ZHANG Zhaohui, LI Baohui, SHI Jiao. Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells[J]. Applied Mathematics and Mechanics, 2018, 39(6): 714-727. doi: 10.21656/1000-0887.390025
Citation: ZHANG Zhaohui, LI Baohui, SHI Jiao. Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells[J]. Applied Mathematics and Mechanics, 2018, 39(6): 714-727. doi: 10.21656/1000-0887.390025

Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells

doi: 10.21656/1000-0887.390025
Funds:  The National Natural Science Foundation of China(51505388);The National Key Research and Development Project of China(2017YFC0405102)
  • Received Date: 2018-01-16
  • Rev Recd Date: 2018-04-25
  • Publish Date: 2018-06-15
  • The thermo-elasticity of 2D lattice structures with periodic unit cells was studied. The lattice structure was homogenized as a pseudo-membrane (PM) structure and the equivalent thermal expansion coefficients (TECs) of the PM were derived. The TECs were expressed as explicit functions of the geometrical and physical parameters of the links in unit cells. Simultaneously, the elastic properties were re-defined based on the new geometry of the unit cell under thermal load. Numerical results were given to show the difference between the deformations of the structure under different thermo-mechanical loads, and a uniform pressure was applied on the top surface of the cantilever beam with or without thermal loads (the temperature increment was positive, negative or null, respectively). In simulation, the deformations of the lattice structure beams (with different sizes of unit cells) and the corresponding PM beams were calculated numerically. The theoretical solution of the beam deformation was also given with the elasticity of the PM beam. Differences between the solutions verify the correctness of the derived equivalent parameters. Results show the validity of the PM method for equivalent thermo-mechanical analysis of 2D lattice structures with periodic unit cells.
  • loading
  • [1]
    董石麟, 夏亨熹. 正交正放类网架结构的拟板(夹层板)分析法(上)[J]. 建筑结构学报, 1982,3(2): 14-25.(DONG Shilin, XIA Hengxi. Analysis of orthogonal and ortho-laid space truss as equivalent (sandwich) plate (part I)[J]. Journal of Building Structures,1982,3(2): 14-25.(in Chinese))
    [2]
    董石麟, 夏亨熹. 正交正放类网架结构的拟板(夹层板)分析法(下)[J]. 建筑结构学报, 1982,3(3): 14-22.(DONG Shilin, XIA Hengxi. Analysis of orthogonal and ortho-laid space truss as equivalent (sandwich) plate (part II)[J]. Journal of Building Structures,1982,3(3): 14-22.(in Chinese))
    [3]
    阎军, 程耿东, 刘书田, 等. 周期性点阵类桁架材料等效弹性性能预测及尺度效应[J]. 固体力学学报, 2005,26(4): 421-428.(YAN Jun, CHENG Gengdong, LIU Shutian, et al. Prediction of equivalent elastic properties of truss materials with periodic microstructure and the scale effects[J]. Acta Mechanica Solida Sinica,2005,26(4): 421-428.(in Chinese))
    [4]
    张卫红, 骆金威, 戴高明, 等. 周期性多孔材料等效剪切模量与尺寸效应研究[J]. 力学学报, 2011,43(1): 144-153.(ZHANG Weihong, LUO Jinwei, DAI Gaoming, et al. Numerical predictions of effective shear modulus and size effect for periodic cellular materials[J]. Chinese Journal of Theoretical and Applied Mechanics,2011,43(1): 144-153.(in Chinese))
    [5]
    胡更开, 郑泉水, 黄筑平. 复合材料有效弹性性质分析方法[J]. 力学进展, 2001,31(3): 361-393.(HU Gengkai, ZHENG Quanshui, HUANG Zhuping. Micromechanics methods for effective elastic properties of composite materials[J]. Advances in Mechanics,2001,31(3): 361-393.(in Chinese))
    [6]
    HASSANI B, HINTON E. A review of homogenization and topology optimization I: homogenization theory for media with periodic structure[J]. Computers and Structures,1998,69(6): 707-717.
    [7]
    GIBSON L J, ASHBY M F. Cellular Solids: Structure and Properties [M]. Cambridge University Press, 1997.
