A global higher-order zig-zag model in terms of the HW variational theorem for multilayered composite beams

Accurate prediction of the transverse shear stresses for multilayered composite structures is still the challenging issue for the displacement-based and the mixed equivalent single-layer models. Therefore, an equivalent single-layer model which can predict accurately transverse shear stresses of multilayered composites without using any postprocessing approaches is expected. To this end, a global higher-order zig-zag model satisfying the transverse shear traction-free condition is developed for bending analysis of laminated composite beams. The number of unknown variables in the proposed model does not depend on the number of layers, and only four variables are involved in the displacement field. To obtain the accurate transverse shear stresses, the functional suitable for beams can be obtained by using the three-field Hu-Washizu (HW) variational principle. The equilibrium equations and analytical solution of the present model can be obtained based on the HW variational equation. By analyzing the bending behaviors of composite beams, the performance of the proposed model is verified. In addition, effects of transverse shear stress on the displacements and in-plane stress of composite beams have been detailedly investigated. Differing from previous equivalent single-layer models, the transverse shear stresses can be accurately calculated from the proposed model, and actively impact on displacements and in-plane stresses of multilayered composite beams.