)\)

Analytics

2.10-2

LAGS_C at node 1004

\(\lambda (x,y)\)

Analytics

2.10-2

DX at node 1004

\({U}_{x}(x,y)\)

Analytics

2.10-2

DY at node 1004

\({U}_{y}(x,y)\)

Analytics

2.10-2

Table 5.3-1