The buckling of plates tapered in thickness

Abstract

Although tapered plates are used frequently in aircraft structures, their buckling behaviour appears to have received little attention. In this report an analysis is given of the buckling of rectangular plates tapered in thickness under uniform load in the direction of taper. A linear thickness variation only is considered, but the method used is equally applicable to other thickness variations in which the flexural rigidity can be expressed as a polynomial in the distance along the plate. Results are given graphically for plates in which opposite pairs of edges are either clamped or simply-supported; transverse displacement of the sides is either free or completely prevented. The analysis is based on the assumption that the buckled shape normal to the direction of taper differs little from the buckled shape across a rectangular plate of constant thickness under end load, With the same boundary conditions along the edges parallel to the loading, but simply-supported at the ends. Assuming this transverse buckled form, a linear differential equation with variable coefficients is obtained for the deflected shape along the plate, using an energy method. A series solution is derived to this equation.