Structural synthesis of non-linear stochastic dynamical systems

A method to carry out reliability-based optimization with a class of nonlinear structural systems subjected to stochastic excitation is introduced. The reliability-based optimization problem is formulated as the minimization of the expected cost of the structure for a specified level of failure probability. Failure is assumed to occur when any one of the output state of interest exceeds in magnitude some specified threshold level within a given time duration. Failure probabilities are approximated locally during the optimization process and they are represented using approximate functions dependent on the design variables. The approximations are based on moving least square interpolants and simulation techniques. The local approximations are then used to define a series of local explicit approximate optimization problems which are solved in an efficient manner. The optimization of a structural system enforced with nonlinear hysteretic devices and subjected to earthquake excitation illustrates the feasibility and efficiency of the suggested approach. At the same time, the effects of the nonlinear devices on the reliability and cost of the final design are investigated.