考虑材料性能不确定性的声振强耦合系统稳健拓扑优化

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摘要针对外声场与结构强耦合问题，亟待开展不确定性优化的发展需求，提出了一种考虑材料性能不确定性的稳健拓扑优化设计方法。采用随机场模型描述材料弹性模量的不确定性，用级数最优线性估值(EOLE)方法将其离散成不相关的随机变量；进而用混沌多项式展开(PCE)方法结合有限元-边界元耦合方法进行随机响应分析。通过材料属性的有理近似(RAMP)模型描述双材料的分布，以辐射声功率级的均值和标准差的加权和作为稳健拓扑优化的目标函数，随机响应的灵敏度同样通过PCE方法获得，最后通过移动渐近线优化算法(MMA)对优化问题进行求解。数值算例表明，本文建立的方法相较于确定性拓扑优化可以获得对材料弹性模量不确定性更加不敏感的设计，这是不确定性优化方法在含外声场的声振强耦合问题上的一个新的拓展研究。

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	郑文治1
	陈海波1
	操小龙2

关键词 ：声振耦合系统, 拓扑优化, 稳健设计, 混沌多项式展开

Abstract：For strongly coupled problem between external acoustic field and structure, there is an urgent need for the development of uncertainty optimization, and a robust topology optimization method considering the uncertainty of material performance is presented. A random field model is used to describe the uncertainty of the elastic modulus of the material, and the expansion optimal linear estimation (EOLE) method is used to discretize it into uncorrelated random variables. The polynomial chaos expansion(PCE) method is combined with the FE-BE coupling method for the random response analysis. The rational approximation of material properties (RAMP) model is used to describe the distribution of bi-materials. A weighted sum of the mean and standard deviation of the radiation sound power level is set as the objective function for robust topology optimization. The sensitivity of the random response is also obtained by the PCE method, and then the optimization problem is solved by the method of moving asymptotes (MMA). Numerical tests show that the proposed method can obtain designs that are less sensitive to the uncertainty of elastic modulus than the deterministic topology optimization, This is a new extension of uncertain optimization methods to strongly coupled problems between external acoustic field and structure.

Key words： coupled structural-acoustic systems topology optimization robust design polynomial chaos expansion

收稿日期: 2022-10-09 出版日期: 2023-11-28

引用本文:

郑文治1，陈海波1，操小龙2. 考虑材料性能不确定性的声振强耦合系统稳健拓扑优化[J]. 振动与冲击, 2023, 42(22): 93-102.
ZHENG Wenzhi1，CHEN Haibo1，CAO Xiaolong2. Robust topology optimization of strongly coupled structural-acoustic systems considering material properties uncertainty. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(22): 93-102.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I22/93

