关于钱氏摄动法的高阶解的计算机求解和收敛性的研究
On Solving High-Order Solutions of Chien’s Perturbation Method to Study Convergence by Computer
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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.Abstract: In this paper,we have obtained the analytical formula of arbitrary n-th order perturbation solution which perturbation parameter is central deflection for circular thin plate under a concentrated load by means of its integral equation.All unkown constants of every perturbation solution can be determined by computer.Hence higher order perturbation solution is obtained.Based on the solution of higher order perturbation,asymptotical property and suitable interval of Chien's perturbation method are also discussed.
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[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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