Static analysis of Mindlin plates: The differential quadrature element method (DQEM)

Abstract

The differential quadrature method (DQM) is a new numerical method for fast solving linear and nonlinear differential equations based on global basis functions. In the present study, a discrete approximate method based on the DQM, the differential quadrature element method (DQEM), is developed for the axisymmetric static analysis of moderately thick circular and annular plates described by the Mindlin shear-deformable theory. The basic idea of the DQEM is: (1) to divide the whole variable domain into several sub-domains (elements); (2) to form discretized element governing equations by applying the DQM to each element; and (3) to assemble all the discretized element governing equations into the overall characteristic equations with the consideration of displacement and stress compatibility conditions between adjacent elements. The annular and circular Mindlin plate elements of differential quadrature (DQ) are established. The convergence characteristics of the proposed method are carefully investigated from the view points of element refinement and element-grid refinement, and some general regulations and suggestions on element division and element-grid selection are provided. A number of numerical examples are calculated, and the results are compared with the corresponding exact solutions, which exhibits high accuracy, simplicity and applicability of the present method.