This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound pressure in reference plane. The sensitivity analysis for the combined optimization is conducted by using either the direct differentiation method or the adjoint variable method. For a shape design, the design variables are the positions of control points in isogeometric analysis, which can control the barrier shape flexibly. In the topology update, the artificial density of an integral element is selected as the design variable to find the optimal distribution of sound absorbing material (SAM) on the barrier surface. In the combined optimization process, the shape and SAM distribution of the sound barrier can be changed in each iteration process to improve the noise reduction. Four different iteration schemes for combined optimization are compared to find an effective one. Numerical tests are provided to demonstrate the validity and efficiency of the proposed methods.

本研究提出了一种采用等几何边界元法设计声屏障的组合形状和拓扑优化方法。组合优化的目标函数定义为参考平面中的声压。通过使用直接微分方法或伴随变量方法进行组合优化的敏感性分析。对于形状设计，设计变量是等几何分析中控制点的位置，可以灵活地控制势垒形状。在拓扑更新中，选择集成元素的人工密度作为设计变量，以在屏障表面上找到吸声材料（SAM）的最佳分布。在组合优化过程中，声屏障的形状和SAM分布可以在每个迭代过程中进行更改，以提高降噪效果。比较了四种用于组合优化的不同迭代方案，以找到有效的方案。数值试验证明了所提方法的有效性和有效性。