NUMERICAL TREATMENT OF HEMIVARIATIONAL INEQUALITIES IN MECHANICS - 2 METHODS BASED ON THE SOLUTION OF CONVEX SUBPROBLEMS

Hemivariational inequality problems describe equilibrium points (solut ions) for structural systems in mechanics where nonmonotone, possibly multivalued laws or boundary conditions are involved. In the case of p roblems which admit a potential function this is a nonconvex, nondiffe rentiable one. In order to avoid the difficulties that arise during th e calculation of equilibria for such mechanical systems, methods based on sequential convex approximations have recently been proposed and t ested by the authors. The first method is based on ideas developed in the fields of quasidifferential and difference convex (d.c.) optimizat ion and transforms the hemivariational inequality problem into a syste m of convex variational inequalities, which in turn leads to a multile vel (two-field) approximation technique for the numerical solution. Th e second method transforms the problem into a sequence of variational inequalities which approximates the nonmonotone problem by an iterativ ely defined sequence of monotone ones. Both methods lead to convex ana lysis subproblems and allow for treatment of large-scale nonconvex str uctural analysis applications. The two methods are compared in this pa per with respect to both their theoretical assumptions and implication s and their numerical implementation. The comparison is extended to a number of numerical examples which have been solved by both methods.