留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

有限元方法形成三维Michell桁架

周克民 李俊峰

周克民, 李俊峰. 有限元方法形成三维Michell桁架[J]. 应用数学和力学, 2005, 26(3): 349-355.
引用本文: 周克民, 李俊峰. 有限元方法形成三维Michell桁架[J]. 应用数学和力学, 2005, 26(3): 349-355.
ZHOU Ke-min, LI Jun-feng. Forming Michell Truss in Therr-Dimensions by Finite Element Method[J]. Applied Mathematics and Mechanics, 2005, 26(3): 349-355.
Citation: ZHOU Ke-min, LI Jun-feng. Forming Michell Truss in Therr-Dimensions by Finite Element Method[J]. Applied Mathematics and Mechanics, 2005, 26(3): 349-355.

有限元方法形成三维Michell桁架

基金项目: 教育部高等学校优秀青年教师教学科研奖励基金资助项目
详细信息
    作者简介:

    周克民(1962- ),男,河北新河人,教授,博士(联系人.Tel:+86-595-22691468;Fax:+86-595-22692097;E-mail:zhoukemin@tsinghua.org.cn).

  • 中图分类号: O343.8;TU323

Forming Michell Truss in Therr-Dimensions by Finite Element Method

  • 摘要: 提出了形成三维Michell桁架的有限元方法.采用正交异性纤维增强复合材料模型模拟Michell桁架.纤维在节点处的密度和方向作为基本设计变量.根据有限元分析得到节点位置的应力和应变.采用迭代方法,将纤维方向调整到主应力方向;根据纤维方向的应变改变纤维密度. 仅需少量迭代即可得到满足Michell准则的应变场和类桁架连续体.最后根据节点处的纤维方向用连续线表示出Michell桁架.几个算例表明了算法的有效性和计算效率.
  • [1] Michell A G M.The limits of economy of material in frame structure[J].Philosophical Magazine,1904,8(6):589—597. doi: 10.1080/14786440409463229
    [2] Prager W, Rozvany G I N.Optimization of structural geometry[A].In:Bednarek A R, Cesari L,Eds.Dynamical Systems[C].New York: Academic Press, 1977, 265—293.
    [3] Rozvany G I N.Structural Design via Optimality Criteria-The Prager Approach to Structural Optimization[M].Dordrecht: Kluwer Academic Publishers,1989,353—368.
    [4] Rozvany G I N.Some shortcomings in Michell's truss theory[J].Structural Optimization,1997,13(2/3):203—204. doi: 10.1007/BF01199243
    [5] Rozvany G I N.Partial relaxation of the orthogonality requirement for classical Michell trusses[J].Structural Optimization,1997,13(4):271—274. doi: 10.1007/BF01197457
    [6] Rozvany G I N.Generalized Michell structures-exact least-weight truss layouts for combined stress and displacement constraints: Part Ⅰ——General theory for plane trusses[J].Structural Optimization, 1995,9(3):178—188. doi: 10.1007/BF01743967
    [7] Rozvany G I N.Generalized Michell structures-exact least-weight truss layouts for combined stress and displacement constraints: Part Ⅱ——analytical solutions within a two-bar topology[J].Structural Optimization,1995,9(3):214—219. doi: 10.1007/BF01743973
    [8] Hemp W S.Optimal Structure[M].Oxford: Clarendon Press, 1973, 70—101.
    [9] Lewinski T, Zhou M, Rozvany G I N.Extended exact solutions for least-weight truss layouts—Paper Ⅰ: cantilever with a horizontal axis of symmetry[J].International Journal of Mechanical Sciences,1994,36(5):375—398. doi: 10.1016/0020-7403(94)90043-4
    [10] Lewinski T, Zhou M, Rozvany G I N.Extended exact solutions for least-weight truss layouts—Paper Ⅱ:unsymmetric cantilevers[J].International Journal of Mechanical Sciences,1994,36(5):399—419. doi: 10.1016/0020-7403(94)90044-2
    [11] CHENG Geng-dong,ZHENG Jiang.Study on topology optimization with stress constraints[J].Engineering Optimization,1992,20(2):129—148. doi: 10.1080/03052159208941276
    [12] Rozvany G I N, Bendse M P,Kirsch U.Layout Optimization of Structures[J].Applied Mechanics Reviews,1995,48(2):41—119. doi: 10.1115/1.3005097
    [13] Bendse M P, Kikuchi N.Generating optimal topologies in structural design using a homogenization method [J].Computer Methods in Applied Mechanics and Engineering,1988,71(2):197—224. doi: 10.1016/0045-7825(88)90086-2
    [14] SUI Yun-kang, YANG De-qing.A new method for structural topological optimization based on the concept of independent continuous variable and smooth model [J].Acta Mechanica Sinica,1998,18(2):179—185.
    [15] Xie Y M, Steven G P.A simple evolutionary procedure for structural optimization[J].Computers and Structures,1993,49(5):885—896. doi: 10.1016/0045-7949(93)90035-C
    [16] Guedes J M, Taylor J E.On the prediction of material properties and topology for optimal continuum structures[J].Structural Optimization,1997,14(3):193—199. doi: 10.1007/BF01812523
    [17] Taylor J E.An energy model for optimal design of linear continuum structures[J].Structural Optimization,1998,16(2/3):116—127.
    [18] Rodrigues H, Soto C, Taylor J E.A design model to predict optimal two-material composite structure[J].Structural Optimization,1999,17(2):186—198.
    [19] Hrnlein H R E M, Kocvara M, Werner R.Material optimization: bridging the gap between conceptual and preliminary design[J].Aerospace Science and Technology,2001,5(8):541—554. doi: 10.1016/S1270-9638(01)01125-7
    [20] Eschenauer H A, Olhoff N.Topology optimization of continuum structures: A review[J].Applied Mechanics Reviews,2001,54(4):331—389. doi: 10.1115/1.1388075
    [21] Rozvany G I N, Bendse M P, Kirsch U.Layout Optimization of structures[J].Applied Mechanics Reviews,1995,48(2):41—119. doi: 10.1115/1.3005097
    [22] 周克民.利用有限元构造Michell桁架的一种方法[J].力学学报,2002,34(6):935—940.
    [23] Cox H L.The Design of Structures of Least Weight[M].Oxford: Pergamon Press,1965,80—114.
  • 加载中
计量
  • 文章访问数:  3096
  • HTML全文浏览量:  101
  • PDF下载量:  971
  • 被引次数: 0
出版历程
  • 收稿日期:  2004-06-20
  • 修回日期:  2004-11-20
  • 刊出日期:  2005-03-15

目录

    /

    返回文章
    返回