Free-edge stress evaluation of general laminated composites using a novel multifield variational beam formulation

Abstract

Free-edge interlaminar stresses in general laminated composites are evaluated using a multifield (stress and displacement) finite element (FE) beam sectional formulation based on the Hellinger-Reissner principle considering three-dimensional (3D) material constitutive model. Both 3D stress and warping displacement fields are modeled as the primary variables while the interlaminar stress continuity and free-edge traction-free conditions of the laminates are ensured without introducing any peculiar assumptions. Nodal stresses are therefore computed directly at each constituent lamina using a domainwise approach while preserving the desired continuity (or discontinuity) at the interfaces through a global equilibrium constraint. The predicted free-edge stresses are validated for laminated composites with various layups subjected to extension and bending loads. Good correlation is shown against other state-of-the-art analytical methods and detailed 3D FE analysis. The proposed approach leads to a quick convergence of interlaminar stresses using fewer FEs with the benefit of assured continuity at the lamina interfaces. The boundary layer regions due to the free-edge are also identified for angle-ply and cross-ply laminates under different mechanical loading cases. The free-edge interlaminar stresses vanish slowly for the cross-ply layups, indicating dominant effect over a maximum of 60% of the laminate width, than the angle-ply ones.