Topology optimization of acoustic metasurfaces by using a two-scale homogenization method
Topology optimization of acoustic metasurfaces by using a two-scale homogenization method
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DOI：
10.1016/j.apm.2021.05.005
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发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Y. Noguchi;T. Yamada
中科院分区：
文献类型：
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作者：
Y. Noguchi;T. Yamada
在本文中，我们提出了一种基于水平集的拓扑优化方法，利用双尺度均匀化方法进行声学超表面的单元设计。在前人工作的基础上，我们首次提出了一种可与拓扑优化相结合的声学超表面均匀化方法。在该方法中，在宏观尺度问题中出现了依赖于超表面单元格的非局部传输条件。接下来，我们在基于水平集的拓扑优化方法框架内制定优化问题，其中目标泛函表示为通过均质化获得的宏观响应，并将单元胞内的材料分布设置为设计变量。基于拓扑导数的概念进行了灵敏度分析。为了验证该方法的有效性，给出了二维数值算例。首先，我们提供了一个数值例子来支持均匀化方法的有效性，然后我们根据声学超表面的波导设置进行了优化计算。此外，我们还讨论了得到的优化结构的机理。
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.