10. H modeling#

10.1. Characteristics of modeling#

It is a 3D model. The master and slave surfaces facing each other are such that their meshes are not compatible. 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. 10.2-1). Solution displacements will be applied as boundary conditions on the other surfaces (in blue in figure 10.2-1).

The outer ring defines the master surface.

10.2. Characteristics of the mesh#

The mesh (Figure 8.2-1) includes:

  • 464 QUAD8 meshes;

  • 400 HEXA20 meshes.

10.3. 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 is defined equal to 2% 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: N97 (5.54327719506785E-01, 2.29610059419021E-01, 0.00000000000000E+00),

N213 (5.54327719506785E-01, 2.29610059419021E-01, 4.00000000000000E-01),

N1256 (5.54327719506760E-01, 2.29610059419083E-01, 1.9999999999999678E-01)

  • GROUPE 2: N100 (4.24264068711920E-01, 4.24264068711937E-01, 0.00000000000000E+00),

N216 (4.24264068711920E-01, 4.24264068711937E-01, 4.00000000000000E-01),

N1253 (5.68158077697052E-01, 1.92863679181931E-01, 3.4999999999999963E-01)

  • GROUPE 3: N103 (2.29610059419306E-01, 5.54327719506668E-01, 0.00000000000000E+00),

N219 (2.29610059419306E-01, 5.54327719506668E-01, 4.00000000000000E-01),

N1214 (2.29610059419285E-01, 5.54327719506676E-01, 1.99999999999678E-01)

Table 10.3-1