Shear Buckling of Thin Plates with Constant In-Plane Stresses

Abstract

This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant uni-axial in-plane loading, and in-plane shear loading that is increased until the critical load is obtained and the plate losses its stability. The solutions are obtained using the multi term extended Kantorovich method. The solution is sought as the sum of multiplications of two one dimensional functions. In this method a solution is assumed in one direction of the plate, and this enables to transform the partial differential equations of the plate equilibrium into a system of ordinary differential equations. These equations are solved exactly by the exact element method [1], and an approximate buckling load is obtained. In the second step, the derived solution is now taken as the assumed solution in one direction, and the process is repeated to find an improved buckling load. This process converges with a small number of solution cycles. For shear buckling this process can only be used if two or more terms are taken in the expansion of the solution. As an example the shear buckling load of a simply supported square plate with different levels of constant compressive load, as shown in Figure 1, is given. In Figure 2 the variation of the normalized shear buckling load as a function of the compression level is shown. Many more new results will be given.