Efficient Robust Optimization of Structures Subjected to Earthquake Load and Characterized by Uncertain Bounded System Parameters

Introduction

The response of a structural system under environmental loads such as wind, water wave, earthquake, etc. is highly uncertain and can be best modelled as a stochastic process. The optimization of structure under such loads is normally dealt in the literature in the form of standard nonlinear optimization problem. The dynamic responses to define the stochastic constraints of the related optimization problem are obtained by random vibration theory. Subsequently, a standard nonlinear optimization problem is formulated where the weight of the structure or a desired stochastic response quantity is minimized. The procedure is termed as stochastic structural optimization (SSO). The details of the relevant developments can be found in (Nigam, 1972), Kang et al. (2006). It may be underlined here that in a typical SSO procedure the dynamic load is considered to be the only source of randomness in many cases and all other system parameters are assumed to be deterministic. But, uncertainty in the system parameters is inevitable to model a realistic structural system and incorporation of such uncertainty creates an interaction between the stochastic descriptions of the loads and the uncertain parameters (Jensen, 2002). Furthermore, the effect of system parameter uncertainty is important as the safety of structure may be endangered due to this (Chaudhuri, & Chakraborty, 2006) and can affect the final optimal design significantly (Schuëller, & Jensen, 2008). Thus, there is a growing interest to consider the effect of uncertainty in the optimization process for economic design of structure ensuring necessary safety requirements.