论文标题
通过使用二尺度均质化方法对声学跨度的拓扑优化
Topology optimization of acoustic metasurfaces by using a two-scale homogenization method
论文作者
论文摘要
在本文中，我们通过使用两规模的均质化方法提出了一种基于水平的拓扑优化方法，用于声学跨空面的单位细胞设计。基于以前的工作，我们首先提出了一种可以与拓扑优化结合使用的声学跨膜的均质化方法。在这种方法中，根据跨表面的单位单元，出现在宏观问题问题中。接下来，我们在基于水平集的拓扑优化方法的框架内提出了一个优化问题，其中，在其中，将目标函数表示为通过均质化获得的宏观响应，而单位单元格中的材料分布则将其设置为设计变量。基于拓扑导数的概念进行灵敏度分析。为了确认该方法的有效性，提供了二维数值示例。首先，我们提供了一个支持均质方法有效性的数值示例，然后我们基于声学元信息的波导设置进行优化计算。此外，我们讨论了获得的优化结构的机制。
In this paper, we propose a level set-based topology optimization method for the unit-cell design of acoustic metasurfaces by using a two-scale homogenization method. Based on previous works, we first propose a homogenization method for acoustic metasurfaces that can be combined with topology optimization. In this method, a nonlocal transmission condition depending on the unit cell of the metasurface appears in a macroscale problem. Next, we formulate an optimization problem within the framework of a level set-based topology optimization method, wherein an objective functional is expressed as the macroscopic responses obtained through the homogenization, and material distributions in the unit cell are set as design variables. A sensitivity analysis is conducted based on the concept of the topological derivative. To confirm the validity of the proposed method, two-dimensional numerical examples are provided. First, we provide a numerical example that supports the validity of the homogenization method, and we then perform optimization calculations based on the waveguide settings of the acoustic metasurfaces. In addition, we discuss the mechanism of the obtained optimized structures.
