考虑混合约束的柔顺机构拓扑优化设计

摘要
图/表
参考文献(25)
相关文章 (15)

全文: PDF (1656 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要为了满足制造工艺和静强度要求，提出一种综合考虑最小尺寸控制和应力约束的柔顺机构混合约束拓扑优化设计方法。采用改进的固体各向同性材料插值模型描述材料分布，利用多相映射方法同时控制实相和空相材料结构的最小尺寸，采用最大近似函数P范数求解机构的最大应力，以机构的输出位移最大化作为目标函数，综合考虑最小特征尺寸控制和应力约束建立柔顺机构混合约束拓扑优化数学模型，利用移动渐近算法求解柔顺机构混合约束拓扑优化问题。数值算例结果表明混合约束拓扑优化获得的柔顺机构能够同时满足最小尺寸制造约束和静强度要求，机构的von Mises等效应力分布更加均匀。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	占金青1
	王云涛1
	刘敏1
	朱本亮2

关键词 ：柔顺机构, 最小尺寸控制, 应力约束, 拓扑优化, 多相映射方法

Abstract：To satisfy manufacturing constraints and static strength requirements, a method for hybrid constrained topology optimization of compliant mechanisms considering both minimum length scale control and stress constraints. The improved solid isotropic material with penalization (SIMP) model is adopted to describe the material distribution. The two-phase projection method is applied to simultaneously achieve minimum length scale control on both solid and void phases. The P norm approach is used to calculate approximately the maximum value of the element stress. The maximization of the output displacement of the compliant mechanism is developed as the objective function. The minimum length scale control and the maximum stress are used as the constraints. The model for hybrid constrained topology optimization of compliant mechanisms is established. The method of moving asymptotes is used to solve the optimization problem. The results of several numerical examples show that the compliant mechanism obtained by hybrid constrained topology optimization can meet both manufacturing constraints and strength requirements, and the von Mises equivalent stresses are more uniformly distributed.

Key words： compliant mechanisms minimum length scale control stress constraints topology optimization multiple phase projection method

收稿日期: 2020-09-08 出版日期: 2022-02-28

引用本文:

占金青1，王云涛1，刘敏1，朱本亮2. 考虑混合约束的柔顺机构拓扑优化设计[J]. 振动与冲击, 2022, 41(4): 159-166.
ZHAN Jinqing1,WANG Yuntao1,LIU Min1,ZHU Benliang2. Topological design of compliant mechanisms with hybrid constraints. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(4): 159-166.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I4/159

