A three-dimensional zig-zag theory for analysis of thick laminated beams

A modified zig-zag technical theory suitable for accurate stress and failure analysis of thick laminated and sandwich beams is developed and tested. The postulated displacement field allows for appropriate jumps in the strains, in order to meet the transverse shear and the transverse normal stress and stress gradient continuity conditions at the laminae interfaces. The free-shear and normal pressure loading conditions are also met. Piecewise third- and fourth-order approximations are assumed in the thickness direction for in-plane and transverse displacements, respectively. The theory is cast in such a way to allow for sublaminates stacking, as this gives an opportunity of refinement for capturing interlaminar stresses. Developments are limited to beams with a rectangular cross-section, in cylindrical bending under transverse sinusoidal loading. Test cases wherein the exact three-dimensional elasticity and other approximate solutions are available are solved in closed-form to show accuracy of the present approach. Based on this numerical investigation, the present theory appears to predict with accuracy the stress field of thick laminated beams with general lay-up.