On the method of orthogonality conditions for solving the problem of large deflection of circular plate

Abstract

In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zang for solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound load, with different boundary conditions), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1–4].