Canonical Dual Approach for Contact Mechanics Problems with Friction

This paper presents an application of Canonical duality theory to the solution of contact problems with Coulomb friction. The contact problem is formulated as a quasi-variational inequality which solution is found by solving its Karush–Kuhn–Tucker system of equations. The complementarity conditions are reformulated by using the Fischer–Burmeister complementarity function, obtaining a non-convex global optimization problem. Then canonical duality theory is applied to reformulate the non-convex global optimization problem and define its optimality conditions, finding a solution of the original quasi-variational inequality. We also propose a methodology for finding the solutions of the new formulation, and report the results on well-known instances from literature.