Finite element analysis of thick homogeneous plates

Abstract

Two alternative four noded, C 1 continuous, 52 degrees of freedom rectangular plate elements based on two higher order shear deformation theories are presented. These elements are developed for the flexural analysis of thick plates for which the through-thickness variation of displacement and stress may be of high order and in which a single element is to be used through the thickness of the plate. A non-parabolic variation of the transverse shear strain/stress across the thickness of the plate is assumed for the first element whereas it is assumed to be parabolic for the second element. In both elements, quintic and quartic variation in the thickness co-ordinate of the plate for inplane and out-of-plane displacements are, respectively, assumed. Numerical results are obtained using these elements for a simply supported plate under sinusoidal load for various ratios of width to length of the plate. The exact elasticity solution (Pagano) and other higher order theory solutions are used to evaluate the performance of these two elements. The interesting features of these two elements are: (1) the transverse normal stress across the thickness of the plate is estimated accurately using constitutive law unlike other displacement based two dimensional finite elements in which equilibrium equations are used to compute the transverse normal stress; and (2) a single element is used across the thickness of the plate to accurately predict all stresses.