Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature.