Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

Abstract

This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.where J Y and J Y denote the lower and upper bounds of interval vector J Y . The symbol m J Y is the mean value of J Y , which can be calculated by averaging the lower and upper bounds value as shown in Eq. (16b). I J Y denotes the variation interval of J Y , which depends on the difference of the lower and upper bound values as shown in Eq. (16c). The deviation J Y  of the symmetrical interval can be acquired by averaging the upper and lower bounds of J Y as shown in Eq. (16d). In the combined form, the J-th hybrid interval random parameter( ) JJ X Y can be formulated as RCTO Volume fraction of solid: 95.6% Volume fraction of Phase 1: 70.3% DCTO Volume fraction of solid: 95.1% Volume fraction of phase 1: 70.7% 33 (b) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 93.0% Volume fraction of phase 1: 72.4% DCTO Volume fraction of solid: 92.7% Volume fraction of phase 1: 72.7% (c) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 90.4% Volume fraction of phase 1: 74.9% DCTO Volume fraction of solid: 88.9% Volume fraction of phase 1: 76.3%JJ J ee JJ J J J J e J J e J J JJ J e e J J J J J J J J e J J e 2 2 J J J J JK J e e J J J J J J J J J J J J J e J J JJ JJ e J J J J JJ J J e J J J J e JJ e J J J J 3m d I e J J J J x X X e J J e J J e J J e J J e J J e J J e e e e J J J J e J J J J e J J J J H T A a J J J J H a J J J J pT A J J J J A e J J J J A e J J J J J J J J a i A Y J J J J p a i A Y J J J J a i J J J J a i A Y J J J J p a i A Y J J J J Ne ia A i J J J J a i J J J J Ne ia A i J J J J

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