A heuristic method for nonconvex optimization in mechanics: Conceptual idea, theoretical justification, engineering applications

Abstract

Structures involving nonmonotone, possibly multivalued reaction-displacement or stress-strain laws cannot be effectively treated by the numerical methods for classical nonlinearities. In this paper we make use of the fact that these problems have as a Variational formulation a hemivariational inequality, leading to a noncovex optimization problem. A new method is proposed which approximates the nonmonotone problem by a series of monotone ones. The method constitutes an iterative scheme for the approximation of the solutions of the corresponding hemivariational inequality. A simple numerical example demonstrates the conceptual idea of the proposed numerical method. In the sequel the method is applied on an engineering problem concerning the ultimate strength analysis of an eccentric braced steel frame.