圆板非线性理论的一种摄动解
A Perturbation Solution in the Nonlinear Theory of Circular Plates
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摘要: 用摄动法分析了几种非线性圆板问题,其所选用的摄动参数,不是某一预先给定的力学量,而是从某些方程中求解得出.这个方法是钱伟长以中心挠度为参数的摄动法的延伸.Abstract: In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien's perturbation method, which uses the central deflection as the perturbation parameter.
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[1] Chien,W.Z.,Large deflection of a circular clamped plate under uniform pres-sure,Chinese Journal of Physics,7,2,(1947),102-113. [2] Schmidt,R.,Finite deflections of a loosely clamped circular plate loaded at its center,Industrial Mathematics,23.part 1,(1973),45-51. [3] Schmidt.R.,Moderately large deflection of a loosely clamped circular plate under a uniformly distributed load,Industrial Mathematics,25,part I.(1975),17-28. [4] 钱伟长、林鸿荪、胡海昌、叶开沅,《弹性圆薄板大挠度问题》,中国科学院出版,(1954年) [5] 钱伟长、叶开沅,圆薄板大挠度问题,物理学报,第10卷第3期,(1954年9月) [6] Timoshenko.S.and Woinowsky-Krieger,S.,Theory of Plates and Shells.(1959). [7] Schmidt.R.,Several perturbation solutions in the nonlinear theory of circular plates and membranes.Industrial Matheamtics,25,part 2.(1975). [8] 叶开沅、刘人怀、张传智、徐一帆,弹性圆底扁球壳在边缘均布力矩作用下的非线性稳定问题,应用数学和力学,第1卷第1期,(1980年). [9] 钱伟长,《奇异摄动理论》<即将出版> -
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