不确定性简谐激励下连续体结构可靠性拓扑优化

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Abstract An effective reliability-based topology optimization method is proposed for the design problem of continuum structure considering the uncertainty of load amplitude and frequency of harmonic excitation. A reliability design optimization model of minimizing structural volume ratio under probabilistic reliability constraint is established, in which the limit state function is the sum of the amplitude squares of the degrees of freedom concerned. The analytic sensitivity formulations of limit state function with respect to design variables and random variables are derived using adjoint variable method. The Performance Measure Approach (PMA) is used to achieve reliability analysis, and the method of moving asymptotes (MMA) is used to update design variables. Finally, three numerical examples and Monte Carlo simulation are tested to verify the effectiveness and stability of the proposed method for the design problem of continuum structure under uncertain harmonic excitation. The influences of the uncertainty of amplitude and frequency of harmonic excitation, reliability index, and coefficient of variations on the optimization results are also discussed.

Key words： Topology optimization harmonic excitation uncertainty reliability-based topology optimization harmonic response analysis

Received: 22 May 2023 Published: 28 March 2024

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	Articles by authors
	WANG Xuan1
	2
	SHI Yuankun1
	CHEN Xiang1
	LONG Kai2

Cite this article:

WANG Xuan1,2,SHI Yuankun1, et al. Reliability-based topology optimization of continuum structures under uncertain harmonic excitations[J]. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(6): 11-18.

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http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2024/V43/I6/11

