Effects of displacement parameters in zig–zag theories on displacements and stresses of laminated composites

The zig–zag theory is well adopted in the analysis of laminated structures as the continuity requirement of displacements and stresses between plies are satisfied. Using the surface conditions and the interlaminar continuity conditions, a large number of displacement parameters can be eliminated from the initial displacement field. However, in the elimination process, care has to be exercised as to which displacement parameters are to be retained. If the derivatives of lateral displacements, namely ∂w∂x and ∂w∂y, are retained in the final displacement field, a C1-type zig–zag model is obtained for the finite element analysis. On the other hand, if all the derivatives ∂w∂x and ∂w∂y are eliminated, we can have a C0-type finite element model, in which only C0 interpolation functions are required. Furthermore, the C1-type model is in general less accurate as displacement parameters ∂w∂x and ∂w∂y are not completely independent. In the analytical treatment of a composite beam, for the same initial displacement field and the same set of displacement and stress compatibility conditions, there are only four independent quantities subject to variation in the C1-type model whereas there are six independent variables subject to variation in the C0-type model. In line with the theoretical prediction, analytical series solutions developed in this paper indicate that C0 model is more accurate than the C1 model in the analysis of composite beams.