Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns

The main purpose of this study is to compare the methods of differential quadrature (DQ) and harmonic differential quadrature (HDQ). For this purpose, DQ and HDQ methods are presented for buckling, bending, and free vibration analysis of thin isotropic plates and columns. Plates of different shapes such as rectangular, circular, square, skew, trapezoidal, annular, and sectorial plate subjected to different boundary conditions are selected to demonstrate the accuracy of the method. Four different support conditions are taken into consideration for columns. Numerical results are presented to illustrate the method and demonstrate its efficiency. It is emphasized that the HDQ method gives more accurate results and needs less grid points than the DQ method.