考虑材料非线性的结构拓扑优化研究综述
作者:
基金项目:

国家自然科学基金重点资助项目(11432011);中国工程物理研究院重点学科项目“计算固体力学”资助。


Review of researches on structure topology optimizationwith material nonlinearity
Author:
  • 摘要
  • | |
  • 访问统计
  • |
  • 参考文献 [35]
  • |
  • 相似文献 [20]
  • | | |
  • 文章评论
    摘要:

    结构拓扑优化作为结构设计的重要组成部分,正变得越来越重要。目前国内外学者对结构拓扑优化的研究仍主要局限于材料的线性变形范围,但实际许多工程结构都会产生材料非线性响应,如设计在一定地震载荷下坏而不倒的房屋结构,此时要得到更加符合实际的拓扑构型,就需要考虑材料非线性进行结构拓扑优化设计。笔者对材料非纯属结构拓扑优化研究进行了综述,并提出了展望。

    Abstract:

    Structure topology optimization, which is an important part of structure design, is becoming more and more important in recent years. At present, the research on structure topology optimization is mainly based on the theory of material linearity, in which the deformation of material is assumed linear. However, the nonlinear behavior of material occurs inevitably in practical engineering structures, such as house structure in earthquake area. It is demanded that the house can not be destroyed within a certain range of earthquke load. Therefore, the material nonlinearity must be taken into account in the research of structure topology optimization, so that the more practical topology structure can be obtained. In this paper, a review of researches on structure topology optimization with material nonlinearity was stated, and a brief expectation was presented.

