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基于解析试函数有限单元法的研究进展

傅向荣 田 歌

傅向荣 田 歌. 基于解析试函数有限单元法的研究进展[J]. 工程力学, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
引用本文: 傅向荣 田 歌. 基于解析试函数有限单元法的研究进展[J]. 工程力学, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
FU Xiang-rong. ADVANCES IN THE FINITE ELEMENT METHOD BASED ON THE ANALYTICAL TRIAL FUNCTIONS[J]. Engineering Mechanics, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
Citation: FU Xiang-rong. ADVANCES IN THE FINITE ELEMENT METHOD BASED ON THE ANALYTICAL TRIAL FUNCTIONS[J]. Engineering Mechanics, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039

基于解析试函数有限单元法的研究进展

doi: 10.6052/j.issn.1000-4750.2012.05.S039
基金项目: 国家自然科学基金项目(11272340,10872108);国家重点基础研究发展计划项目(2010CB731503)
详细信息
  • 中图分类号: O343

ADVANCES IN THE FINITE ELEMENT METHOD BASED ON THE ANALYTICAL TRIAL FUNCTIONS

  • 摘要: 基于解析试函数的有限单元法是一种将有限单元的离散法与解析法成果有机融合的方法,在有限单元理论的几个传统问题中取得了一些进展。该文介绍近几年该类方法在克服剪切闭锁以及消除网格畸变对单元性能影响等方面的研究进展;通过运用含应力函数变分原理,得到了一类不受网格畸变影响的高次精度精确单元;利用特征微分方程解法,给出了一个在弹性力学问题中构造独立完备解析试函数的通用方法。
  • [1] Courant R. Variational methods for the solution of problems of equilibrium and vibration [J]. Bulletin of the American Mathematical Society, 1943, 49: 1―23.
    [2] Turner M J, Clough R W, Martin H C, Topp L J. Stiffness and deflection analysis of complex structures [J]. Journal of Aeronautical Sciences, 1956, 23(9): 805―823.
    [3] Clough R W. The finite element method in plane stress analysis [C]. Proceedings 2nd Conference on Electronic Computation, Pittsburgh. Pennsylvania: ASCE, 1960, 9: 8―9.
    [4] 冯康. 基于变分原理的差分格式[J]. 应用数学与计算数学, 1965, 2(4): 238―262.
    Feng Kang. Difference scheme based on variational principle [J]. Applied Mathematica and Computational Mathematics, 1965,2(4):238―262. (in Chinese)
    [5] 龙驭球, 龙志飞, 岑松. 新型有限元论[M]. 北京: 清华大学出版社, 2004: 315―420.
    Long Yuqiu, Long Zhifei, Cen Song. Advanced theory of the finite element method [M]. Beijing: Tsinghua University Press, 2004: 315―420. (in Chinese)
    [6] Cen S , Fu X R, Zhou M J. 8- and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes [J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(29/30/31/32): 2321―2336.
    [7] Cen S, Zhou M J, Fu X R. A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions [J]. Computers and Structures, 2011, 5/6(89): 517―528.
    [8] Fu X R, Cen S, Li C F, Chen X M. Analytical trial function method for development of new 8-node plane element based on the variational principle containing airy stress function [J]. Engineering Computations, 2010(27): 442―463.
    [9] Fu X R, Cen S, Long Y Q, Jiang X G, Ju J S. The analytical trial function method (ATFM) for finite element analysis of plane [J]. Key Engineering Materials, 2008(385/386/387): 617―620.
    [10] 龙驭球, 支秉琛, 匡文起, 单建. 分区混合有限元法计算应力强度因子[J]. 力学学报, 1982, 18(4): 341―353.
    Long Yuqiu, Zhi Bingchen, Kuang Wenqi, Shan Jian. Sub-region mixed finite element method for the calculation of stress intensity factor [J]. Chinese Journal of Theoretical and Applied Mechanics, 1982, 18(4): 341―353. (in Chinese)
    [11] Cruse T A. Numerical evaluation of elastic S.I.F. by boundary integral equation method in the surface crack [C]. New York: The Winter Annual Meeting of ASME (J.L. Swedlow ed.), 1972: 153―170.
    [12] Cheung Y K, Woo C W, Wang Y H. The stress intensity factor for a double edge cracked plate by boundary collocation methods [J]. International Journal of Fracture, 1988, 37: 217―231.
    [13] Pin Tong, T H H Pian, Lasry S J. A hybrid-element approach to crack problems in plane elasticity [J]. International Journal for Numerical Methods in Engineering, 1973, 7: 297―308.
    [14] T H H Pian. Derivation of element stiffness matrices by assumed stress distributions [J]. AIAA Journal, 1964: 1333―1336.
    [15] 钟万勰, 纪峥. 理性有限元[J]. 计算结构力学及其应用, 1996, 13(1): 1―8.
