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工程设计学报
工程设计学报  2018, Vol. 25 Issue (4): 450-456    DOI: 10.3785/j.issn.1006-754X.2018.04.012
优化设计     
负泊松比微结构拓扑优化设计
杜义贤, 李荣, 徐明, 田启华, 周祥曼
三峡大学 机械与动力学院, 湖北 宜昌 443002
Topology optimization design for negative Poisson's ratio microstructure
DU Yi-xian, LI Rong, XU Ming, TIAN Qi-hua, ZHOU Xiang-man
College of Mechanical and Power Engineering, China Three Gorges University, Yichang 443002, China
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摘要：

在构建负泊松比结构拓扑优化模型时，直接用负泊松比的数学表达式构造目标函数，将使得目标函数高度非线性，迭代过程敏度分析困难。采用线性拟合法，构建了具有线性特征的负泊松比微结构拓扑优化目标函数，基于能量法和均匀化方法，结合拓扑优化理论，构建了一种可以快速准确求解负泊松比的拓扑优化设计模型，求解该模型得到了一种优化的拓扑构型及相应的负泊松比值。根据优化求解得到的结构模型，参考国家标准GB/T 22315-2008《金属材料弹性模量和泊松比试验方法》，利用有限元软件对其泊松比进行仿真计算，然后采用激光加工方式制造试样，并测试其泊松比，经过与优化模型求解得到的泊松比值对比分析，验证了所构建优化模型的正确性。本文方法既避免了以负泊松比表达式为优化函数时会出现的高度非线性问题，也降低了求解的复杂程度，为负泊松比微结构的设计提供了一种参考方法。
关键词： 微结构;  拓扑优化;  负泊松比;  拓扑构型    
Abstract:

Constructing the objective function through the math expression of the negative Poisson's ratio directly will make the objective function highly non-linear and the sensitivity analysis of the iterative process difficult when constructing the topology optimization model of negative Poisson's ratio structure. Firstly, the topology optimization objective function of negative Poisson's ratio microstructure with linear characteristic was constructed by the linear fitting method; Secondly, employing the strain energy-based method and the homogenization method and combining the topological optimization theory, a topology optimization design model was constructed, which could solve the negative Poisson's ratio quickly and accurately. The optimal topological configuration and the corresponding negative Poisson ratio were obtained by solving the model. According to the structure model obtained through optimization, referring to the national standard GB/T 22315-2008 the elastic modulus of metal materials and Poisson's ratio testing method, the Poisson's ratio was simulated by finite element software, and an experimental sample was processed by laser processing. Next, the Poisson's ratio was tested and compared with the Poisson's ratio obtained from the optimization model to verify the correctness of the optimized model. The method not only avoids the highly non-linear problem when using the negative Poisson's ratio expression as the optimization function, but also reduces the solving complexity, which provides a reference method for the design of negative Poisson's ratio microstructure.
Key words: microstructure    topology optimization    negative Poisson's ratio    topological configuration
收稿日期: 2017-11-17 出版日期: 2018-08-28
CLC:  TB122  
基金资助:

国家自然科学基金资助项目（51775308，51475265，51705287）
作者简介: 杜义贤(1978-),男,湖北松滋人,教授,博士,从事结构优化与分析、CAD/CAE/CAM技术、材料-结构一体化设计等研究,E-mail:duyixian@aliyun.com,https://orcid.org/0000-0001-7474-9469
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引用本文:

杜义贤, 李荣, 徐明, 田启华, 周祥曼. 负泊松比微结构拓扑优化设计[J]. 工程设计学报, 2018, 25(4): 450-456.

DU Yi-xian, LI Rong, XU Ming, TIAN Qi-hua, ZHOU Xiang-man. Topology optimization design for negative Poisson's ratio microstructure[J]. Chinese Journal of Engineering Design, 2018, 25(4): 450-456.

链接本文:

https://www.zjujournals.com/gcsjxb/CN/10.3785/j.issn.1006-754X.2018.04.012    或    https://www.zjujournals.com/gcsjxb/CN/Y2018/V25/I4/450

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