7. E modeling#

7.1. Characteristics of modeling#

It is a 3D model. The master and slave surfaces are facing each other with compatible meshes. To avoid having calculations that are too slow, we will only take a quarter of the geometry.

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 pressure does not vary in the longitudinal direction. To have a model in accordance with the plane deformations, zero longitudinal displacement will be imposed on the two upper surfaces (in red in FIG. 7.2-1). Solution displacements will be applied as boundary conditions on the other surfaces (in blue in figure 7.2-1).

The outer ring defines the master surface.

7.2. Characteristics of the mesh#

The mesh (Figure 7.2-1) includes:

  • 448 QUAD4 meshes;

  • 384 HEXA8 meshes.

_images/100000000000035100000293598FCE7FF9E9D556.png

Figure 7.2-a : The E modeling mesh

7.3. Tested sizes and results#

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

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

The minimum value and the maximum value of the contact pressure (LAGS_C) and the displacement components (DX, DY, DZ) are calculated for the following groups of nodes:

  • GROUPE 1: N47 (5.54327719507606E-01, 2.29610059417040E-01, 0.00000000000000E+00),

N103 (5.54327719507606E-01, 2.29610059417040E-01, 4.00000000000000E-01),

N412 (5.54327719507606E-0, 2.29610059417040E-01, 1.9999999999999678E-01)

  • GROUPE 2: N50 (4.24264068712436E-01, 4.24264068711421E-01, 0.00000000000000E+00),

N106 (4.24264068712436E-01, 4.24264068711421E-01, 4.00000000000000E-01),

N403 (4.24264068712436E-01, 4.24264068711421E-01, 1.99999999999678E-01)

  • GROUPE 3: N53 (2.29610059417922E-01, 5.54327719507241E-01, 0.00000000000000E+00),

N109 (2.29610059417922E-01, 5.54327719507241E-01, 4.00000000000000E-01),

N394 (2.29610059417922E-01, 5.54327719507241E-01, 1.9999999999999678E-01)

Table 7.3-1