[1] DU J, OLHOFF N. Minimization of sound radiation from vibrating bi-material structures using topology optimization [J]. Structural and Multidisciplinary Optimization, 2007, 33(4-5): 305-321.
[2] DU J, YANG R. Vibro-acoustic design of plate using bi-material microstructural topology optimization [J]. Journal of Mechanical Science and Technology, 2015, 29(4): 1413-1419.
[3] ZHANG X, KANG Z. Topology optimization of damping layers for minimizing sound radiation of shell structures [J]. Journal of Sound and Vibration, 2013, 332(10): 2500-2519.
[4] 吴振云, 赵文畅, 陈海波. 基于非负声强的约束阻尼板拓扑优化研究 [J]. 振动与冲击, 2021, 40(11): 33-41.
WU Zhenyun, ZHAO Wenchang, CHEN Haibo. Topology optimization of constrained damping plate based on non-negative sound intensity [J]. Journal of vibration and shock, 2021, 40(11): 33-41.
[5] SHU L, YU W, MA Z. Level set based topology optimization of vibrating structures for coupled acoustic–structural dynamics [J]. Computers & Structures, 2014, 132: 34-42.
[6] CHEN N, YU D, XIA B, et al. Microstructural topology optimization of structural-acoustic coupled systems for minimizing sound pressure level [J]. Structural and Multidisciplinary Optimization, 2017, 56(6): 1259-1270.
[7] DAVID S, BURNETT. A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion [J]. The Journal of the Acoustical Society of America, 1994, 96(5): 2798-2816.
[8] CREMERS L, FYFE K R. On the use of variable order infinite wave envelope elements for acoustic radiation and scattering [J]. The Journal of the Acoustical Society of America, 1995, 97(4): 2028-2040.
[9] EVERSTINE G C, HENDERSON F M. Coupled finite element/boundary element approach for fluid–structure interaction [J]. The Journal of the Acoustical Society of America, 1990, 87(5): 1938-1947.
[10] FRITZE D, MARBURG S, HARDTKE H-J. FEM–BEM-coupling and structural–acoustic sensitivity analysis for shell geometries [J]. Computers & Structures, 2005, 83(2-3): 143-154.
[11] ZHAO W, CHEN L, CHEN H, et al. Topology optimization of exterior acoustic‐structure interaction systems using the coupled FEM‐BEM method [J]. International Journal for Numerical Methods in Engineering, 2019, 119(5): 404-31.
[12] 苗晓飞, 赵文畅, 陈海波. 基于分段常数水平集方法的声振耦合系统拓扑优化 [J]. 振动与冲击, 2022, 41(04): 192-199.
MIAO Xiaofei, ZHAO Wenchang, CHEN Haibo. Topology optimization in coupled structural-acoustic systems based on a piecewise constant level set method [J]. Journal of vibration and shock, 2022, 41(4):192-199.
[13] DU J, SUN C. Reliability-based vibro-acoustic microstructural topology optimization [J]. Structural and Multidisciplinary Optimization, 2016, 55(4): 1195-1215.
[14] JALALPOUR M, TOOTKABONI M. An efficient approach to reliability-based topology optimization for continua under material uncertainty [J]. Structural and Multidisciplinary Optimization, 2015, 53(4): 759-772.
[15] 赵清海, 张洪信, 蒋荣超, 等. 考虑载荷不确定性的多材料结构稳健拓扑优化 [J]. 振动与冲击, 2019, 38(19): 182-190.
ZHAO Qinghai, ZHANG Hongxin, JIANG Rongchao, et al. Robust topology optimization design of a multi-material structure considering load uncertainty [J]. Journal of vibration and shock, 2019, 38(19): 182-190.
[16] 李冉, 刘书田. 考虑表面层厚度不确定的稳健性拓扑优化方法 [J]. 力学学报, 2021, 53(05): 1471-1479.
LI Ran, LIU Shutian. Robust topology optimization of structures considering the uncertainty of surface layer thickness [J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1471-1479.
[17] YIN S, CHEN N, YU D, et al. Microstructural topology optimization for minimizing the sound pressure level of structural–acoustic coupled systems with multi-scale random parameters [J]. Engineering Optimization, 2018, 51(7): 1185-1206.
[18] KESHAVARZZADEH V, FERNANDEZ F, TORTORELLI D A. Topology optimization under uncertainty via non-intrusive polynomial chaos expansion [J]. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 120-147.
[19] ZHANG X, HE J, TAKEZAWA A, et al. Robust topology optimization of phononic crystals with random field uncertainty [J]. International Journal for Numerical Methods in Engineering, 2018, 115(9): 1154-1173.
[20] TORII A J, SANTOS D P D S, DE MEDEIROS E M. Robust topology optimization for heat conduction with polynomial chaos expansion [J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020, 42(6):1-13.
[21] KANG Z, WU C, LUO Y, et al. Robust topology optimization of multi-material structures considering uncertain graded interface [J]. Composite Structures, 2019, 208: 395-406.
[22] BURTON A J, MILLER G F. The application of integral equation methods to the numerical solution of some exterior boundary-value problems [J]. Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, 1971, 323(1553): 201-210.
[23] MARBURG S. The Burton and Miller Method: Unlocking Another Mystery of Its Coupling Parameter [J]. Journal of Computational Acoustics, 2016, 24(01):1550016.
[24] LI C, DERKIUREGHIAN A. Optimal discretization of random-fields [J]. Journal of Engineering Mechanics-Asce, 1993, 119(6): 1136-1154.
[25] XU S, CAI Y, CHENG G. Volume preserving nonlinear density filter based on heaviside functions [J]. Structural and Multidisciplinary Optimization, 2009, 41(4): 495-505.
[26] SIGMUND O, PETERSSON J. Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima [J]. Structural Optimization, 1998, 16(1): 68-75.