Incremental and Dynamic Inequality Problems

Abstract

This chapter is devoted to the numerical treatment of incremental and dynamic inequality problems. The first Section deals with the elastoplastic analysis of cable structures, where we assume that the cables may become slack. With respect to this problem, we illustrate the application of multilevel decomposition techniques to the analysis of inequality problems with many unknowns. The second Section contains the incremental elastoplastic analysis of structures presenting geometric nonlinearities and physical destabilizing effects. Within every load increment a variational inequality is formulated which gives rise to a minimization problem. The last Section concerns the dynamic unilateral contact problem. The resulting variational inequality is discretized with respect to time, and within every time step a minimization problem arises which is solved by an appropriate optimization alogrithm.