An improved plate theory of {1,2}-order for thick composite laminates

Abstract

A new two-dimensional laminate plate theory is developed for the linear elastostatic analysis of thick composite plates. The theory employs equivalent single-layer assumptions for the displacements, transverse shear strains, and transverse normal stress. The inplane and transverse displacements are respectively linear and quadratic expansions through the laminate thickness, where the low-order expansion coefficients correspond to the variables of Reissner's first-order shear-deformable theory. The transverse shear strains and transverse normal stress are assumed to be quadratic and cubic respectively through the thickness ; they are expressed in terms of the kinematic variables of the theory by means of a least-squares compatibility requirement for the transverse strains and explicit enforcement of exact traction boundary conditions on the top and bottom plate surfaces. Application of the virtual work principle results in the loth-order equations of equilibrium and associated Poisson boundary conditions. A major advantage of this theory over other higher-order theories lies in its perfect suitability for finite element approximation : simple C0 continuous interpolations for the kinematic variables of the first-order theory (and, optionally, C−1 interpolations for the two higher-order displacements) are needed to formulate effective and robust two-dimensional plate elements capable of full three-dimensional ply-by-ply strain and stress recovery within the framework of general-purpose finite element codes. In assessing the predictive capability of the theory, analytic solutions for the problem of cylindrical bending are derived and compared with exact three-dimensional elasticity results and those of the earlier version of the {1,2}-order plate theory.