A new and efficient zigzag theory for laminated composite plates

This paper develops a new and efficient zigzag theory named as C-311 for laminated composite plates. The new local zigzag displacement model of C-311 nonlinearly distributes through the thickness coordinate and satisfies the piece-wise continuity at the layer surface, and combines three-order displacement model to form the initial displacement field of the present theory. By enforcing the inter-laminar transverse stress continuity and the free surface conditions, the local displacement unknown variables can be eliminated, and the final displacement field of C-311 is expressed by a fixed number of unknown variables. In addition, the equilibrium equations and boundary conditions of the present theory can be obtained from the virtual work principle. To test the prediction accuracy of C-311, a simple-supported cross-ply square plate is investigated under mechanical loading. Numerical results show that compared to several classical laminated plates theories, the present theory can predict accurately mechanical behaviors of thick multilayered composite plates and heterogeneous laminated plates. Especially the C-311 can give an acceptable accuracy of the transverse shear stress derived from the constitutive equations directly, and that is benefit for practical engineering applications in the finite element method.