    Zhong Wanxie, Ji Zheng. Rational finite element [J]. Computational Structural Mechanics and Applications, 1996, 13(1): 1―8. (in Chinese)
    [16] 傅向荣. 基于解析试函数的广义协调元[D]. 北京: 清华大学, 2002: 1―101.
    Fu Xiangrong. The generalized conforming element based on the analytical trial functions [D]. Beijing: Tsinghua University, 2002: 1―101. (in Chinese)
    [17] Henshell R D, Shaw K G. Crack-tip finite elements are unnecessary [J]. International Journal for Numerical Methods in Engineering, 1975, 9: 495―507.
    [18] Shi Z C. On the accuracy of the quasiconforming and generalized conforming finite elements [J]. Chinese Annals of Mathematics, 1990, 11b(2): 148―155.
    [19] Williams M L. Stress singularities resulting from various boundary conditions in angular corners of plates in extension [J]. Journal of Applied Mechanics, 1952, 24: 526―528.
    [20] 胡海昌. 弹性力学的变分原理及其应用[M]. 北京: 科学出版社, 1981: 465―476.
    Hu Haichang. Variational principle of the elastics and its applications [M]. Beijing: Science Press, 1981: 465―476. (in Chinese)
    [21] 王敏中. 高等弹性力学[M]. 北京: 北京大学出版社, 2002: 1―48.
    Wang Minzhong. Advanced elastics [M]. Beijing: Peking University Press, 2002: 1―48. (in Chinese)
    [22] 王敏中, 王炜. 各向异性弹性力学问题的通解[C]. 北京: 力学与工程, 清华大学出版社, 1999: 231―235.
    Wang Minzhong, Wang Wei. The general solution of anisotropic elasticity [J]. Beijing: Mechanics and Engineerings, Tsinghua University Press, 1999: 231―235. (in Chinese)
    [23] Lekhnitskii S G. Theory elasticity of an anisotropic body [M]. Moscow: Mir Publishers, 1981: 1―20.
    [24] 丁皓江, 王国庆, 陈伟球. 用‘调和函数’表示的压电介质平面问题的通解[J]. 应用数学和力学, 1997, 18(8): 703―709.
    Ding Haojiang, Wang Guoqing, Chen Weiqiu. General solution of plane problem of piezoelectric media expressed by ‘Harmonic Functions’ [J]. Applied Mathematics and Mechanics, 1997, 18(8): 703―709. (in Chinese)
    [25] Wang Z K, Zheng B L. The general solution of three-dimensional problems in piezoelectric media [J]. International Journal of Solids and Structures, 1995, 32: 105―115.
    [26] 田歌. 弹性力学一般问题解析试函数法及其单元构造研究[D]. 北京: 中国农业大学, 2011: 1―144.
    Tian Ge. The analytical trial functions of the elasticity and the construction of the associated finite elements [D]. Beijing: China Agricultural University, 2011: 1―144. (in Chinese)
    [27] 王文婕, 田歌, 傅向荣, 赵阳. 各向异性材料平面问题基本解析解的特征方程解法[J]. 工程力学, 2012, 29(9): 11―16.
    Wang Wenjie, Tian Ge, Fu Xiangrong, Zhao Yang. A new strategy for formulating the fundamental analytical solutions by solving the characteristic equations of plane problems with anisotropic materials [J]. Engineering Mechanics, 2012, 29(9): 11―16. (in Chinese)
    [28] 傅向荣, 袁明武, 岑松, 田歌. 三维弹性力学问题解析试函数的特征方程解法[J]. 应用数学和力学, 2012, 33(10): 1253―1264.
    Fu Xiangrong, Yuan Mingwu, Cen Song, Tian Ge. Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity [J]. Appplied Mathematics and Mechanics, 2012, 33(10): 1253―1264. (in Chinese)
    [29] 王敏中, 王炜, 武际可. 弹性力学教程(修订版)[M]. 北京: 北京大学出版社, 2011: 395―409.
    Wang Minzhong, Wang Wei, Wu Jike. Course of elasticity [M]. Beijing: Peking University Press, 2011: 395―409. (in Chinese)
    [30] 田歌, 傅向荣, 邓娇, 张鹏, 刘浩宇. 基于解析试函数的各向异性材料厚薄通用板单元[J]. 工程力学, 2012, 29(11): 65―70, 79.
    Tian Ge, Fu Xiangrong, Deng Jiao, Zhang Peng, Liu Haoyu. Thick and thin plate elements with anisotropic materials based on analytical trial functions [J]. Engineering Mechanics, 2012, 29(11): 65―70, 79. (in Chinese)
    [31] 龙驭球, 傅向荣. 基于解析试函数的广义协调四边形厚板元[J]. 工程力学, 2002, 19(3): 10―15.
    Long Yuqiu, Fu Xiangrong. Two generalized conforming quadrilateral thick plate elements based on analytical trial functions [J]. Engineering Mechanics, 2002, 19(3): 10―15. (in Chinese)
    [32] Wang M Z, Xu B X, Zhao Y T. General representations of polynomial elastic fields [J]. Journal of Applied Mechanics, 2012, 79(2): 021017.
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出版历程
  • 收稿日期:  2011-05-05
  • 修回日期:  2012-10-22
  • 刊出日期:  2012-12-25

