Reliability-based topology optimization framework of two-dimensional phononic crystal band-gap structures based on interval series expansion and mapping conversion method

In this study, a non-probabilistic reliability-based topological optimization (NRBTO) method is investigated for the optimized design of the band-gap structure of two-dimensional phononic crystals (PnCs), in which unknown but bounded (UBB) uncertainty issues from the material uncertainty are taken into account. A measurement metric is first defined based on the interval set-theoretical model, which may transform the band-gap setting into a non-probabilistic reliability format. The interval series expansion and adjoins vector methods are then utilized to obtain design sensitivity expressions between frequency measures and design variables. The method of moving asymptote (MMA) is adopted as well to iteratively solve the reliability-oriented band-gap optimization problem for PnCs. To effectively tackle the gray-scale units, a mapping conversion method is involved eventually. The usage and validity of the present methodology are verified through three examples, and numerical results show that considering the uncertainty effect of UBB throughout the topology optimization process has an important impact on the final layout scheme. Additionally, the optimization of the out-of-plane modes of PnCs (both the band-gap upper bound and the filling rate constraint are considered) indicates that the topological configuration may always change accompanied with the filling rate increases.

Automated summary

The study investigates a non-probabilistic reliability-based topological optimization method for the optimized design of two-dimensional phononic crystals' band-gap structure, considering unknown but bounded uncertainty issues from material uncertainty. By defining a measurement metric, design sensitivity expressions, and using the method of moving asymptote, the reliability-oriented band-gap optimization is iteratively solved. The study also verifies the methodology's effectiveness through three examples and the impact of considering uncertainty effect on the final layout scheme is highlighted.