[1] Pedersen N L. Maximization of eigenvalues using topology optimization[J]. Structural and multidisciplinary optimization, 2000, 20: 2-11. [2] Du J, Olhoff N. Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps[J]. Structural and Multidisciplinary Optimization, 2007, 34(2): 91-110. [3] Silva O M, Neves M M, Lenzi A. A critical analysis of using the dynamic compliance as objective function in topology optimization of one-material structures considering steady-state forced vibration problems[J]. Journal of Sound and Vibration, 2019, 444: 1-20. [4] Li Q, Sigmund O, Jensen J S, et al. Reduced-order methods for dynamic problems in topology optimization: A comparative study[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 387: 114149. [5] Kang Z, He J, Shi L, et al. A method using successive iteration of analysis and design for large-scale topology optimization considering eigenfrequencies[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 362: 112847. [6] 付君健，张跃，杜义贤，等. 周期性多孔结构特征值拓扑优化[J]. 振动与冲击，2022, 41(3): 73-81. FU Jun-jian, ZHANG Yue, DU Yi-xian, et al. Eigenvalue topology optimization of periodic cellular structures [J]. Journal of Vibration and Shock, 2022, 41(3): 73-81. [7] Ma Z D, Kikuchi N, Cheng H C. Topological design for vibrating structures[J]. Computer methods in applied mechanics and engineering, 1995, 121(1-4): 259-280 [8] 龙凯，左正兴. 谐响应下的连续体拓扑优化[J]. 中国机械工程，2007，18(13)：1556-1559. LONG Kai, ZUO Zheng-xing. Topological optimization of continuum structure subjected to harmonic excitation [J]. China Mechanical Engineering, 2007, 18(13): 1556-1559. [9] Liu H, Zhang W, Gao T. A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations[J]. Structural and Multidisciplinary Optimization, 2015, 51: 1321-1333. [10] 房占鹏，郑玲，唐重才. 指定频带简谐激励下约束阻尼结构拓扑优化[J]. 振动与冲击，2015，34(14)：135-141. FANG Zhan-peng, ZHENG Ling, TANG Zhong-cai. Topology optimization for constrained layer damping structures under specified-band harmonic excitations [J]. Journal of Vibration and Shock, 2015, 34(14): 135-141. [11] Niu B, He X, Shan Y, et al. On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation[J]. Structural and Multidisciplinary Optimization, 2018, 57: 2291-2307. [12] Zhao X, Wu B, Li Z, et al. A method for topology optimization of structures under harmonic excitations[J]. Structural and Multidisciplinary Optimization, 2018, 58: 475-487. [13] 徐家琪，马永其. 动力学自然单元法的谐波激励下的连续体结构拓扑优化[J]. 振动与冲击，2019，38(21)：252-258. XU Jia-qi，MA Yong-qi. Topology optimization of continuum structures under frequency excitation load based on dynamic natural element method. [J]. Journal of Vibration and Shock, 2019, 38(21): 252-258. [14] Long K, Wang X, Liu H. Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming[J]. Structural and Multidisciplinary Optimization, 2019, 59: 1747-1759. [15] Montero D S, Silva O M, Cardoso E L. Topology optimization for harmonic vibration problems using a density-weighted norm objective function[J]. Structural and Multidisciplinary Optimization, 2020, 62: 3301-3327. [16] Zhao J, Yoon H, Youn B D. An adaptive hybrid expansion method (ahem) for efficient structural topology optimization under harmonic excitation[J]. Structural and Multidisciplinary Optimization, 2020, 61: 895-921. [17] Wang Y L, Zhu J H, Li Y, et al. Shape preserving design with topology optimization for structures under harmonic resonance responses[J]. Structural and Multidisciplinary Optimization, 2022, 65(5): 145. [18] Wang B, You H, Ma X, et al. Multigrid reduced-order topology optimization scheme for structures subjected to stationary random excitations[J]. Structural and Multidisciplinary Optimization, 2023, 66(5): 102. [19] Zargham S, Ward T A, Ramli R, et al. Topology optimization: a review for structural designs under vibration problems[J]. Structural and Multidisciplinary Optimization, 2016, 53: 1157-1177. [20] Dunning P D, Kim H A. Robust topology optimization: minimization of expected and variance of compliance[J]. AIAA journal, 2013, 51(11): 2656-2664. [21] Kharmanda G, Olhoff N, Mohamed A, et al. Reliability-based topology optimization[J]. Structural and Multidisciplinary optimization, 2004, 26: 295-307. [22] Yang B, Cheng C, Wang X, et al. Robust reliability-based topology optimization for stress-constrained continuum structures using polynomial chaos expansion[J]. Structural and Multidisciplinary Optimization, 2023, 66(4): 1-17. [23] Zhang X, Kang Z, Zhang W. Robust topology optimization for dynamic compliance minimization under uncertain harmonic excitations with inhomogeneous eigenvalue analysis[J]. Structural and Multidisciplinary Optimization, 2016, 54: 1469-1484. [24] 王栋.载荷作用位置不确定条件下结构动态稳健性拓扑优化设计[J]. 力学学报，2021，53(05)：1439-1448. WANG Dong. Robust dynamic topology optimization of continuum structure subjected to harmonic excitation of loading position uncertainty[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(05): 1439-1448. [25] Valentini F, Silva O M, Cardoso E L. Robust topology optimization for harmonic displacement minimization of structures subjected to uncertainty in the excitation frequency[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 379: 113767. [26] Tu J, Choi K K, Park Y H. A new study on reliability-based design optimization[J]. Journal of Mechanical Design. 1999: 121 (4): 557–564. [27] Cheng C, Yang B, Wang X, et al. Reliability-based topology optimization using the response surface method for stress-constrained problems considering load uncertainty[J]. Engineering Optimization, 2022: 1-17. [28] Hasofer A M, Lind N C. Exact and invariant second-moment code format[J]. Journal of the Engineering Mechanics division, 1974, 100(1): 111-121. [29] Wang X, Meng Z, Yang B, et al. Reliability-based design optimization of material orientation and structural topology of fiber-reinforced composite structures under load uncertainty[J]. Composite Structures, 2022, 291: 115537. [30] 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: 68-75. [31] Svanberg K. The method of moving asymptotes—a new method for structural optimization[J]. International journal for numerical methods in engineering, 1987, 24(2): 359-373.