Finite element analysis of thick homogeneous plates

Two alternative four noded, C-1 continuous, 52 degrees of freedom rectangul ar 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 t he thickness of the plate. A non-parabolic variation of the transverse shea r 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 bo th elements, quintic and quartic variation in the thickness co-ordinate of the plate for inplane and out-of-plane displacements are, respectively, ass umed. Numerical results are obtained using these elements for a simply supp orted plate under sinusoidal load for various ratios of width to length of the plate. The exact elasticity solution (Pagano) and other higher order th eory solutions are used to evaluate the performance of these two elements. The interesting features of these two elements are: (1) the transverse norm al stress across the thickness of the plate is estimated accurately using c onstitutive law unlike other displacement based two dimensional finite elem ents in which equilibrium equations are used to compute the transverse norm al stress; and (2) a single element is used across the thickness of the pla te to accurately predict all stresses. (C) 1999 Elsevier Science Ltd. All r ights reserved.