双向压缩简支矩形板后屈曲平衡路径的迭代算法*

本文从von Kármán板大挠度方程出发,在双重三角级数解的基础上,提出一种简单、快速和有效求解双向压缩简支矩形板后屈曲平衡路径的迭代算法.     

修正多重尺度法在求解圆薄板具有很大挠度问题时的应用

本利用修正的多重尺度法＾［１～２］重新研究固支圆薄板在均匀压力作用下，挠度很大时解的渐近性态。结果表明与钱伟长教授用首创的合成展形法求解该问题＾［３］的结果相一致，但较后更简捷。本结果还表明［４］中所指出［１～２］方法的局限性是非本质的，并改正［３］中一些计算错误。     

An iteration algorithm for solving postbuckling equilibrium path of simply-supported rectangular plates under biaxial compression

In this paper,on the basis of von Kárman large deflection equations and itsdouble trigonometric series solution,we present a simple,fast and effective iterationalgorithm for solving simply-supported rectangular plate subjected to biaxial compression.     

关于一类带有慢变系数的二阶微分方程的渐近解

本文研究一类带有慢变系数的二阶常微分方程解的渐近展开式.指出已有工作的不足,利用改进的多重尺度法改进和拓广了文献[1～4]的结果.     

Application of the modified method of multiple scales to solving the problem of a thin clamped circular plate of a very large deflection

In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.     

修正多重尺度法在求解圆簿板具有很大挠度问题时的应用*

本文利用修正的多重尺度法[1～2]重新研究固支圆薄板在均匀压力作用下,挠度很大时解的渐近性态.结果表明与钱伟长教授用首创的合成展开法求解该问题[3]的结果相一致,但较后者更简捷.本文结果还表明文[4]中所指出文[1～2]方法的局限性是非本质的,并改正文[3]中一些计算错误.     

On the asymptotic solutions for a class of second order differential equations with slowly varying coefficients

In this paper we study the asymptotic expansions of the solutions for a class of secondorder ordinary differential equations with slowly varying coefficients.The defect of theknown works on these problems is noted,and the results in[1—4]are improved andextended by means of the modified method of multiple scales.