In this paper, we propose a level set-based shape optimization method for acoustic wave propagation problems with a deformable structure. First, we propose a mathematical model for acoustic wave propagation with a deformed structure based on coordinate transformation and the Eulerian approach. Next, we formulate the shape optimization problem and perform sensitivity analysis based on the shape derivative concept. We then construct an optimization algorithm based on the framework of a level set-based shape and topology optimization method. Finally, we provide two-dimensional optimization examples that demonstrate the effectiveness of our proposed method in providing optimized designs with desired functionality, while considering the structural deformation.

翻译：本文针对含可变形结构的声波传播问题，提出了一种基于水平集的形状优化方法。首先，基于坐标变换和欧拉方法建立了含变形结构的声波传播数学模型。其次，构建了形状优化问题，并基于形状导数概念进行了灵敏度分析。随后，基于水平集形状与拓扑优化方法框架，设计了相应的优化算法。最后，通过二维优化算例验证了所提方法在考虑结构变形时，能有效获得具有预期功能的优化设计。