Shear Buckling of Thin Plates With Constant In-plane Stresses

This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant in-plane stresses, 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 transformation of the partial differential equation of the plate equilibrium into a system of ordinary differential equations. These equations are solved exactly by the exact element method, 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. Many examples are given for shear buckling loads for various cases of tension and compression bi-directional loading.