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.
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).