Research on Topology Optimization of Compliant Mechanisms Based on Level Set Band Method

doi:10.12141/j.issn.1000-565X.230117

Abstract

Abstract:

The level set method uses a zero level set of the implicit level set function to describe the structure boundary in topology optimization problems. Since it can conveniently express structural topological changes and keep the structure boundary clear and smooth, the level set method has quickly become one of the important methods in the field of topology optimization. However, due to the discontinuity of topological changes during the optimization process, the level set method is prone to facing problems such as numerical instability and initial design dependence. In recent years, the level set band method has been proposed to effectively improve this phenomenon and has become an important means to improve the topological expression ability of the level set methods. This paper introduced the level set band into the parameterized level set-based topology optimization methods, and studied its application in compliant mechanism optimization design problems. The level set band method introduces a level set band area near the zero level set of the level set function. The level set function interpolation can be used to obtain the material density continuously distributed in the [0,1] interval within the bandwidth range. During the optimization process, the material density within the bandwidth range can gradually converge to a 0-1 distribution by gradually reducing the of the level set bandwidth. This method combines the advantages of the variable density method to maintain continuous material density changes during the optimization process, which can improve the stability of the parameterized level set method, obtain better objective function values, and effectively evaluate the initial design dependence of the level set method. This paper verified the effectiveness of the proposed method by studying various compliant mechanism optimization examples from the aspects of different initial designs, irregular design domain, geometric nonlinearity, etc. The optimization results show that the proposed method has good applicability for complex design problems in practical engineering.

Key words: topology optimization, compliant mechanism, parametrized level set method, level set band method, geometrical nonlinearity

CLC Number:

TB125

WEI Peng, HE Lei, XU Weipeng, et al. Research on Topology Optimization of Compliant Mechanisms Based on Level Set Band Method[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(3): 93-101.

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References 19

1	HOWELL L L ．Compliant mechanisms［M］．New York：John Wiley & Sons，Inc，2001.
2	BENDSØE M P， SIGMUND O ．Material interpolation schemes in topology optimization［J］．Archive of Applied Mechanics，1999，69（9）：635-654.
3	HUANG X， XIE Y M ．Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method［J］．Finite Elements in Analysis and Design，2007，43（14）：1039-1049.
4	OSHER S， SETHIAN J A ．Fronts propagating with curvature-dependent speed：algorithms based on Hamilton-Jacobi formulations［J］．Journal of Computational Physics，1988，79（1）：12-49.
5	SETHIAN J A， WIEGMANN A ．Structural boundary design via level set and immersed interface methods［J］．Journal of Computational Physics，2000，163（2）：489-528.
6	朱本亮．基于水平集方法的分布式柔顺机构拓扑优化设计研究［D］．广州：华南理工大学，2014.
7	ANANTHASURESH G K， KOTA S， KIKUCHI N ．Strategies for systematic synthesis of compliant MEMS［C］∥Proceedings of the 1994 ASME Winter Annual Meeting，Symposium on MEMS：Dynamics Systems and Control．Chicago IL：ASME，1994：677-686.
8	SIGMUND O ．On the design of compliant mechanisms using topology optimization［J］．Journal of Structural Mechanics，1997，25（4）：493-524.
9	李兆坤，张宪民．基于可靠性的柔顺微夹持机构几何非线性拓扑优化［J］．华南理工大学学报（自然科学版），2008，36（8）：110-116.
	LI Zhao-kun， ZHANG Xian-min ．Reliability-based topology optimization of compliant micro-gripper with geometrical nonlinearity［J］．Journal of South China University of Technology （Natural Science Edition），2008，36（8）：110-116.
10	张宪民，胡凯，王念峰，等．基于并行策略的热固耦合多材料柔顺机构设计［J］．华南理工大学学报（自然科学版），2016，44（10）：22-29.
	ZHANG Xian-min， HU Kai， WANG Nian-feng，et al ．Design of thermal-mechanical coupling multiple-material compliant mechanisms based on parallel strategy［J］．Journal of South China University of Technology （Natural Science Edition），2016，44（10）：22-29.
11	张宪民，欧阳高飞．水平集方法及其在柔顺机构拓扑优化中的应用（英文）［J］．华南理工大学学报（自然科学版），2007，35（10）：26-36.
	ZHANG Xian-min， OUYANG Gao-fei ．Level set method and its applications to topology optimization of compliant mechanisms［J］．Journal of South China University of Technology （Natural Science Edition），2007，35（10）：26-36.
12	ZHU B， ZHANG X， WANG N ．Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method［J］．Structural and Multidisciplinary Optimization，2013，47：659-672.
13	WEI P， LI Z Y， LI X P，et al ．An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions［J］．Structural and Multidisciplinary Optimization，2018，58（2）：831-849.
14	WEI P， WANG W， YANG Y，et al ．Level set band method：a combination of density-based and level set methods for the topology optimization of continuums［J］．Frontiers of Mechanical Engineering，2020，15：390-405.
15	WEI P， YANG Y， CHEN S，et al ．A study on basis functions of the parameterized level set method for topology optimization of continuums［J］．Journal of Mechanical Design，2021，143（4）：0417011/1-17.
16	JIANG C， JIA H， QIN L，et al ．Topology optimization and control of rotating compliant mechanism［C］∥Proceedings of the 2009 Chinese Control and Decision Conference．［S.l.］：IEEE，2009：1347-1350.
17	LUO Y， WANG M Y， KANG Z ．Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique［J］．Computer Methods in Applied Mechanics and Engineering，2015，286：422-441.
18	CHEN Q， ZHANG X， ZHU B ．A 213-line topology optimization code for geometrically nonlinear structures［J］．Structural and Multidisciplinary Optimization，2019，59：1863-1879.
19	CHEN Z， WEN G， WANG H，et al ．Multi-resolution nonlinear topology optimization with enhanced computational efficiency and convergence［J］．Acta Mechanica Sinica，2022，38（2）：421299.

