A predictor-corrector zig-zag model for the bending of laminated composite plates

Abstract

A predictor-corrector approach based on the zig-zag model is proposed for the bending of thick laminated composite plates. The main purpose of the approach is to reduce the differences between the assumed variation of the transverse shear stresses provided by the constitutive equations and the computed variation of the same stresses from the equilibrium equations of elasticity. In the predictor phase, a linear or cubic zig-zag model is adopted and the layerwise polynomial approximation of the transverse shear stresses through the thickness is determined from the equilibrium equations of elasticity. This approximation is then used in a general higher-order zig-zag model in the corrector phase in order to improve the predictions for the displacements and stresses. The present predictor-corrector zig-zag model satisfies the continuity of the in-plane displacements and the transverse shear stresses at the interfaces while maintaining the same number of variables as in Mindlin's theory. The numerical results for the bidirectional bending of both symmetric and antisymmetric thick laminates are in excellent agreement with the exact elasticity results of Pagano. They also show a marked improvement over the results from the linear zig-zag model of Di Sciuva and the cubic zig-zag model of Lee et al., especially at the interfaces.