基于最大应力约束的柔顺机构拓扑优化设计

doi:10.3901/JME.2018.23.032

机械工程学报 ›› 2018, Vol. 54 ›› Issue (23): 32-38.doi: 10.3901/JME.2018.23.032

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基于最大应力约束的柔顺机构拓扑优化设计

占金青^1,2, 龙良明¹, 刘敏¹, 张宪民²

1. 华东交通大学机电与车辆工程学院南昌 330013;
2. 华南理工大学广东省精密装备与制造技术重点实验室广州 510641

收稿日期:2018-05-11 修回日期:2018-08-09 出版日期:2018-12-05 发布日期:2018-12-05
通讯作者: 张宪民(通信作者),男,1964年出生,博士,教授,博士研究生导师。主要研究方向为柔顺机构理论及精密装备技术等。E-mail:zhangxm@suct.edu.cn
作者简介:占金青,男,1979年出生,博士,副教授。主要研究方向为柔顺机构优化设计。E-mail:zhan_jq@126.com;龙良明,男,1992年出生,硕士研究生。主要研究方向为柔顺机构拓扑优化设计。E-mail:long_lm@126.com;刘敏,男,1990年出生,博士,讲师。主要研究方向为柔性铰链优化设计。E-mail:lmin2016@foxmail.com
基金资助:
国家自然科学基金（51665011）、江西省自然科学基金（20161BAB206152）和广东省精密装备与制造技术重点实验室开放基金（PEM201601）资助项目。

Topological Design of Compliant Mechanisms with Maximum Stress Constraint

ZHAN Jinqing^1,2, LONG Liangming¹, LIU Min¹, ZHANG Xianmin²

1. School of Mechanotronics and Vehicle Engineering, East China Jiaotong University, Nanchang 330013;
2. Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technique, South China University of Technology, Guangzhou 510641

Received:2018-05-11 Revised:2018-08-09 Online:2018-12-05 Published:2018-12-05

摘要/Abstract

摘要： 采用拓扑优化方法获得柔顺机构构型容易出现类铰链结构，导致应力集中、疲劳可靠性差。为了抑制类铰链结构，提出了一种基于最大应力约束的柔顺机构拓扑优化设计方法。采用改进的固体各向同性材料惩罚模型（Solid isotropic material with penalization，SIMP），以柔顺机构的互应变能最大化作为目标函数，采用P范数方法对所有单元的局部应力凝聚化成一个全局化应力约束，利用自适应约束缩放法使得P范数应力更加接近最大应力，以机构的最大应力和体积作为约束，建立柔顺机构最大应力约束拓扑优化模型，采用全局收敛移动渐近线算法求解柔顺机构最大应力约束拓扑优化问题。结果表明，采用P范数方法进行柔顺机构最大应力约束拓扑优化设计，能够有效抑制类铰链结构。随着应力约束极限值减少，获得机构构型由集中式柔顺机构逐渐转变为分布式柔顺机构，应力分布更加均匀，但机构的互应变能逐渐减小。

关键词: P范数方法, 柔顺机构, 拓扑优化, 最大应力约束

Abstract: Topological design of compliant mechanisms may be prone to generate de facto hinges which results in stress concentration and poor fatigue performance. In order to suppress the hinges, a method for topology optimization of compliant mechanisms with maximum stress constraint is proposed. The modified solid isotropic material with penalization approach is adopted. The maximization of mutual strain energy of compliant mechanisms is applied as the objective function. The stress constraints for all elements are aggregated into a global stress constraint using the P-norm method. The adaptive constraint scaling method is adopted to transforms the P-norm stress to approximate the maximum stress. The maximum stress and structural volume are used as the constraints. The model for topological design of compliant mechanisms with maximum stress constraint is established. The globally convergent version of the method of moving asymptotes is applied to solve the optimization problem. The results of numerical examples show that the appearance of de facto hinges can be suppressed effectively using the proposed method. As the stress limit is decreased, the obtained mechanisms is gradually transformed from the lumped compliant mechanism to the distributed compliant mechanism. At the same time the stress is more uniformly distributed, the mutual strain energy of the mechanism decreases.

Key words: compliant mechanisms, maximum stress constraints, P-norm approach, topology optimization

中图分类号:

TH122
TB114

占金青, 龙良明, 刘敏, 张宪民. 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, ZHANG Xianmin. Topological Design of Compliant Mechanisms with Maximum Stress Constraint[J]. Journal of Mechanical Engineering, 2018, 54(23): 32-38.

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基于最大应力约束的柔顺机构拓扑优化设计

Topological Design of Compliant Mechanisms with Maximum Stress Constraint

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