Automatic identification of the worst load combination for structural safety assessment using an optimization approach

This paper proposes a pair of novel mathematical programming approaches to automatically identify the worst load combination corresponding to the extreme maximum and minimum responses of nonlinear structural behavior under multiple load cases. The proposed schemes encompass various assumptions founded on nonlinear solid mechanics, including 2nd-order nonlinear geometry, elastoplastic materials and contact-like conditions. Motivated by practical engineering purposes, the analysis further accounts for dependent pattern loads to obtain accurate bound predictions. Each of the critical bounds can be captured within a single step by processing a challenging nonconvex and nonsmooth optimization problem, known as a 0–1 mathematical program with equilibrium constraints or 0–1 MPEC. A penalty algorithm is proposed to furnish the optimal solution of the 0–1 MPEC. This involves iteratively solving a series of reformulated mixed integer nonlinear programming or MINLP problems to enforce the complementarity condition. Four numerical examples are provided to illustrate application and robustness of the proposed schemes.