Stochastic bandgap optimization for multiscale elastic metamaterials with manufacturing imperfections

Bandgaps are endowed to elastic metamaterials (EMMs) attributed to the rationally designed unit cells and extensive works are devoted to bandgap enlargement for improving the applicability of EMMs in multidisciplinary applications. Nonetheless, most existing optimization frameworks neglect manufacturing imperfections, such as microscale heterogeneity and system uncertainties, which can significantly affect bandgap behaviors. Without properly accounting for these effects, the design may fail to achieve the optimal goal, exhibiting consistently ultra-wide wave attenuation bands in practical EMMs. Herein, in this paper, a stochastic bandgap optimization framework is developed for EMMs involving manufacturing imperfections, aiming at optimizing the first two statistical moments of the normalized bandwidth (NB) simultaneously. To alleviate the large computational costs in approximating statistical moments, a surrogate model is employed to reveal the constitutive relationship between system parameters and NB for the multiscale EMM. Moreover, to solve the optimization problem effectively and efficiently, a high-order mutation strategy is proposed to develop an improved particle swarm optimization (PSO) variant, namely the adaptively high-order mutation-based PSO (AHMPSO). To demonstrate the viability and efficiency of the proposed framework, a numerical investigation is implemented on a 3D EMM, which highlights enlarged bandwidths coupling with an improvement in the robustness of optimum.