An efficient approach to reliability-based topology optimization of continuum structures with multimodal distributions

Abstract

Reliability-based topology optimization (RBTO) considering uncertainties has attracted great attention recently. In practical applications, some random variables follow multimodal distributions, thus, RBTO with multimodal distributions should be taken into account. However, conventional reliability analysis methods will result in large computational error in this case. Therefore, this paper proposes an efficient approach to RBTO of continuum structures with multimodal distributions using sequential approximate integer programming with trust region (SAIP-TR) and direct probability integral method (DPIM). Firstly, discrete variable topology optimization method based on the SAIP-TR is adopted to obtain clear topology configurations. Secondly, the DPIM is presented to address the failure probability estimation of structures involving random variables with multimodal distributions, and an efficient approach for calculating the sensitivity of probabilistic constraints with respect to design variables is also derived based on the DPIM. Moreover, since the optimal design in the initial stages will not fail, a two-stage strategy is proposed to further reduce the computational cost. In the first stage, a deterministic topology optimization is carried out with the worst-case as the constraint until the performance function corresponding to the intermediate design reaches the predefined threshold. In the second stage, the optimal result of the first stage is taken as the initial design to perform the reliability-based topology optimization. To reduce the number of structural analyses, only a part of representative points that contribute more to the calculation of failure probability and sensitivity analysis are concerned in each optimization process. Finally, several numerical examples illustrate the efficiency and accuracy of the proposed approach for reliability-based topology optimization considering multimodal distribution.