Buckling of plates with variable thickness—an analog equation solution

Abstract

In this paper the analog equation method (AEM) is applied to buckling analysis of plates with variable thicknss. According to this method the displacement and its derivatives in the fourth order partial differential equation with variable coefficients are expressed in terms of a fictitious load which is established from the integral equation solution of an adjoint analog equation. The orginal eigenvalue problem for a differential equation of buckling is converted into a typical linear eigenvalue problem for the discrete values of the fictitious load, from which the buckling loads are established numerically. Numerical results are presented which illustrate the effectiveness of the proposed method.