    [8]
    TOLLENAERE H, CAILLERIE D. Continuous modeling of lattice structures by homogenization[J].Advances in Engineering Software,1998,29(7/9): 699-705.
    [9]
    〖JP2〗OSTOJA-STARZEWSKI M. Lattice models in micromechanics[J]. Applied Mechanics Reviews,2002,55(1): 35-60.〖JP〗
    [10]
    WADLEY H N G, FLECK N A, EVANS A G. Fabrication and structural performance of periodic cellular metal sandwich structures[J]. Composites Science and Technology,2003,63(16): 2331-2343.
    [11]
    ABOUDI J, GILAT R. Micromechanical analysis of lattice blocks[J]. International Journal of Solids and Structures,2005,42(15): 4372-4392.
    [12]
    HUTCHINSON R G, FLECK N A. The structural performance of the periodic truss[J]. Journal of Mechanics and Physics of Solids,2006,54(4): 756-782.
    [13]
    周加喜, 邓子辰. 类桁架夹层板的等效弹性常数研究[J]. 固体力学学报, 2008,29(2): 187-192.(ZHOU Jiaxi, DENG Zichen. On the effective elastic constants of truss-core panel[J]. Chinese Journal of Solid Mechanics,2008,29(2): 187-192.(in Chinese))
    [14]
    张洪武, 吴敬凯, 付振东. 周期性点阵桁架材料力学性能分析的一种新的多尺度计算方法[J]. 固体力学学报, 2011,32(2): 109-118.(ZHANG Hongwu, WU Jingkai, FU Zhendong. A new multiscale computational method for mechanical analysis of periodic truss materials[J]. Chinese Journal of Solid Mechanics,2011,32(2): 109-118.(in Chinese))
    [15]
    梁军, 黄富华, 杜善义. 周期性单胞复合材料有效弹性性能的边界力方法[J]. 复合材料学报, 2010,27(2): 108-112.(LIANG Jun, HUANG Fuhua, DU Shanyi. Boundary force method to predict the effective elastic properties of periodical unit cell composite material[J]. Acta Materiae Compositae Sinica,2010,27(2): 108-112.(in Chinese))
    [16]
    史姣, 蔡坤, 王正中. 拟膜分析法及应用[J]. 应用基础与工程科学学报, 2008,16(5): 749-756.(SHI Jiao, CAI Kun, WANG Zhengzhong. Pseudo-membrane method and its application[J]. Journal of Basic Science and Engineering,2008,16(5): 749-756.(in Chinese))
    [17]
    蔡坤, 陈飙松, 张洪武. 二维连续体结构的拓扑和材料一体化设计[J]. 应用基础与工程科学学报, 2008,16(1): 92-102.(CAI Kun, CHEN Biaosong, ZHANG Hongwu. Integrative design of topology and material of two-dimensional continuum structures[J]. Journal of Basic Science and Engineering,2008,16(1): 92-102.(in Chinese))
    [18]
    蔡坤, 史姣. 含周期性索-杆胞元的二维网格结构拟膜分析[J]. 工程力学, 2011,28(10): 27-33.(CAI Kun, SHI Jiao. Pseudo-membrane method for two-dimensional lattice structure with periodic cable-link cells[J]. Engineering Mechanics,2011,28(10): 27-33.(in Chinese))
    [19]
    吴世平, 唐绍锋, 梁军, 等. 周期性复合材料热力耦合性能的多尺度方法[J]. 哈尔滨工业大学学报, 2006,38(12): 2049-2053.(WU Shiping, TANG Shaofeng, LIANG Jun, et al. Multi-scale method for thermo-elasticity properties of composite materials with small periodic configuration[J]. Journal of Harbin Institute of Technology,2006,38(12): 2049-2053.(in Chinese))
    [20]
    张卫红, 汪雷, 孙士平. 基于导热性能的复合材料微结构拓扑优化设计[J]. 航空学报, 2006,27(6): 1229-1233.(ZHANG Weihong, WANG Lei, SUN Shiping. Topology optimization for microstructures of composite materials based on thermal conductivity[J]. Acta Meronautica et Astronautica Sinica,2006,27(6): 1229-1233.(in Chinese))
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (858) PDF downloads(807) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return