迭代步数	零水平集	密度分布	水平集曲面
1
15
51
59
74

初始设计	未引入水平集带方法的优化结果	引入水平集带方法的优化结果

	目标函数值： 0.834 0	目标函数值： 0.858 2

	目标函数值： 0.829 5	目标函数值： 0.853 7

	目标函数值： 0.843 5	目标函数值： 0.857 1

	目标函数值： 0.855 5	目标函数值： 0.857 7

算例	未引入水平集带	引入水平集带	增幅/%
1	0.008 5	0.008 5	0.00
2	0.008 0	0.008 5	6.25
3	0.007 8	0.008 5	8.97
4	0.007 8	0.008 6	10.26

项目	算例1	算例2	算例3	算例4
初始设计
优化结果（未引入）
迭代曲线（未引入）
优化结果（引入）
迭代曲线（引入）

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[2]	ZHANG Xian-min HU Kai WANG Nian-feng GUO Hao. Design of Thermal-Mechanical Coupling Multiple-Material Compliant Mechanisms Based on Parallel Strategy [J]. Journal of South China University of Technology(Natural Science Edition), 2016, 44(10): 22-29.
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[8]	Li Zhao-kun Zhang Xian-min . Reliability-Based Topology Optimization of Compliant Micro-Gripper with Geometrical Nonlinearity [J]. Journal of South China University of Technology (Natural Science Edition), 2008, 36(8): 110-116.
[9]	Fu Yong-qing Zhang X ian-min. Topology Extraction ofCompliantMechanism Based on Wavelet and Cubic Spline Interpolation [J]. Journal of South China University of Technology (Natural Science Edition), 2007, 35(12): 6-10.
[10]	Zhang Xian-min Ouyang Gao-fei. Level Set Method and Its Applications to Topology Optimization of Compliant Mechanisms [J]. Journal of South China University of Technology (Natural Science Edition), 2007, 35(10): 26-36.
[11]	Li Jia-chun Ye Bang-yan Tang Yong Guan Qi-ming Liu Wei. Algorithm of Topology Optimization Criteria for Heat Conduction Structure Based on Density Approach [J]. Journal of South China University of Technology (Natural Science Edition), 2006, 34(2): 27-32.