Free-Edge Effects in Anisotropic Laminates Under Extension, Bending and Twisting, Part I: A Stress-Function-Based Variational Approach

A variational method involving Lekhnitskii’s stress functions is used to determine the interlaminar stresses in a multilayered strip of laminate subjected to arbitrary combinations of axial extension, bending, and twisting loads. The stress functions in each layer are approximated by polynomial functions of the thickness coordinate. The equilibrium equations, the traction-free boundary conditions, and the continuity conditions of the interlaminar stresses are exactly satisfied in the present analysis, while the compatibility equations and the continuity of the displacements across the interfaces are enforced in an averaged sense by applying the principle of complementary virtual work. This yields an eigenvalue problem for the interfacial values of the stress functions and their normal derivatives. Interlaminar stresses for all three distinct loading cases may be obtained, in a single solution process, by combining the eigenfunctions with appropriate particular solutions (peculiar to each loading case) so as to ensure satisfaction of the traction-free boundary condition at the free edge.