Exact solution for buckling of FCFC stepped rectangular plates

Abstract

This paper investigates the buckling problem of rectangular plates with stepped thickness. In the present work two opposite and parallel edges are clamped, while two others are free. The supposed deflection function satisfies the clamped boundary conditions along the related edges. A rectangular plate with a single step, with only two subplates, is considered. Our theory is also applicable to multistepped plates. Furthermore, the assumed function of deflection must also satisfy the governing differential equation. Having satisfied that condition, an ordinary nonlinear differential equation is obtained. In order to get an ordinary differential equation, as it was in the Levy theory, we had to apply the Galerkin-Bubnov theorem of identity. After getting the linear differential equation, eight boundary conditions needed to be specified. Only two of them were constant (Levy case), but six boundary conditions were functions of x. The Galerkin-Bubnov theorem had to be applied to these boundary conditions in order to obtain the corresponding system of algebraic equations, thus solving for the critical force Nx. The proposed procedure could be considered as an extension of the Levy buckling theory. © 2010 Elsevier Inc.