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.
DU Yi-xian, LI Rong, XU Ming, TIAN Qi-hua, ZHOU Xiang-man. Topology optimization design for negative Poisson's ratio microstructure. Chinese Journal of Engineering Design, 2018, 25(4): 450-456.
秦浩星,杨德庆.任意负泊松比超材料结构设计的功能基元拓扑优化法[J].复合材料学报,2018,35(4):1014-1023. QIN Hao-xing, YAN De-qing. Functional primitive topology optimization for structural design of any negative Poisson's ratio metamaterials[J]. Acta Materiae Compositae Sinica, 2018, 35(4):1014-1023.
[[2]]
贺燕飞,邓庆田,尹冠生.负泊松比复合材料弹性性能分析[C]//第25届全国结构工程学术会议论文集(第Ⅰ册)[2017-11-10]. http://cpfd.cnki.com.cn/Article/CPFDTOTAL-LXFY201608003023.htm. HE Yan-fei, DENG Qing-tian, YIN Guan-sheng. Elasticity analysis of negative Poisson's compounded materials[C]//Proceedings of the 25th National Conference on Structural Engineering (No.Ⅰ).[2017-11-10]. http://cpfd.cnki.com.cn/Article/CPFDTOTAL-LXFY201608003023.htm.
[[3]]
杨呜波,阳霞,李忠明,等.负泊松比材料的结构与性能[J].高分子材料科学与工程,2001,17(6):15-18. YANG Wu-bo, YANG Xia, LI Zhong-ming, et al. Structure and properties of negative Poisson's ratio materials[J]. Polymer Materials Science & Engineering, 2001, 17(6):15-18.
[[4]]
赵亚斌,卢子兴.对负泊松比泡沫材料杨氏模量预测模型的修正[C]//第14届全国结构工程学术会议论文集(第一册).[2017-11-10]. http://www.doc88.com/p-1186130749900.html. ZHAO Ya-bin, LU Zi-xing. Correction to the model predicting Young's modulus of foam materials with negative Poisson's ratio[C]//Proceedings of the Fourteenth National Conference on Structural Engineering (No.Ⅰ),[2017-11-10]. http://www.doc88.com/p-1186130749900.html.
[[5]]
卢子兴,赵亚斌.一种有负泊松比效应的二维多胞材料力学模型[J].北京航空航天大学学报,2006,32(5):594-597. LU Zi-xing, ZHAO Ya-bin. Mechanical model of two-dimensional cellular materials with negative Poisson's ratio[J]. Journal of Beijing of Aeronautics and Astronautics, 2006, 32(5):594-597.
[[6]]
杨智春,邓庆田.负泊松比材料与结构的力学性能研究及应用[J].力学进展,2011,41(3):335-350. YANG Zhi-chun, DENG Qing-tian. Research and application of mechanical properties of material and structure with negative Poisson's ratio[J]. Advances in Mechanics, 2011, 41(3):335-350.
[[7]]
卢子兴, 刘强, 杨振宇. 拉胀泡沫材料力学性能[J]. 宇航材料工艺, 2011, 41(1):7-13. LU Zi-xing, LIU Qiang, YANG Zhen-yu. Mechanical properties of auxetic foams[J]. Aerospace Materials & Technology, 2011, 41(1):7-13.
[[8]]
张严,杜义贤,杜大翔,等.极限弹性性能的材料微结构拓扑优化设计[J].三峡大学学报(自然科学版),2016,38(2):71-74. ZHANG Yan, DU Yi-xian, DU Da-xiang, et al. Topology optimization for material microstructures with extreme elastic properties[J]. Journal of China There Gorges University (Natural Sciences), 2016, 38(2):71-74.
[[9]]
LU Yin, WANG Yang. Optimality criteria method for topology optimization under multiple constraints[J]. Computers & Structures, 2001, 79(20/21):1839-1850.
[[10]]
ALDERSON A, ALDERSON K L. Elastic constants of 3-, 4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[J]. Composites Science & Technology, 2010, 70(7):1042-1048.
[[11]]
ALDERSON K L, EVANS K E. The fabrication of microporous polyethylene having a negative Poisson's ratio[J]. Polymer, 1992, 33(20):4435-4438.
[[12]]
ZHANG Wei-hong, DAI Gao-ming, WANG Feng-wen, et al. Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures[J]. Acta Mechanica Sinica, 2007, 23(1):77-89.
[[13]]
刘书田,程耿东.基于均匀化理论的梯度功能材料优化设计方法[J].宇航材料工艺,1995(6):21-27. LIU Shu-tian, CHENG Geng-dong. Gradient function based on homogenization theory material optimization design method[J]. Aerospace Materials & Technology, 1995(6):21-27.
[[14]]
SIGMUND O. A 99 line topology optimization code written in MATLAB[J]. Structural & Multidisciplinary Optimization, 2001, 21(2):120-127.
[[15]]
ANDREASSEN E, CLAUSEN A. Efficient topology optimization in MATLAB using 88 lines of code[J]. Structural & Multidisciplinary Optimization, 2011, 43(1):1-16.
[[16]]
XIA Liang, BREITKOPF P. Design of materials using topology optimization and energy-based homogenization approach in MATLAB[J]. Structural & Multidisciplinary Optimization, 2015, 52(6):1229-1241.
[[17]]
ZHANG Wei-hong, WANG Feng-wen, DAI Gao-ming, et al. Topology optimal design of material microstructures using strain energy-based method[J]. Chinese Journal of Aeronautics, 2007, 20(4):320-326.
[[18]]
ZUO Z H, HUANG X, RONG J H, et al. Multi-scale design of composite materials and structures for maximum natural frequencies[J]. Materials & Design, 2013, 51:1023-1034.