    参考文献
    [1] 谢亿民, 杨晓英, Steven G P, 等. 渐进结构优化法的基本理论及应用[J]. 工程力学, 1999, 16(16): 70-81. XIE Yiming, YANG Xiaoying, Steven G P, et al. The theory and application of evolutionary structural optimization method[J]. Engineering Mechanics, 1999,16(16):70-81.(in Chinese)
    [2] 周克民, 李俊峰, 李霞. 结构拓扑优化方法研究综述[J].力学进展, 2005, 35(1): 69-76. ZHOU Keming, LI Junfeng, LI Xia. A review on topology optimization of structures[J]. Advances in Mechanics, 2005, 35(1): 69-76. (in Chinese)
    [3] Hassani B, Hinton E. Homogenization and structural topology optimization theory[M]. Practice and Software, London: Springer, 1999.
    [4] Xie Y M, Steven G P. Evolutionary structural optimization[M]. Springer-Verlag, Berlin, 1997.
    [5] Sigmund O. Design of material structures using topology optimization[D]. Denmark: Technical University of Denmark, 1994.
    [6] Zhou M, Rozvany G I N. The COC algorithm, part Ⅱ: topological, geometry and generalized shape optimization[J]. Computer Methods in Applied Mechanics & Engineering, 1991, 89(1-3):309-336.
    [7] Svanberg K. The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2):359-373.
    [8] Bendsøe M P, Sigmund O. Topology optimization: theory, methods and applications[J]. Handbook of Global optimization, 2003,34(88):179-203.
    [9] Eschenauer H A, Olhoff N. Topology optimization of continuum structures: a review[J]. Applied Mechanics Reviews, 2001, 54(4): 331-390.
    [10] Eschenauer H A, Kobelev V V, Schumacher A. Bubble method for topology and shape optimization of structures[J]. Structural & Multidisciplinary Optimization, 1994, 8(1):42-51.
    [11] Sigmund O, Petersson J. Numerical instabilities in topology optimization:a survey on procedures dealing with checkerboards, mesh-dependencies and local minima[J]. Structural Optimization, 1998, 16(1):68-75.
    [12] Yoon G H, Kim Y Y. Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization[J]. International Journal for Numerical Methods in Engineering, 2007, 69(10): 2196-2218.
    [13] Shin M K, Park K J, Park G J. Optimization of structures with nonlinear behavior using equivalent loads[J]. Computer Methods in Applied Mechanics & Engineering, 2007, 196(4-6):1154-1167.
    [14] Kim Y I, Park G J. Nonlinear dynamic response structural optimization using equivalent static loads[J]. Computer Methods in Applied Mechanics & Engineering,2010, 199(9-12): 660-676.
    [15] Ryu Y S, Haririan M, Wu C C, et al. Structural design sensitivity analysis of nonlinear response[J]. Computers & Structures, 1985,21(1-2):245-255.
    [16] Tsay J J, Arora J S. Nonlinear structural design sensitivity analysis for path-dependent problems, Part 1: general theory[J]. Computer Methods in Applied Mechanics & Engineering, 1990, 81(2): 183-208.
    [17] Pedersen C B W. Crashworthiness design of transient frame structures using topology optimization[J]. Computer Methods in Applied Mechanics & Engineering, 2004, 193(6-8): 653-678.
    [18] Schwarz S, Maute K, Ramm E. Topology and shape optimization for elastoplastic structural response[J]. Computer Methods in Applied Mechanics & Engineering, 2001, 190(15-17):2135-2155.
    [19] Cho S, Jung H S. Design sensitivity analysis and topology optimization of displacement-loaded non-linear structures[J]. Computer Methods in Applied Mechanics & Engineering, 2003, 192(22-24):2539-2553.
    [20] Jung D, Gea H C. Topology optimization of nonlinear structures[J]. Finite Elements in Analysis & Design, 2004, 40(11): 1417-1427.
    [21] Boroomand B, Barekatein A R. On topology optimization of linear and nonlinear plate problems[J]. Structural & Multidisciplinary Optimization, 2009, 39(1):17-27.
    [22] Yuge K, Iwai N, Kikuchi N. Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method[J]. Structural Optimization, 1999, 17(4):286-299.
    [23] Terada K, Yuge K, Kikuchi N. Elasto-plastic analysis of composite materials using the homogenization method: 1st report, formulation[J].Nihon Kikai Gakkai Ronbunshu A Hen/transaction of The Japan Society of Mechanical Engineers Part A, 1995, 61(590): 2199-2205.(in Japanese)
    [24] Bruns T E, Tortorelli D A. Topology optimization of non-linear elastic structures and compliant mechanisms[J]. Computer Methods in Applied Mechanics & Engineering, 2010, 190(26-27):3443-3459.
    [25] Jog C S. A dual algorithm for the topology optimization of non-linear elastic structures[J]. International Journal for Numerical Methods in Engineering, 2009, 77(4):502-517.
    [26] Chang D H, Yoo K S, Park J Y, et al. Optimum design for nonlinear problems using modified ant colony optimization[J].International Proceedings of Computer Science Information Tech, 2012, 41: 45.
    [27] Maute K, Schwarz S, Ramm E. Adaptive topology optimization of elastoplastic structures[J]. Structural Optimization, 1998, 15(2):81-91.
    [28] Huang X, Xie Y M. Topology optimization of nonlinear structures under displacement loading[J]. Engineering Structures, 2008, 30(7):2057-2068.
    [29] Lee H A, Park G J. Topology optimization for structures with nonlinear behavior using the equivalent static loads method[J]. Journal of Mechanical Design, 2012, 134(3):310-311.
    [30] 豆麟龙, 尹益辉, 张元章, 等. 弹塑性材料的结构拓扑优化[J]. 机械强度, 2014: 36(6), 966-970. DOU Linlong, YIN Yihui, ZHANG Yuanzhang, et al. Structural topology optimization of elasto-plastic material[J]. Journal of Mechanical Strength, 2014,36(6): 966-970. (in Chinese)
    [31] Mayer R R, Kikuchi N, Scott R A. Application of topological optimization techniques to structural crashworthiness[J]. International Journal for Numerical Methods in Engineering, 1996, 39(8):1383-1403.
    [32] Patel N M, Kang B S, Renaud J E, et al. Crashworthiness design using topology optimization[J]. Dissertations & Theses-Gradworks, 2007, 131(6): 1-12.
    [33] Swan C C, Kosaka I. Voigt-Reuss topology optimization for structures with nonlinear material behavior[J]. International Journal for Numerical Methods in Engineering, 1997, 40(20): 3785-3814.
    [34] Kato J, Lipka A, Ramm E. Multiphase material optimization for fiber reinforced composites with strain softening[J]. Structural and Multidisciplinary Optimization, 2009, 39(1): 63-81.
    [35] Bogomolny M, Amir O. Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling[J]. International Journal for Numerical Methods in Engineering, 2012, 90(13):1578-1597.
    引证文献
    网友评论
    网友评论
    分享到微博
    发 布
引用本文

尹益辉,刘远东,豆麟龙.考虑材料非线性的结构拓扑优化研究综述[J].重庆大学学报,2016,39(5):34-38.

复制
分享
文章指标
  • 点击次数:1410
  • 下载次数: 2324
  • HTML阅读次数: 752
  • 引用次数: 0
历史
  • 收稿日期:2016-03-31
  • 在线发布日期: 2016-10-31
文章二维码