A C0 zig-zag model for the analysis of angle-ply composite thick plates

Abstract

From a theoretical and practical viewpoint, the zig-zag theory is well adopted in the analysis of laminated composite structures. Nevertheless, for the available zig-zag models, artificial constraints in which the first derivatives of transverse displacement are replaced by the assumed variables have to be employed to avoid C1 interpolation functions in the finite element implementation. Such artificial constraints violate continuity conditions of interlaminar transverse stresses at interfaces. To avoid using artificial constraints, a C0-type zig-zag model is proposed in this paper. C0 interpolation functions are only required in the finite element formulation as first derivatives of transverse displacement have all been eliminated from the displacement field based on stress compatibility conditions between plies and on the top and bottom surfaces of the plate. Moreover, the number of variables involved in the proposed zig-zag model is less than that of the existing zig-zag models, yet accurate results are produced comparable to analytical solutions and three-dimensional finite element results. Effects of ply orientations, boundary conditions and length-to-thickness ratio on displacements and stresses of laminated composite plates have been studied.