Discrete Variable Structural Optimization of Systems under Stochastic Earthquake Excitation - Structural Seismic Design Optimization and Earthquake Engineering - page 51

Chapter 3
Discrete Variable
Structural Optimization of
Systems under Stochastic
Earthquake Excitation
Héctor Jensen
Universidad Tecnica Federico Santa Maria, Chile
Marcos Valdebenito
Universidad Tecnica Federico Santa Maria, Chile
Juan Sepúlveda
Universidad Tecnica Federico Santa Maria, Chile
Luis Becerra
Universidad Tecnica Federico Santa Maria, Chile
ABSTRACT
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 ap-
propriate 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.