Collaborative Design Optimization of Damping Layers and Stiffener Layout of Thin-walled Stiffened Plate Structures for Dynamics Performances

doi:10.3969/j.issn.1004-132X.2021.16.003

Abstract

Abstract: In order to reduce the vibrations of thin-walled stiffened plate structures in dynamic environment, a topology optimization method was proposed for designing the layout of reinforced ribs and damping layers. The penalization model of damping material and the ground structure approach were combined in the optimization. The density of stiffened rib and element density of the damping material were introduced as the independent design variables. Two constraints on the material used in the stiffened ribs and the damping layers were considered. The collaborative design optimization of damping layers and stiffening ribs was established with dynamic compliance as the objective function. The optimized topological design of stiffeners and damping materials was realized simultaneously. Several numerical examples of stiffened plate with different damping properties and various excitation frequencies were given to verify the effectiveness of the proposed method.

Key words: topology optimization, stiffened plate, damping layer, harmonic excitation

摘要： 为减小薄壁加筋结构在动态环境下的振动，提出了加筋肋布局和阻尼层拓扑一体化设计方法。以含表层阻尼材料的薄壁加筋板结构为研究对象，结合阻尼材料惩罚模型与基结构优化方法，引入筋条密度和阻尼单元密度两类独立设计变量，考虑筋条和阻尼材料的体积约束，建立最小化动态柔度的阻尼材料拓扑和筋条布局的协同优化模型，实现面向动态响应最小化的含阻尼层的薄壁加筋结构最优设计。通过不同阻尼、不同频率下的含表面阻尼层加筋板的多个数值算例，验证了所提方法和模型的有效性。

关键词: 拓扑优化, 加筋板, 阻尼层, 简谐激励

CLC Number:

TB535.1

NIU Bin, YAN Jiaming, MAO Yuming, LIU Haiyang. Collaborative Design Optimization of Damping Layers and Stiffener Layout of Thin-walled Stiffened Plate Structures for Dynamics Performances[J]. China Mechanical Engineering, 2021, 32(16): 1912-1920.

牛斌, 闫家铭, 毛玉明, 刘海洋. 面向动力学性能的薄壁加筋板结构阻尼与筋条布局协同优化设计[J]. 中国机械工程, 2021, 32(16): 1912-1920.

References

［1］BENDSOE M P, SIGMUND O. Topology Optimization:Theory, Methods, and Applications［M］. Berlin:Springer Science & Business Media, 2013.

［2］张锦江, 杨智春. 具有多阶频率与振型约束的结构动力学优化设计［J］. 强度与环境. 2007, 34(1):11-16.

ZHANG Jinjiang, YANG Zhichun. Structural Dynamics Optimization Design with Constraints of Multiple Natural Frequencies and Modal Shape［J］. Structure & Environment Engineering, 2007, 34(1):11-16.

［3］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.

［4］OLHOFF N, DU J. Generalized Incremental Frequency Method for Topological Design of Continuum Structures for Minimum Dynamic Compliance Subject to Forced Vibration at a Prescribed Low or High Value of the Excitation Frequency ［J］. Structural and Multidisciplinary Optimization, 2016, 54(5):1113-1141.

［5］SIGMUND O, JENSEN J S. Systematic Design of Phononic Band-gap Materials and Structures by Topology Optimization［J］. Philosophical Transactions of the Royal Society of London A:Mathematical, Physical and Engineering Sciences, 2003, 361:1001-1019.

［6］DORN W S, GORMORY R E. Automatic Design of Optimal Structure［J］. Journal de Mecanique, 1964, 3(1):25-52.

［7］LAM Y C, SANTHIKUMAR S. Automated Rib Location and Optimization for Plate Structures［J］. Structural and Multidisciplinary Optimization, 2003, 25(1):35-45.

［8］ANSOLA R, CANALES J, TARRAGO J A, et al. Combined Shape and Reinforcement Layout Optimization of Shell Structures［J］. Structural and Multidisciplinary Optimization, 2004, 27(4):219-227.

［9］丁晓红, 李国杰, 蔡戈坚, 等. 薄板结构的加强筋自适应成长设计法［J］. 中国机械工程, 2005, 16(12):1057-1060.

DING Xiaohong, LI Guojie, CAI Gejian,et al. Adaptive Growth Method of Rib Distribution for Thin Plate Structure［J］. China Mechanical Engineering, 2005, 16(12):1057-1060.

［10］INOUE K, YAMANAKA M, KIHARA M. Optimum Stiffener Layout for the Reduction of Vibration and Noise of Gearbox Housing［J］. Journal of Mechanical Design, 2002, 124(3):518-523.

［11］LI B, YAN S, HONG J. A Growth-based Topology Optimizer for Stiffness Design of Continuum Structures under Harmonic Force Excitation［J］. Journal of Zhejiang University—Science A(Applied Physics & Engineering), 2016, 17(12):946-993.

［12］王睿, 张晓鹏, 亢战. 以动柔度为目标的结构阻尼材料层拓扑优化［J］. 振动与冲击, 2013, 32(22):36-40.

WANG Rui, ZHANG Xiaopeng,KANG Zhan. Topology Optimization of Damping Layer in Structures for Minimizing Dynamic Compliance［J］. Journal of Vibration and Shock, 2013, 32(22):36-40.

［13］ZHANG X, KANG Z. Vibration Suppression Using Integrated Topology Optimization of Host Structures and Damping Layers［J］. Journal of Vibration and Control, 2014, 22(1):60-76.

［14］刘海, 高行山, 常俊玲. 加筋板自由阻尼铺层的拓扑优化研究［J］. 强度与环境, 2014, 41(2):27-33.

LIU Hai, GAO Hangshan, CHANG Junling. Damping Material Optimal Distribution of Stiffened Plate with Free Damping Treatment Using Topology Optimization［J］. Structure & Environment Engineering, 2014, 41(2):27-33.

［15］桂洪斌, 赵德有, 郑云龙. 敷设粘弹性阻尼的加筋板振动和阻尼分析［J］. 中国造船, 2002, 43(3):40-47.

GUI Hongbin, ZHAO Deyou, ZHENG Yunlong. Vibration and Damping Analysis of Stiffened Plate with Viscoelastic Damping Treatment［J］. Shipbuilding of China, 2002, 43(3):40-47.

［16］臧献国, 于德介, 姚凌云, 等. 基于模态振型的自由阻尼层厚度分布优化［J］. 中国机械工程, 2010, 21(5):515-518.

ZANG Xianguo, YU Dejie, YAO Lingyun,et al, Optimization of Thickness Distribution of Unconstrained Damping Layer Based on Mode Shapes［J］. China Mechanical Engineering, 2010, 21(5):515-518.

［17］ALFOUNEH M, TONG L. Maximizing Modal Damping in Layered Structures via Multi-objective Topology Optimization［J］. Engineering Structures, 2017, 132:637-647.

［18］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(6):2291-2307.

［19］BRUNS T E, TORTORELLI D A. Topology Optimization of Non-linear Elastic Structures and Compliant Mechanisms［J］. Computer Methods in Applied Mechanics and Engineering, 2001, 190(26):3443-3459.

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