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2维梁有限变形的精确理论和近似理论 被引量：1

Exact and Approximate Finite Deformation Theories of 2-D Beam
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摘要 提出了用以判别梁的有限变形精确理论与近似理论的3条准则，在李明瑞的2维梁有限变形精确理论的基础上推导出几种合理的简化理论，将Reissuer-Simo理论补充成为完整的近似理论，通过算例对各种理论作了比较。 The criteria used to classify exact and approximate finite deformation theories areproposed. Based on the exact finite deformation theory of 2-D beam proposed by Li, severaluseful approximate finite deformation theories are derived. The Reissner-Simo theory isdiscussed and made into complete approximate. Numerical examples are calculated indifferent theories for comparison.
作者 李进京 李明瑞 李辛
机构地区 中国农业大学工程基础科学部
出处 《中国农业大学学报》 CAS CSCD 北大核心 1999年第2期36-42,共7页 Journal of China Agricultural University
基金 国家自然科学基金
关键词 二维梁 有限变形 精确理论 近似理论 2-D beam finite deformation exact theory approximate theory criteria
分类号 O343.5 [理学—固体力学]
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参考文献6

  • 1黄文,李明瑞,黄文彬.杆系结构的几何非线性分析──Ⅰ．平面问题[J].计算结构力学及其应用,1995,12(1):7-16. 被引量：11
  • 2Li Mingrui，Comput Meth Appl Mech Eng，1998年，156卷，247页
  • 3Li Mingrui，Comput Meth Appl Mech Eng，1997年，146卷，53页
  • 4Li Mingrui，Prog Nat Sci，1997年，7卷，6期，649页
  • 5藤宁钧，计算结构力学及其应用，1987年，4卷，2期，25页
  • 6老亮（译），弹性和塑性力学中的变分法，1984年，146页

共引文献10

同被引文献25

  • 1Simo JC. A finite strain beam formulation. The three-dimensional dynamic problem, Part I. Computer Methods in Applied Mechanics and Engineering, 1985, 49(1): 55-70.
  • 2Simo JC, Vu-Quoc L. A three-dimensional finite-strain rod model, Part II: Computational aspects. Computer Methods in Applied Mechanics and Engineering, 1986, 58(1): 79-116.
  • 3Reissner E. On one-dimensional finite-strain beam theory: The plane problem. Journal of Applied Mathematics and Physics, 1972, 23:794-804.
  • 4Petrov E, Geradin M. Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids Part 1; Beam concept and geometrically exact nonlinear formulation, Com- puter Methods in Applied Mechanics and Engineering, 1998, 165(1- 4): 43-92.
  • 5Petrov E, G6radin M. Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids, Part 2: Anisotropic and advanced beam models. Computer Methods in Applied Mechanics and Engineering, 1998, 165(1-4): 93-127.
  • 6Ibrahimbegovic A. On finite element implementation of geometri- cally nonlinear Reissner's beam theory: Three-dimensional curved beam elements. Computer Methods in Applied Mechanics and En. gineering, 1995, 122(1-2): 11-26.
  • 7Ibrahimbegovi6 A, Frey E Kozar I. Computational aspects of vector- like parametrization of three-dimensional finite rotations. Interna- tional Journal for Numerical Methods in Engineering, 1995, 38(21 ): 3653-3673.
  • 8Ritto-Correa M, Camotim D. On the differentiation of the Rodrigues formula and its significance for the vector-like parameterization of Reissner-Simo beam theory. International Journal for Numerical Methods in Engineering, 2002, 55(9): 1005-1032.
  • 9Simo JC, Vu-Quoc L. On the dynamics in space of rods undergoing large motions-A geometrically exact approach. Computer Meth- ods in Applied Mechanics and Engineering, 1988, 66(2): 125-161.
  • 10Zupan D, Saje M. Finite-element formulation of geometrically ex- act three-dimensional beam theories based on interpolation of strain measures. Computer Methods in Applied Mechanics and Engineering. 2003.192(49-50): 5209-5248.

引证文献1

二级引证文献3

中国农业大学学报
1999年 第2期

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