Modified Differential Quadrature Method Using Basis Functions Satisfying Multiple Boundary Conditions for Buckling Analyses of Beams and Rectangular Plates

Abstract

The paper presents a modified differential quadrature method (DQM) to solve buckling problems of beams and rectangular plates. The proposed method addresses the problem of applying multiple boundary conditions at each boundary point by developing a novel approach that constructs basis functions satisfying multiple boundary conditions. The weighting coefficient matrices of high-order derivatives in the DQM can then be calculated directly from the basis function, and additional equations about boundary conditions can be avoided. The method is first applied to derive the basis functions of beams with various boundary conditions and to solve beam buckling problems. Then, the method is extended to the buckling of rectangular plates, where the plate deflection is assumed as the sum of multiplications of two basis functions for beams with the corresponding boundary conditions. To verify the accuracy of the proposed method, several examples are presented, and very good agreement is observed between the results obtained by the proposed method and those reported in the literature as well as those obtained by the finite element method.