Full and directional band gap acoustic metamaterials offer the promising ability of controlling and prohibiting propagation of acoustic/elastic waves in specified frequency ranges or directions. However, there is no guarantee that the optimization problem will be solved successfully with the existing gradient-based topology optimization methods because of the complexity of the problem and strong dependence on initial guesses. In this study, we developed a systematic topological optimization method based on material-field series expansion (MFSE) framework for full and directional band gap acoustic metamaterials design. Herein, the number of involved design variables of the MFSE method is greatly reduced to no more than 50, and an optimal band gap design of acoustic metamaterials is therefore able to be obtained with non-gradient optimization algorithms. Then, the Kriging-based optimization algorithm with a self-adaptive strategy is adopted for solving the optimization problem. The optimized designs finally converge to the orderly material distribution and numerical validations show improved full and directional propagation properties as expected. The realization of two-dimension acoustic metamaterials demonstrates that the proposed method can generate meaningful optimized topologies of PnCs for the full frequency band and directional propagation with a broad frequency range.

全带和定向带隙声超材料提供了控制和禁止声/弹性波在指定频率范围或方向上传播的有希望的能力。但是，由于问题的复杂性以及对初始猜测的强烈依赖，因此无法保证使用现有的基于梯度的拓扑优化方法可以成功解决优化问题。在这项研究中，我们开发了一种基于材料场序列扩展（MFSE）框架的系统拓扑优化方法，用于全方向性带隙声超材料的设计。此处，MFSE方法涉及的设计变量的数量大大减少到不超过50，因此，可以通过非梯度优化算法获得声学超材料的最佳带隙设计。然后，采用具有自适应策略的基于克里格的优化算法来解决优化问题。经过优化的设计最终收敛到有序的材料分布，并且数值验证显示出预期的改进的全向传播特性。二维声学超材料的实现表明，所提出的方法可以为整个频带和宽频率范围内的定向传播生成有意义的PnC优化拓扑。经过优化的设计最终收敛到有序的材料分布，并且数值验证显示出预期的改进的全向传播特性。二维声学超材料的实现表明，所提出的方法可以为整个频带和宽频率范围内的定向传播生成有意义的PnC优化拓扑。经过优化的设计最终收敛到有序的材料分布，并且数值验证显示出预期的改进的全向传播特性。二维声学超材料的实现表明，所提出的方法可以为整个频带和宽频率范围内的定向传播生成有意义的PnC优化拓扑。