Based on functional element topology optimization design method, taking the bearing capacity of the metamaterials structure as the objective, that is, the structural stiffness of the functional element is maximized as the objective function, with the specified Poisson’s ratio as constraints, then the optimization model is established and solved. The optimized structure of the functional primitives is deduced to construct the finite element model for checking the Poisson’s ratio of functional element. The functional element are distributed in a periodic order to form a metamaterials structure, and the in-plane and out-plane structural bearing properties of the metamaterials are calculated and analyzed. Analysis shows that the optimal metamaterial structure has better structural bearing capacity than the traditional honeycomb structure, and the proposed functional element topology optimization method provides a feasible method for the design of new metamaterial structures.
［1］CUI T, SMITH D R, LIU R. Metamaterials: Theory, design and applications［M］. New York: Springer, 2010.
［2］TANG W, MEI Z, CUI T. Theory, experiment and applications of metamaterials［J］. Science China Phy-sics, Mechanics & Astronomy, 2015, 58(12): 127001.
［3］COMPTON B G, LEWIS J A. 3D-printing of lightweight cellular composites［J］. Advanced Materials, 2014, 26(34): 5930-5935.
［4］任小军, 张鹏, 王小军, 等. 烧结金属多孔材料的渗透和导热性能测试及孔隙特征分析［J］. 上海交通大学学报, 2013, 47(03): 352-357.
REN Xiaojun, ZHANG Peng, WANG Xiaojun, et al. Permeability, thermal conductivity and the pore characters of sintered porous metal materials［J］. Journal of Shanghai Jiao Tong University, 2013, 47(03): 352-357.
［5］张玉光. 薄膜型声学超材料隔声特性研究［D］. 长沙: 国防科学技术大学, 2014.
ZHANG Yuguang. Research on the sound insulation properties of membrane-type acoustic metamaterials［D］. Changsha: National University of Defense Technology, 2014.
［6］PRAWOTO Y. Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio［J］. Computational Materials Science, 2012, 58: 140-153.
［7］ELIPE J C A, LANTADA A D. Comparative study of auxetic geometries by means of computer-aided design and engineering［J］. Smart Materials and Structures, 2012, 21(10): 105004-105015.
［8］BENDSE M P. Optimal shape design as a material distribution problem［J］. Structural and Multidisciplinary Optimization, 1989, 1(4): 193-202.
［9］SIGMUND O, MAUTE K. Topology optimization approaches［J］. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031-1055.
［10］WANG B, HAO P, LI G, et al. Two-stage size-layout optimization of axially compressed stiffened pa-nels［J］. Structural & Multidisciplinary Optimization, 2014, 50(2): 313-327.
［11］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(04): 1014-1023.
QIN Haoxing, YANG Deqing. Functional element topology optimal method of metamaterial design with arbitrary negative Poisson’s ratio［J］. Acta Materiae Compositae Sinica, 2018, 35(04): 1014-1023.
［12］GIBSON L J, ASHBY M F. Cellular solids: Structure and properties ［M］. London: Cambridge University Press, 1997.
［13］WAN H, OHTAKI H, KOTOSAKA S, et al. A study of negative Poisson’s ratios in auxetic honeycombs based on a large deflection model［J］. Euro-pean Journal of Mechanics A/Solids, 2004, 23(1): 95-106.
［14］富明慧, 徐欧腾. 关于蜂窝芯体面外等效剪切模量的讨论［J］. 固体力学学报, 2014, 35(04): 334-340.
FU Minghui, XU Outeng. Discussion on equivalent transverse shear modules of honeycomb core［J］. Chinese Journal of Solid mechanics, 2014, 35(04): 334-340.
［15］YOON G, KIM I, RHO J. Challenges in fabrication towards realization of practical metamaterials［J］. Microelectronic Engineering, 2016, 163: 7-20.
［16］管国阳, 矫桂琼, 张增光. 2D-C/SiC复合材料的宏观拉压特性和失效模式［J］. 复合材料学报, 2005, 22(4): 81-85.
GUAN Guoyang, JIAO Guiqiong, ZHANG Zengguang. Uniaxial macro-mechanical property and fai-lure mode of a 2D-woven C/SiC composite［J］. Acta Materiae Compositae Sinica, 2005, 22(4): 81-85.
［17］CARNEIRO V H, PUGA H, MEIRELES J. Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements［J］. Acta Mechanica Sinica, 2016, 32(2): 295-300.
［18］DEATON J D, GRANDHI R V. A survey of structural and multidisciplinary continuum topology optimization: Post 2000［J］. Structural and Multidisciplinary Optimization, 2014, 49(1): 1-38.
［19］KATO J, YACHI D, TERADA K, et al. Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis［J］. Structural and Multidisciplinary Optimization, 2014, 49(4): 595-608.
［20］SIGMUND O, MAUTE K. Topology optimization approaches［J］. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031-1055.
［21］YE H L, WANG W W, CHEN N, et al. Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables［J］. Acta Mechanica Sinica, 2017, 33(5): 1-13.
［22］HUANG X, ZHOU S W, XIE Y M, et al. Topology optimization of microstructures of cellular materials and composites for macrostructures［J］. Computational Materials Science, 2013, 67: 397-407.
［23］VAN DIJK N P, MAUTE K, LANGELAAR M, et al. Level-set methods for structural topology optimization: A review［J］. Structural and Multidisciplinary Optimization, 2013, 48(3): 437-472.
［24］BENDSOE M P, SIGMUND O. Topology optimization: theory, methods, and applications［M］. Springer Science & Business Media, 2013.
［25］蒋伟, 马华, 王军, 等. 基于环形蜂窝芯结构的负泊松比机械超材料［J］. 科学通报, 2016, 61(13): 1421-1427.
JIANG Wei, MA Hua, WANG Jun, et al. Mechanical metamaterials with negative Poisson’s ratio based on circular honeycomb core［J］. Chinese Science Bulletin, 2016, 61(13): 1421-1427.
［26］黎彪, 程刚, 刘志全, 等. 球铰接杆式支撑臂构型参数分析［J］. 中国空间科学技术, 2012, 32(2): 29-34.
LI Biao, CHENG Gang, LIU Zhiquan, et al. Con-figuration parameter analysis for ADAM-type articulated mast［J］. Chinese Space Science and Technology, 2012, 32(2): 29-34.
