Discrete variable structural optimization of systems under stochastic earthquake excitation

The reliability-based design optimization of structural systems under stochastic excitation involving discrete sizing type of design variables is considered. The design problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The excitation is modeled as a non-stationary stochastic process with uncertain model parameters. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal, and quadratic approximations. The approximations are combined with an effective stochastic sensitivity analysis in order to generate explicit expressions of the reliability constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. Two example problems that consider structures with passive energy dissipation systems under earthquake excitation are presented to illustrate the effectiveness of the approach reported herein.