Exact Solution of Nonlinear Circular Plate on Elastic Foundation

Abstract

A large deflection problem of a concentrated loaded circular plate on an elastic foundation is treated. By means of a step‐by‐step iterative method, first the exact solution's analytic forms and their convergence are obtained. Then a numerical procedure, which can be carried out by computer, is given to calculate the exact solution of the problem with an arbitrary boundary condition. Last, the numerical results of the exact solution of the problem with a rigidly clamped boundary condition and ν=0.3 are obtained in detail. The results of the exact solution are more reliable than those of other approximate solutions. They not only can be directly applied in engineering, but also can offer a way to study the problems of large deflection of plates and shells.