Buckling analysis of thin rectangular plates under uniaxial or biaxial compressive point loads by the differential quadrature method

Abstract

To obtain accurate buckling load for rectangular plates under compressive point loads, one of the important factor is that the in-plane stress distributions within the plate prior to buckling should be accurate enough. Although the differential quadrature method (DQM) has been successfully used in a variety of fields including the buckling analysis of thin rectangular plates under non-uniformly distributed edge compressions, however, the DQM has some difficulty in dealing with singular functions such as the Dirac-delta function appeared in the stress boundary condition. In this paper, novel formulations are presented to overcome the difficulty encountered in dealing with the Dirac-delta functions by using the DQM. The normal stress boundary condition is numerically integrated before being discretized in terms of the differential quadrature. Detailed formulations are given. Buckling of rectangular plates under either uniaxial or biaxial compressive point loads is successfully analyzed. It is demonstrated that accurate buckling loads can be obtained by the DQM for rectangular plates with nine combinations of boundary conditions and various aspect ratios. The compactness and computational efficiency of the DQM are retained in solving the partial differential equations with boundary conditions involving Dirac-delta functions. The accuracy of the differential quadrature (DQ) results is verified by comparing them with existing analytical solutions and finite element data. New results are tabulated which can be a reference for other researchers to develop new numerical methods.