Abstract
Structures involving nonmonotone, possibly multivalued reaction-displacement or stress-strain laws cannot be effectively treated by the numerical methods for classical non-linearities. 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 con-ceptual 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.
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Mistakidis, E. A Heuristic Method for Nonconvex Optimization in Mechanics: Conceptual Idea, Theoretical Justification, Engineering Applications. Journal of Global Optimization 17, 301–316 (2000). https://doi.org/10.1023/A:1026565801488
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DOI: https://doi.org/10.1023/A:1026565801488