Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method
Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method
复制标题
使用耦合 FEM-BEM 方法对外部声-结构相互作用系统进行拓扑优化
DOI：
10.1002/nme.6055
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
Steffen Marburg
中科院分区：
文献类型：
--
作者：
Wenchang Zhao;Leilei Chen;Haibo Chen;Steffen Marburg
本文提出了一种用于外部声-结构相互作用问题的有效拓扑优化程序，其中耦合系统通过边界元法（BEM）和有限元法（FEM）来制定。到目前为止，基于耦合FEM-BEM的拓扑优化仍然面临着一些需要解决的问题，特别是耦合系统的有效设计灵敏度分析。在这项工作中，我们主要在两个方面对这些问题做出了贡献。首先，推导了伴随变量法（AVM）公式用于任意目标函数的灵敏度分析，并且在灵敏度分析中考虑了结构域和声学域之间的反馈耦合。其次，除了在声学 BEM 响应分析中应用快速多极方法 (FMM) 之外，FMM 现在也进行了更新，以适应 AVM 方程中出现的不同乘法。这些加速节省了大量的计算时间和内存。数值测试表明，所开发的方法可以应用于大规模问题。最后，从数值研究中得出了优化设计的一些基本观察结果。
This paper presents an efficient topology optimization procedure for exterior acoustic‐structure interaction problems, in which the coupled systems are formulated by the boundary element method (BEM) and the finite element method (FEM). So far, the topology optimization based on the coupled FEM‐BEM still faces several issues needed to be addressed, especially the efficient design sensitivity analysis for the coupled systems. In this work, we contribute to these issues in two main aspects. Firstly, the adjoint variable method (AVM) formulations are derived for sensitivity analysis of arbitrary objective function, and the feedback coupling between the structural and acoustic domains are taken into consideration in the sensitivity analysis. Secondly, in addition to the application of fast multipole method (FMM) in the acoustic BEM response analysis, the FMM is now updated to adapt to the arising different multiplications in the AVM equations. These accelerations save considerable computing time and memory. Numerical tests show that the developed approach permits its application to large‐scale problems. Finally, some basic observations for the optimized designs are drawn from the numerical investigations.