基于混合有限元-边界元的声振系统多材料拓扑优化方法研究  

Multi-material topology optimization method of acoustic-structure interaction systems based on mixed FEM-BEM

作　　者：林心玥 赵文畅 操小龙[2] 陈海波[1] LIN Xinyue;ZHAO Wenchang;CAO Xiaolong;CHEN Haibo(CAS Key Laboratory of Mechanical Behavior and Design of Materials,Department of Modern Mechanics,University of Science and Technology of China,Hefei 230027,China;Beijing Research Institute of Mechanical and Electrical Engineering,Beijing 100074,China)

机构地区：[1]中国科学技术大学近代力学系中国科学院材料力学行为与设计重点实验室,合肥230027 [2]北京机电工程研究所,北京100074

出　　处：《振动与冲击》2024年第22期106-117,共12页Journal of Vibration and Shock

基　　金：国家自然科学基金(12172350)。

摘　　要：针对结构和外声场相互作用的声振强耦合系统,建立了基于混合有限元-边界元的多材料拓扑优化设计方法。为处理优化过程中声振耦合面的变化,设置固定的虚拟界面将计算域划分为有界域和无界域,分别由混合位移-压力有限元方法(混合有限元方法)和边界元方法进行离散。运用混合有限元方法能够避免对声振耦合面的显式表征,且能使有限元与边界元离散交界面固定不变,有效减少计算成本。运用有序固体各向同性材料惩罚模型,建立单一设计变量下的多材料拓扑优化模型。以结构的辐射声功率级作为优化的目标函数,并采用伴随变量法进行灵敏度分析,最后通过移动渐进线优化算法对优化问题进行求解。通过基于Heaviside函数的分段投影密度滤波器进行优化后处理,得到数值稳定的多材料优化设计。数值模拟表明,该研究建立的多材料优化方法不仅具有高优化灵活度,同时可以降低声振耦合系统的辐射声功率级,是一个有效的拓扑优化方法。A multi-material topology optimization method based on mixed finite element method-boundary element method was proposed for acoustic-structure interaction systems in external acoustic field.To handle the changing coupling interface during optimization,a fixed virtual interface was introduced to divide the computational domain into bounded and unbounded domains.The bounded domain was discretized with the mixed displacement-pressure finite element method(Mixed FEM),while the unbounded domain was discretized with the boundary element method.The mixed FEM avoids explicitly representing the acoustic-structural coupling interface and maintains a fixed discretized boundary between the finite element method-boundary element method,resulting in reduced computational cost.The ordered-solid isotropic material with penalization model was employed to establish a multi-material topology optimization model described by a single design variable within the bounded domain.In the optimization problem,the structural radiated sound power level was adopted as the objective function and the adjoint variable method was employed for sensitivity analysis.Finally,the optimization problem was solved using the method of moving asymptotes.A post-processing step using a piecewise projected density filter based on Heaviside function was applied to achieve numerically stable multi-material optimization design.The numerical simulations demonstrate that the proposed multi-material optimization method not only has high optimization flexibility,but also can reduce the radiated sound power level of the acoustic-structure interaction system,which is an effective topology optimization method.

关 键 词：声振耦合系统 拓扑优化 混合有限元 边界元 多材料设计 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3