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

多变量样条元法分析弹性地基板的弯曲、振动与稳定问题*

沈鹏程 何沛祥

沈鹏程, 何沛祥. 多变量样条元法分析弹性地基板的弯曲、振动与稳定问题*[J]. 应用数学和力学, 1997, 18(8): 725-733.
引用本文: 沈鹏程, 何沛祥. 多变量样条元法分析弹性地基板的弯曲、振动与稳定问题*[J]. 应用数学和力学, 1997, 18(8): 725-733.
Shen Pengcheng, He Peixiang. Analysis of Bending, Vibration and Stability for Thin Plate on Elastic Foundation by the Multivariable Spline Element Method[J]. Applied Mathematics and Mechanics, 1997, 18(8): 725-733.
Citation: Shen Pengcheng, He Peixiang. Analysis of Bending, Vibration and Stability for Thin Plate on Elastic Foundation by the Multivariable Spline Element Method[J]. Applied Mathematics and Mechanics, 1997, 18(8): 725-733.

多变量样条元法分析弹性地基板的弯曲、振动与稳定问题*

基金项目: * 国家自然科学基金

Analysis of Bending, Vibration and Stability for Thin Plate on Elastic Foundation by the Multivariable Spline Element Method

  • 摘要: 本文应用双三次乘积型二元B样条函数来构造弹性地基板的位移、弯矩和扭矩等多种场函数,由混合变分原理导出多变量样条无法方程.文中,对弹性地基板的弯曲、振动与稳定问题作了分析与计算.由于,本文方法设定了各自独立的场函数,因此,所算得的场未知量如位移、弯矩和扭矩值的精度均比较高.
  • [1] H. Antes, Bicubic fundamental splines in plate bending. In t. J Numer Meth. Engng., 8(1974), 503-511.
    [2] 石钟慈,样条有限元,计算数学,(1979), 50-72
    [3] T. Mizusawa-T. Kajita and M. Naruoka, Vibration of skew plates by using B-splinefunctions-J. Soumd Vibr., 62-2 (1979), 301~308.
    [4] 吴兹潜、张佑傲、范寿昌.《结构分析的样条有限条法》.广州科技出版社(1985).
    [5] 沈鹏程、黄大德,样条高斯配点法分析加劲板壳的振动与屈曲问题.计算结构力学及其应用.7(1) (1990), 25-36.
    [6] Shen Pengcheng. Huang Dade and Wang Zongmon, Static, vibration and stabilityanalysis of stiffened plates using spline functions, Int. J. Conrputers & Structures, 27, 1(1987), 7~78.
    [7] Shen Pengcheng and Wang Jianguo, A semianalytical method for static analysis ofshallow shells. Int. J. Computers & Structures, 31, 5 (1989), 825~831.
    [8] Shen Pengcheng and Huang Dade. Dynamic analysis of stiffened pliltes and shells usingspline Gauss collocation method. Int. J. Computers & Structures 36. 4 (1990), 623~629.
    [9] Shen Pengcheng and Huang Dade. Analysis of stiffened structures on foundation usingspline Gauss collocation method. Second World Congress on Computational Meshanics Stuttgart, Gemany. Aug. 27~31. 1990. Proc. Vol. 2 (1990)451~454.
    [10] Shen Pengcheng and H. B. Kan. The multivariable spline element analysis for plate bendingproblems. Int. J. Computers and Structures 40 (1992), 1343~1349.
    [11] Shen Pengcheng, Analysis of plates and beams on foundation by using spline flnite elementmethod. Int. Conf on Computational Engineering Science. Aug. 12~16. 1991.Melbourne.Australia (1991).
    [12] 沈鹏程,《结构分析中的样条有限元法》,水利电力出版社(1992).
    [13] Shen Pengcheng and He Peixiang. Vibration analysis for plates using multivariable splineelement method, Int. J. Solids & Struectures, 29 24 (1992), 3289~3295.
    [14] Kyuichiro Washizu Varialional Method in Elasticity and Plasticity,decond edition,Pergamon Press (1975).
    [15] F. Fujii and Hoshino, Discrete and non-discrete mixed methods applied to eigenvalueproblems of plates, J Soltnd and Vthralion, 87, 4 (1983), 525~534.
    [16] R. M. Prenter, Splines and Variational Methods-John Wiley and Sons, Inc. (1975).
    [17] 钱伟长,《变分法与有限元》(上册).北京,科学出版社(1980),
    [18] 胡海昌,《弹性力学的变分原理及其应用》,北京,科学出版社(1981).
    [19] S. Timoshenko and S. Woinowsky-Krieger, Tleory of Plales and Shells, McGraw-Hill,NewYork (1959).
    [20] R. D. Blevins, Formulas for Nalural Frequency and Mode Shape, Van Nostrand,Reinhold Co. (1979).
    [21] S. Timoshenko and J. N. Gere, Theory of Elastic Stabilily, McGraw-Hill (1961).
    [22] S. Watkin Divid, On the construction of conforming rectangular plate elements, Int. J.Numer. Melh. Engng., 10 (1976), 925~933.
  • 加载中
计量
  • 文章访问数:  2047
  • HTML全文浏览量:  85
  • PDF下载量:  535
  • 被引次数: 0
出版历程
  • 收稿日期:  1994-10-04
  • 修回日期:  1995-10-15
  • 刊出日期:  1997-08-15

目录

    /

    返回文章
    返回