[1] 杜义贤, 李涵钊, 谢黄海,等. 基于序列插值模型和多重网格方法的多材料柔性机构拓扑优化[J]. 机械工程学报, 2018, 54(13): 47-56.
DU Yixian, LI Hanzhao, XIE Huanghai, et al. Topology optimization of multiple materials compliant mechanisms based on sequence interpolation model and multigrid [J]. Journal of Mechanical Engineering, 2018, 54(13): 47-56.
[2] 阚琳洁, 张建国, 邱继伟. 柔性机构时变可靠性分析的时变随机响应面法[J]. 振动与冲击, 2019, 38(2): 253-258.
KAN Linjie, ZHANG Jianguo, WANG Pidong. Time-varying stochastic response surface method for the time-varying reliability analysis of flexible mechanisms[J]. Journal of Vibration and Shock, 2019, 38(2): 253-258.
[3] ZHU B, ZHANG X, ZHANG H, et al. Design of Compliant Mechanisms Using Continuum Topology Optimization: A review[J]. Mechanism and Machine Theory, 2020, 143(1): 103622.
[4] LIU M, ZHAN J, ZHU B, et al. Topology Optimization of Compliant Mechanism Considering Actual Output Displacement Using Adaptive Output Spring Stiffness[J]. Mechanism and Machine Theory, 2020, 143(4): 103728.
[5] CHEN G, HOWELL L L. Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms. Chinese Journal of Mechanical Engineering, 2018, 31(1): 14.
[6] GUEST J K, PRÉVOST J H, BELYTSCHKO T. Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions[J]. International Journal Numerical Methods in Engineering, 2004, 61(2): 238-254.
[7] GUEST J K. Topology Optimization with Multiple Phase Projection[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 199(1): 123-135.
[8] 容见华, 赵圣佞, 李方义, 等.涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计[J]. 机械工程学报，2019, 55(19): 174-185.
RONG Jianhua, ZHAO Shengning LI Fangyi, et al. Clear Structure Topology Optimization Design Involving Void Phase Minimum Length Scale Control[J]. Journal of Mechanical Engineering, 2019, 55(19): 174-185.
[9] SIGMUND O. Morphology-based Black and White Filters for Topology Optimization[J]. Structural and Multidisciplinary Optimization, 2007, 33(4-5): 401-424.
[10] WANG F, LAZAROV B S, SIGMUND O. On Projection Methods, Convergence and Robust Formulations in Topology Optimization[J]. Structural and Multidisciplinary Optimization, 2011, 43(6): 767-784.
[11] ZHOU M, LAZAROV B S, WANG F, et al. Minimum Length Scale in Topology Optimization by Geometric Constraints[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 293: 266-282.
[12] SAXENA A, ANANTHASURESH G K. Topology Optimization of Compliant Mechanisms with Strength Considerations[J]. Mechanics of Structures and Machines, 2001, 29(2): 199-221.
[13] CHU S, GAO L, XIAO M, et al. Stress-based Multi-material Topology Optimization of Compliant Mechanisms[J]. International Journal for Numerical Methods in Engineering, 2017, 113(7): 1021-1044.
[14] LOPES C G, NOVOTNY A A. Topology Design of Compliant Mechanisms with Stress Constraints Based on the topological derivative concept[J]. Structural and Multidisciplinary Optimization, 2016, 54(4) : 1-10.
[15] LEON D M D, ALEXANDERSE J, FONSECA J S O, et al. Stress-constrained Topology Optimization for Compliant Mechanism Design[J]. Structural and Multidisciplinary Optimization, 2015, 52(5): 929-943.
[16] 占金青, 龙良明, 刘敏, 等. 基于最大应力约束的柔顺机构拓扑优化设计[J]. 机械工程学报, 2018, 54(23): 32-38.
ZHAN Jinqing, LONG Liangming, LIU Min. Topological Design of Compliant Mechanisms with Maximum Stress Constraint. [J]. Journal of Mechanical Engineering, 2018, 54(23): 32-38.
[17] PEREIRA A D A, CARDOSO E L. On The Influence of Local and Global Stress Constraint and Filtering Radius on The Design of Hinge-free Compliant Mechanisms[J]. Structural and Multidisciplinary Optimization, 2018(2): 1-15.
[18] XUE Xiaoguang, LI Guoxi, XIONG Jingzhong, et al. Power Flow Response Based Dynamic Topology Optimization of Bi-material Plate Structures[J]. Chinese Journal of Mechanical Engineering, 2013, 26(3): 620-628.
[19] CARSTENSEN J V, GUEST J K. Projection-based Two-phase Minimum and Maximum Length Scale Control in Topology Optimization[J]. Structural and Multidisciplinary Optimization, 2018, 58: 1845-1860.
[20] 朱大昌, 宋马军. 平面整体式三自由度全柔顺并联机构拓扑优化构型设计及振动频率分析[J]. 振动与冲击, 2016, 35(3): 27-33.
ZHU Dachang, SONG Majun. Configuration Design and Vibration Frequency Analysis with Topology Optimization for Planar Integrated 3-DOF Fully Compliant Parallel Mechanism[J]. Journal of Vibration and Shock, 2016, 35(3): 27-33.
[21] XU S, CAI Y, CHENG G. Volume Preserving Nonlinear Density Filter Based on Heaviside Functions[J]. Structural and Multidisciplinary Optimization, 2010, 41(4): 495-505.
[22] LEE K, AHN K, YOO J. A Novel P-norm Correction Method for Lightweight Topology Optimization under Maximum Stress Constraints[J]. Computers and Structures, 2016, 171(7): 18-30.
[23] LE C, NORATO J, BRUNS T, et al. Stress-based Topology Optimization for Continua[J]. Structural and Multidisciplinary Optimization, 2010, 41(4): 605-620.
[24] OEST J, LUND E. Topology Optimization with Finite-life Fatigue Constraints[J]. Structural and Multidisciplinary Optimization, 2017, 56(5): 1-15.
[25] 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.