Stress analysis of long multilayered plates subjected to invariant loading: Analytical solutions by a layerwise stress model

This paper deals with the analysis of long multilayered plates subjected to invariant loading along the longitudinal direction. By assuming that the strain field is independent of the longitudinal coordinate, the general form of the displacement field is obtained for a rectangular plate. It is shown that there are only four types of loading which can be applied at the longitudinal ends of the plate: traction, out-of-plane bending, torsion and in-plane bending. In addition to these loads, the plate can be subjected to any loading on its top/bottom surfaces and any force/displacement boundary conditions at its lateral edges provided that these loads and boundary conditions are invariant along the longitudinal direction. Based on the obtained displacement field, a layerwise stress model, called the LS1 model, is used to solve the problem. The analytical LS1 solutions are obtained for general long multilayered plates with arbitrary lateral boundary conditions subjected to all types of invariant loads. Various numerical examples, related to different load conditions, are investigated and the LS1 results are compared to those obtained by a three-dimensional finite element (3D-FE) analysis. Excellent agreements in terms of overall stiffness matrix and free-edge interlaminar stresses are found between the LS1 and 3D-FE models.