基于解析试函数有限单元法的研究进展

doi: 10.6052/j.issn.1000-4750.2012.05.S039
    基金项目:  国家自然科学基金项目(11272340,10872108);国家重点基础研究发展计划项目(2010CB731503)
  • 中图分类号: O343

摘要: 基于解析试函数的有限单元法是一种将有限单元的离散法与解析法成果有机融合的方法,在有限单元理论的几个传统问题中取得了一些进展。该文介绍近几年该类方法在克服剪切闭锁以及消除网格畸变对单元性能影响等方面的研究进展;通过运用含应力函数变分原理,得到了一类不受网格畸变影响的高次精度精确单元;利用特征微分方程解法,给出了一个在弹性力学问题中构造独立完备解析试函数的通用方法。

English Abstract

傅向荣 田 歌. 基于解析试函数有限单元法的研究进展[J]. 工程力学, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
引用本文: 傅向荣 田 歌. 基于解析试函数有限单元法的研究进展[J]. 工程力学, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
FU Xiang-rong. ADVANCES IN THE FINITE ELEMENT METHOD BASED ON THE ANALYTICAL TRIAL FUNCTIONS[J]. Engineering Mechanics, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
Citation: FU Xiang-rong. ADVANCES IN THE FINITE ELEMENT METHOD BASED ON THE ANALYTICAL TRIAL FUNCTIONS[J]. Engineering Mechanics, 2012, 29(增刊Ⅱ): 78-84. doi: 10.6052/j.issn.1000-4750.2012.05.S039
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