Variational boundary-integral-equation approach to unilateral contact problems in elasticity

On the basis of the boundary integral equation method, three variational principles for the frictionless unilateral contact problem in elasticity are presented. Two of them are saddle-point principles for the boundary unknowns (including the contact displacements); a third one is a maximum principle for the unknown contact displacements only. A discretization by boundary elements leads to algebraic formulations in the shape either of quadratic programming problems, or of linear complementarity problems, all characterized by symmetry and sign definiteness of the coefficient matrices. The method is also applicable to contact problems between two uncompenetrable elastic solids, as well as to the crack problem of fracture mechanics.