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

Structures involving nonmonotone, possibly multivalued reaction-displacemen t or stress-strain laws cannot be effectively treated by the numerical meth ods for classical nonlinearities. In this paper we make use of the fact tha t these problems have as a Variational formulation a hemivariational inequa lity, leading to a noncovex optimization problem. A new method is proposed which approximates the nonmonotone problem by a series of monotone ones. Th e method constitutes an iterative scheme for the approximation of the solut ions of the corresponding hemivariational inequality. A simple numerical ex ample 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.