Generalized Differential Quadrature Method for Buckling Analysis

This paper presents a computationally efficient and highly accurate numerical method for analyzing the elastic buckling of columns and plates. The proposed generalized differential quadrature method (GDQM) proposes a simple numerical approach to determine the weighting coefficients for derivative approximations without any restriction on the choice of grid points. It will be shown here that the GDQM is very easy to use and implement numerically. During the solution procedure, different boundary conditions can be easily incorporated. Applications of the GDQM to the buckling analysis of columns and plates have shown that accurate critical buckling loads can be achieved using considerably fewer grid points; thus, less storage and computing time are required during computation. The numerical results obtained, wherever possible, are compared with those from existing literature in order to verify their accuracy.