6. D modeling#
6.1. Characteristics of modeling#
Same as C modeling but we play with Young’s modules and Poisson’s coefficients:
Outer ring: \({E}_{1}\mathrm{=}1.0E9\), \({\nu }_{1}\mathrm{=}0.3\)
Inner crown: \({E}_{2}\mathrm{=}1.0E8\), \({\nu }_{2}\mathrm{=}0.2\)
The outer ring defines the master surface.
6.2. Characteristics of the mesh#
Idem modeling A.
6.3. Tested sizes and results#
The contact pressure (LAGS_C) is calculated for the node \(A\) with coordinates \((0.6\mathrm{,0}.0)\), the node that at the initial moment is located farthest to the right of the interface between the two rings. The calculated values are compared to the value obtained according to equation 1.5 for an external pressure of \(p\mathrm{=}1.0E7\). The rotation of the inner ring is applied. We look at the variations in external pressure during this rotation.
Identification |
Reference |
Aster |
tolerance |
LAGS_C at node \(A\) Integration diagram AUTO |
|
Analytics |
\(\mathrm{1,7}\text{\%}\) |
LAGS_C at node \(A\) Integration diagram GAUSS |
|
Analytics |
\(\mathrm{1,9}\text{\%}\) |
6.4. Comments#
When the displacements become too significant due to low stiffness of the rings, the calculated value differs from that calculated analytically, once this solution has been developed on the hypothesis of small deformations and the simulation has been carried out in large displacements.
On the other hand, when the stiffness of the rings is too great, the fluctuation in contact pressure increases significantly. This comes from the fact that when a displacement is imposed on a structure, the stresses to which it is subjected may be too high (or even infinite) in order to be compatible with the laws of mechanics. For a very rigid structure, a small displacement is possible only with considerable constraints.