Augmented Lagrangian methods for a class of convex and nonconvex contact problems

The aim of this contribution is threefold. First, we formulate unilateral contact problems for three models of plates and the Koiter shell model. Contact conditions have been formulated on the face being in contact with an obstacle and not on the mid-plane of the plate or the middle surface of the shell. Such a rigorous approach results in nonconvex minimization problems even in the case of thin, geometrically linear plates. Existence theorems are formulated for each model considered. Second, the Ito and Kunisch (1990, 1995) augmented Lagrangians methods have been extended to nonconvex problems. Third, nonconvex duality theory by Rockafellar and Wets (1998), valid for finite-degree-of-freedom systems has been extended to continuous systems. Specific examples have also been provided.