Applications of Zig-Zag Theories to Sandwich Beams

Abstract

A sublaminate model for analysis of laminated and sandwich beams is developed that incorporates a general zig-zag approximation within each sublaminate. The displacements are postulated so that the transverse shear and the transverse normal stress and stress gradient continuity conditions are met in the sublaminate. Four variations, respectively with linear or cubic approximation, with and without zig-zag representation, are confronted. The aim is to assess the practical advantages of higher-order approximations of displacements within sublaminates. The numerical applications concern laminated and sandwich beams loaded by a sinusoidally distributed transverse load and a laminated beam thermally loaded. Also, cases with reduced elastic moduli of faces and core, simulating damage or failure, are investigated to assess accuracy when the layers exhibit distinctly different material properties. Comparisons are made with the 3-D elasticity solution and with various models in literature. The present model provides practical advantages when the material properties change abruptly across the thickness and the laminates are thick. A single sublaminate is required for modeling the faces of sandwich beams and solid laminates, contrary to the models with zig-zag terms neglected. This corroborates the capability of zig-zag representation within sublaminates to improve accuracy.