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

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

Subrata Chakraborty (Bengal Engineering and Science University, Shibpur, India) and Soumya Bhattacharjya (Bengal Engineering and Science University,Shibpur, India)
DOI: 10.4018/978-1-4666-1640-0.ch005
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Abstract

An efficient robust design optimization (RDO) procedure is proposed in the framework of an adaptive response surface method (RSM) for structures subjected to earthquake load and characterized by uncertain but bounded system parameters. The basic idea of the proposed RDO approach is to improve the robustness of a design by using a new dispersion index which utilizes the relative importance of the gradients of the performance function. The same concept is also applied to the constraints. The repeated computations of stochastic responses and their sensitivities for evaluating the stochastic constraint of the associated optimization problem are efficiently obtained in the framework of an adaptive RSM. The proposed RDO approach is elucidated through the optimization of a three-storied concrete frame structure. The numerical study depicts that the proposed RDO results are in conformity with the conventional RDO results. However, definite improvements are achieved in terms of robustness and computational time requirements indicating its efficiency over the conventional RDO approach.
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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.

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