Multi-objective optimization of elastic metaplates for lightweight and ultrawide bandgaps

There is inevitably a conflict between multiple objectives when designing elastic metaplates (EMPs) with desirable functionalities from the perspective of practical applications. The non-dominated sorting genetic algorithm-II (NSGA-II) and the improved fast plane wave expansion method (IFPWEM) are combined to develop a multi-objective topological optimization method for EMPs with ideal efficiency and accuracy regarding lightweight and bandgap characteristics. The results indicate that initial designs featuring concentrated scat-terers can yield Pareto front solutions with greater structural diversity. Additionally, the appropriate mesh resolution and the number of iterations are determined based on convergence and computational costs. Note that the post-processing method is proposed to improve the manufacturability by utilizing the connected component labeling algorithm while achieving convergence at least 15 generations earlier than the results without post-processing. The bandgap characteristics can be effectively improved by 2.34 and 2.19 at the same relative density compared to the conventional unit cell embedded with square or circular scatterers, demonstrating the superiority of the method. Additionally, the optimization objectives are further strengthened by reducing the symmetries of the unit cells. The wave propagation within finite periodic lattices is also investigated numerically and experimentally. The results of this study would provide useful guidance for developing and optimizing EMPs in the future.

Automated summary

A multi-objective topological optimization method for elastic metaplates (EMPs) is proposed, combining the non-dominated sorting genetic algorithm-II (NSGA-II) and the improved fast plane wave expansion method (IFPWEM) to achieve high efficiency and accuracy in lightweight and bandgap characteristics. The results show that initial designs with concentrated scatterers can produce more structurally diverse Pareto front solutions. The appropriate mesh resolution and number of iterations are determined based on convergence and computational costs. A post-processing method is proposed to improve manufacturability and achieve convergence earlier, and the method demonstrates improved bandgap characteristics compared to conventional unit cells.