An equivalent single layer shear deformation plate theory with superposed shape functions for laminated composite plates

Abstract

A single layer shear deformation plate theory with superposed shape functions for laminated composite plates has been proposed. Some of the previously developed, five degrees of freedom shear deformation theories, including parabolic [1], hyperbolic [2], exponential [3] and trigonometric [4] plate theories have been superposed by applying different theories in the different in- plane directions of the composite plate. Statics and dynamics of composite plate problems have been investigated. It was obtained that using different shape functions in the different in-plane directions may decrease the percentage error of stress and deflection. Present hyperbolic-exponential and parabolic-exponential theories predict stiffer properties (give lower bending and stress values, and higher frequency, and buckling loads when compared to the 3-D elasticity). Some improvements were determined for y-z component of the transverse shear stress using hyperbolic-exponential and parabolic-exponential theories for symmetric cross-ply composite plates when compared to available single shape function plate models. Global behaviours (vibration frequency and critical buckling loads) are predicted within %5 accuracy similar to plate theories with single shape functions.