Topology optimization for auxetic metamaterials based on isogeometric analysis

被引:136
作者
Gao, Jie [1 ,2 ]
Xue, Huipeng [1 ]
Gao, Liang [2 ]
Luo, Zhen [1 ]
机构
[1] Univ Technol Sydney, Sch Mech & Mechatron Engn, 15 Broadway, Ultimo, NSW 2007, Australia
[2] Huazhong Univ Sci & Technol, State Key Lab Digital Mfg Equipment & Technol, 1037 Luoyu Rd, Wuhan 430074, Hubei, Peoples R China
基金
澳大利亚研究理事会;
关键词
Auxetic metamaterials; Topology optimization; Isogeometric analysis; Homogenization; LEVEL-SET; MECHANICAL METAMATERIALS; POISSONS RATIO; SHAPE OPTIMIZATION; DESIGN; COMPOSITES; BEHAVIOR; ELEMENT;
D O I
10.1016/j.cma.2019.04.021
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, an effective and efficient topology optimization method, termed as Isogeometric Topology Optimization (ITO), is proposed for systematic design of both 2D and 3D auxetic metamaterials based on isogeometric analysis (IGA). Firstly, a density distribution function (DDF) with the desired smoothness and continuity, to represent the topological changes of structures, is constructed using the Shepard function and non-uniform rational B-splines (NURBS) basis functions. Secondly, an energy-based homogenization method (EBHM) to evaluate material effective properties is numerically implemented by IGA, with the imposing of the periodic boundary formulation on material microstructure. Thirdly, a topology optimization formulation for 2D and 3D auxetic metamaterials is developed based on the DDF, where the objective function is defined as a combination of the homogenized elastic tensor and the IGA is applied to solve the structural responses. A relaxed optimality criteria (OC) method is used to update the design variables, due to the non-monotonic property of the problem. Finally, several numerical examples are used to demonstrate the effectiveness and efficiency of the proposed method. A series of auxetic microstructures with different deformation mechanisms (e.g. the re-entrant and chiral) can be obtained. The auxetic behavior of material microstructures are numerically validated using ANSYS, and the optimized designs are prototyped using the Selective Laser Sintering (SLS) technique. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码:211 / 236
页数:26
相关论文
共 65 条
  • [1] Structural optimization using sensitivity analysis and a level-set method
    Allaire, G
    Jouve, F
    Toader, AM
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 194 (01) : 363 - 393
  • [2] Design of manufacturable 3D extremal elastic microstructure
    Andreassen, Erik
    Lazarov, Boyan S.
    Sigmund, Ole
    [J]. MECHANICS OF MATERIALS, 2014, 69 (01) : 1 - 10
  • [3] How to determine composite material properties using numerical homogenization
    Andreassen, Erik
    Andreasen, Casper Schousboe
    [J]. COMPUTATIONAL MATERIALS SCIENCE, 2014, 83 : 488 - 495
  • [4] [Anonymous], 1995, Applied Mechanics Reviews, DOI [10.1115/1.3005097, DOI 10.1115/1.3005097]
  • [5] [Anonymous], 2009, Isogeometric analysis
  • [6] [Anonymous], 1978, A Pratical Guide to Splines
  • [7] [Anonymous], 1968, P 1968 ACM NAT C
  • [8] Bendsoe M. P., 2004, Topology optimization: theory, methods, and applications
  • [9] GENERATING OPTIMAL TOPOLOGIES IN STRUCTURAL DESIGN USING A HOMOGENIZATION METHOD
    BENDSOE, MP
    KIKUCHI, N
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1988, 71 (02) : 197 - 224
  • [10] Material interpolation schemes in topology optimization
    Bendsoe, MP
    Sigmund, O
    [J]. ARCHIVE OF APPLIED MECHANICS, 1999, 69 (9-10) : 635 - 654