Abstract
A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO) problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA) and the sequential optimization and reliability assessment (SORA). To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM) is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.
Highlights
The subject for optimal structural topologies under uncertainty is very important, challenging, and attractive for researchers
A comparison study between reliability index approach (RIA) and performance measure approach (PMA) has been summarized for reliability-based topology optimization (RBTO) formulation [16], where the results clearly show that PMA has better convergence and efficiency than RIA
This paper presents a mathematical framework that integrates the reliability concept into topology optimization to solve RBTO problems under uncertainty
Summary
The subject for optimal structural topologies under uncertainty is very important, challenging, and attractive for researchers. Mathematical Problems in Engineering expanding active research field, topology optimization integration with probability constraint is still quite challenging, that is, the numerical difficulty for direct estimation failure probability Such difficulties have motivated the development of various uncertainty propagation methods, such as MonteCarlo simulation (MCS) method [10], the first and second order reliability methods (FORM/SORM) [11], response surface method (RSM) [12], and the stochastic response surface method (SRSM) [13]. Empirical evidence suggests that such double-loop approaches lead to substantially high computational cost and weak convergence stability, especially involving virtual simulation models (i.e., finite element models) To overcome these difficulties, some authors proposed different methods to solve RBTO problems seeking for simplification and efficiency formulations.
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