基于整体应变的柔顺机构多目标拓扑优化设计
第２２卷第６期
２０１５年１２月工程设计学报Chinese Journal of Engineering Design Vol ．２２No ．６Dec ．２０１５收稿日期：２０１５‐０６‐０４．本刊网址?在线期刊：http ：／／www ．j ournals ．
zju ．edu ．cn ／g csjxb 基金项目：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 ：sookoo ５２１＠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 ．DOI ：１０．３７８５／j ．issn ．１００６‐７５４X ．２０１５．０６．０１０
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）
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
中图分类号：T P １２４ 文献标志码：A 文章编号：１００６‐７５４X （２０１５）０６‐０５７５‐０６
Multi ‐objective topology optimization of design compliant mechanisms based on global strain
SU N Kai ，BO Rui ‐feng ，LU Jian ‐p eng ，LI Rui ‐q in
（School of Mechanical and Power Engineering ，North University of China ，Taiyuan ０３００５１，China ）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 p resented ．U nder this method ，a global effective strain function was minimized to represent structural rigidity ，rather than minimizing the strain energy as the objective function ．T hus the strain could be well distributed within the w hole mechanism ，instead of concentrating on compli ‐ant 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 ob ‐j ective as minimizing the global effective strain and maximizing mutual strain energy was estab ‐lished ．Based on the solid isotropic material with penalization approach ，the compromise pro ‐g ramming method was used to study the multi ‐objective optimization problem of compliant mech ‐anisms ．T he sensitivity of the objective functions was analyzed by the adjoint metrix method ．T he multi ‐objective topology optimization problem was solved using the algorithm of moving as ‐y mptotes ．Finally ，this method was further investigated and realized with a numerical example to show its correctness and effectiveness ．T he results show that the global effective strain based to ‐p ology 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 ；g lobal effective strain ；strain energy