Reliability analysis of a mechanical contact between deformable solids

The contact problems in mechanics are very complex. The behavior of a structure, where a contact occurs, depends on some assumptions on the design parameters and is in general highly nonlinear. Several deterministic numerical methods have been developed on finite element codes and give accurate solutions of contact problems. However some design variables could be random and the deterministic results could be unacceptable. Thus a new reliability analysis of a mechanical contact is presented. A reliability–mechanical combination based on an augmented Lagrangian method and a response surface method is proposed to compute the failure probability of this nonlinear problem. Then the advantages of this probabilistic approach are exposed and commentated on an Hertz numerical application.