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.

Application of the Modified Method of Multiple Scales to Solving the Problem of a Thin Clamped Circular Plate a Very Large Deflection

In this paper, asymptotic b.;haviour of the solution lo fhs problem of a thin clamped circular plate under uniform normal pressure at very largo deflection is restudied by means of the modified method of multiple scales given in[l-2].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 seems to be relatively simpler than the method used in [3]. It is also shown that the restriction of the method of paper [l-2] pointed out in paper[ 4 ] is not essential, and several computation errors in [ 3 ] are corrected as well.