## 留言板

 引用本文: 叶开沅, 周又和. 关于钱氏摄动法的高阶解的计算机求解和收敛性的研究[J]. 应用数学和力学, 1986, 7(4): 285-293.
Ye Kai-yuan, Zhou You-he. On Solving High-Order Solutions of Chien’s Perturbation Method to Study Convergence by Computer[J]. Applied Mathematics and Mechanics, 1986, 7(4): 285-293.
 Citation: Ye Kai-yuan, Zhou You-he. On Solving High-Order Solutions of Chien’s Perturbation Method to Study Convergence by Computer[J]. Applied Mathematics and Mechanics, 1986, 7(4): 285-293.

## On Solving High-Order Solutions of Chien’s Perturbation Method to Study Convergence by Computer

• 摘要: 本文借助于中心受集中载荷圆板小挠度问题的积分方程,获得了摄动参数为中心挠度的任意n阶摄动解的解析式.于是,任意次摄动解的所有待定系数能用计算机求解.因此,获得了相当高阶的摄动解.在此基础上,讨论了钱氏摄动法的渐近性和适用区.
•  [1] Chien Wei-zang,Large deflection of a circular clamped plate under uniform pressure,Chinese Journal of Physics,7(1947),102-113. [2] 钱伟长、叶开沅,圆板大挠度问题,物理学报,10,3(1954),209-238. [3] 黄择言,弹性圆薄板在均布边缘力矩作用下的弯曲,物理学报,12,6(1956).597-606. [4] 叶开沅,边缘载荷下环形板的犬挠度间题,物理学报.9,2(1953),110-129. [5] 钱伟长、林鸿荪、胡海昌、叶开沅.《弹性圆薄板大挠度问题》,科学出版社(1954),49-55. [6] Nash,W.A.and I.D.Cooly,Large deflection of a clamped elliptical plate subjected to uniform pressure,Transactions of ASME J.of Appl.Mech.,26,2(1959),291-293. [7] Chien Wei-zang and Yeh Kai-yuan,Large deflection of a rectangular plate under uniform pressure,Proc.Math.Intern.Congr.Appl Mech.,Brussels,6(1957),403-409. [8] Schmidt,R.and D.A.DaDeppo,A new approach to the analysis of shells,plates and memberanes with finite deflection,Int.J.of Non-linear Mech.,9,5(1974),409-419. [9] DaDeppo,D.A.and R.Schmidt,Moderately large deflections of a loosing clamped circular plate under a uniformly distributed load,Indus.Math.,25,1(1975),17-28. [10] 陈山林、光积昌,圆薄板大挠度问题的摄动参数,应用数学和力学,2,1(1981),131-144. [11] 陈山林,圆板大挠度的钱伟长解及其渐近特性,应用数学和力学,3,(1982),513.

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##### 出版历程
• 收稿日期:  1985-09-11
• 刊出日期:  1986-04-15

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