Dynamic large deflection analysis of plates using mixed finite elements

Abstract

A four-node isoparametric mixed quadrilateral element is developed for large deflection dynamic analysis of plates. Dynamic von Karman plate equations are modified to include the effect of transverse shear deformations as in Reissner plate theory. Finite element equations of motion are obtained via a mixed-Galerkin approach with three moment and three displacement components as dependent variables. Resulting nonlinear time dependent equations are solved by using Newmark's step-by-step direct integration algorithm in conjunction with Picard type successive iterations within each time step. With the effective treatment of nonlinear terms, an iterative scheme with a constant coefficient matrix is developed. The efficiency and the accuracy of the proposed algorithm are demonstrated with numerical results. The effect of thickness and the effect of applying Reissner type boundary conditions, on the dynamic response of simply supported plates are investigated. Guidelines are established for the selection of appropriate time steps to provide accuracy, convergence and stability.