Differential quadrature method for Mindlin plates on Winkler foundations

This paper presents an approximate analysis of rectangular plates resting on Winkler foundations based on the Mindlin plate theory. The plates are subject to any combination of free, simply supported and clamped boundary conditions. Solutions to the problem are obtained using the differential quadrature method (DQM) by solving the governing differential equations. Numerical results are compared with existing literature to establish the validity and accuracy of the method. This study shows numerically the effects of shear deformation on the deflections and stress resultants at some selected locations. The distributions of the bending and twisting moments and shear force for several plates are presented graphically by varying the relative thickness ratio h/a to further show the significant effect of shear deformation.