Improved Differential Quadrature Finite Element Method for Free Vibration of Mindlin Plates with Arbitrary Elastic Boundaries

Abstract

This paper proposes an improved differential quadrature finite element method (DQFEM) by combining the virtual boundary spring technique with the standard DQFEM, in order to deal with free vibration of Mindlin plates with arbitrary elastic constraints. The incorporation of the virtual boundary spring technique makes it easy to impose general elastic constraints including some classical boundary conditions and avoids the deficiencies of the classical elimination method, which is widely used to process boundary conditions. The improved DQFEM formulation for rectangular and curvilinear quadrilateral elements is established. Convergence characteristics of the present approach are discussed, and the minimum number of nodes to derive convergent results and the appropriate value of the boundary spring stiffness to simulate classical boundary are obtained. Numerical examples are carried out for Mindlin plates with various boundary conditions and thickness ratios, covering both rectangular and irregular geometries. By numerical comparisons, the high accuracy and the remarkable efficiency of the present method are demonstrated. Additionally, adopting the virtual spring boundary can improve the efficiency to some extent compared with the standard DQFEM.