Stability of shear deformable rectangular plates using refined finite element model

Abstract

Stability characteristics of moderately thick rectangular isotropic plates subjected to in-plane loads, such as uniaxial or biaxial compression, shear and biaxial compression-tension, are studied in this paper. For this purpose, a simple higher-order theory involving only four unknowns is employed. This theory allows parabolic variation of transverse shear strains and stresses through the thickness and satisfies the condition of vanishing of transverse shear stresses at the top and bottom surfaces of the plate. The components of the in-plane displacements are expressed as in classical plate theory. However, transverse displacement is assumed as a function of the square of the thickness coordinate. A four node rectangular C¹ continuous finite element having eight degrees of freedom per node is developed. The merits and disadvantages of the higher-order theory and corresponding finite element employed here are demonstrated through a number of numerical examples.