Rapid Methods for the Resolution of Contact Problems in Static Linear Elasticity

In this paper, the two dimensional Signorini static contact problem in linear elasticity is presented. We present the weak formulation of frictionless and the frictional contact problems. In the both cases, the boundary integral operators are used to propose a boundary variational formulation whose resolution by the generalized Newton method is presented. Moreover a particular formulation by the fixed point method associated with the augmented Lagrangian is proposed for efficient analysis of contact problems with friction (Tresca and Coulomb) and powerful algorithms are constructed. The discretization is carried over by using the Galerkin method. The resulting linear system is solved by using preconditioned Conjugate Gradient (CG) iterative solver.