关于钱氏摄动法的高阶解的计算机求解和收敛性的研究

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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.

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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