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工程设计学报
工程设计学报  2015, Vol. 22 Issue (6): 575-580    DOI: 10.3785/j.issn. 1006-754X.2015.06.010
建模、分析、优化和决策     
基于整体应变的柔顺机构多目标拓扑优化设计
孙 楷，薄瑞峰，路建鹏，李瑞琴
中北大学 机械与动力工程学院，山西 太原 030051
Multi-objective topology optimization of design compliant mechanisms based on global strain
SUN Kai, BO Rui-feng, LU Jian-peng, LI Rui-qin
School of Mechanical and Power Engineering, North University of China, Taiyuan 030051, China
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摘要： 针对传统方法在拓扑优化中会出现局部应变集中的缺陷，提出了一种基于整体有效应变的柔顺机构多目标拓扑优化方法.该方法不再以应变能最小作为目标函数，而是以整体有效应变最小来表征机构的刚度最大，从而将应变均匀地分布在整个系统中.考虑到柔顺机构对刚度和柔度的要求，以整体有效应变最小化和互应变能最大化为目标建立了多目标拓扑优化模型，在变密度法的基础上，利用妥协规划法研究了柔顺机构的多目标优化问题.其中，目标函数的灵敏度分析采用伴随矩阵求解方法，并采用移动渐进算法求解拓扑优化问题.最后，通过柔顺夹钳设计的数值算例来说明该方法的有效性和先进性.结果表明，该方法能够减少基于传统优化方法的结构中的局部大应变，从而有效提升柔顺机构的可靠性.
关键词： 柔顺机构;  多目标拓扑优化;  整体有效应变;  应变能    
Abstract: To overcome the disadvantages of the traditional topology optimization method, a global effective strain based multi-objective topology optimization method of compliant mechanisms was presented. Under this method, a global effective strain function was minimized to represent structural rigidity, rather than minimizing the strain energy as the objective function. Thus the strain could be well distributed within the whole mechanism, instead of concentrating on compliant joints to cause a localized high strain. Considering the requirement of rigidity and flexibility on compliant mechanism, the multi-objective topology optimization problem that defined the objective as minimizing the global effective strain and maximizing mutual strain energy was established. Based on the solid isotropic material with penalization approach, the compromise programming method was used to study the multi-objective optimization problem of compliant mechanisms. The sensitivity of the objective functions was analyzed by the adjoint metrix method. The multi-objective topology optimization problem was solved using the algorithm of moving asymptotes. Finally, this method was further investigated and realized with a numerical example to show its correctness and effectiveness. The results show that the global effective strain based topology optimization method can effectively reduce localized high strain of the traditional method to improve the reliability of the compliant mechanism.
Key words: compliant mechanism    multi-objective topology optimization    global effective strain    strain energy
收稿日期: 2015-06-04 出版日期: 2015-12-28
基金资助:

国家自然科学基金资助项目（51275486）；山西省回国留学人员科研资助项目（2014050）；山西省国际科技合作项目（2015081016）
作者简介: 孙楷（1990-），男，山西闻喜人，硕士生，从事机构与机器人研究，E-mail:sookoo521@163.com. 通信联系人：薄瑞峰（1972-），男，山西定襄人，教授，从事产品创新设计与概念设计、计算智能与智能优化设计等研究，E-mail:brfcxh@163.com.
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引用本文:

孙 楷，薄瑞峰，路建鹏，李瑞琴. 基于整体应变的柔顺机构多目标拓扑优化设计[J]. 工程设计学报, 2015, 22(6): 575-580.

SUN Kai, BO Rui-feng, LU Jian-peng, LI Rui-qin. Multi-objective topology optimization of design compliant mechanisms based on global strain. Chinese Journal of Engineering Design, 2015, 22(6): 575-580.

链接本文:

https://www.zjujournals.com/gcsjxb/CN/10.3785/j.issn. 1006-754X.2015.06.010    或    https://www.zjujournals.com/gcsjxb/CN/Y2015/V22/I6/575

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