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

Abstract

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 scatterers 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.