A state space finite element for laminated composites with free edges and subjected to transverse and in-plane loads

On the basis of the theory of three-dimensional elasticity, this paper presents a state space finite element solution for the stresses in cross-ply laminates subjected to combined transverse and in-plane loads. The state space formulation is introduced to solve for through-thickness stress distributions, while the traditional finite elements are used to approximate in-plane variations of the state variables. One of the direct applications of this solution is for the analysis of free-edge effect in cross-ply laminates. By appropriately describing the applied in-plane boundary tractions or boundary displacements, plates having complete free edges or boundary cross-sections with localized stress-free surfaces can be analyzed. Compared with the traditional finite element method, the new solution provides not only continuous through-thickness distributions of both displacements and transverse stresses, but also excellent approximations to the stress singularities in the vicinity of free edges or the above-mentioned localized stress-free surfaces.