Two-dimensional analytical solution of elastic stresses for balanced single-lap joints—Variational method

A two-dimensional (2D) analytical method that is capable of providing an explicit closed-form solution is presented for the prediction of elastic stresses in balanced single-lap adhesive-bonded joints, assuming only a longitudinal normal stress linear distribution in the joint thickness direction. By selecting the four appropriate in-plane loading stress functions, the theory can predict the 2D stress distribution at any point, and the tensile force, shearing and bending moment at any cross section accurately, in both the adhesive and adherends. The method is based on 2D elasticity theory in conjunction with the variational theorem of complementary energy. Minimizing the energy functional leads to four coupled, fourth-order ordinary differential equations with constant coefficients for the determination of the stresses. All boundary conditions, including shear stress-free surfaces, are satisfied. The analytical method was verified by comparing with our previous 2D solutions, and the 2D geometrically nonlinear finite element analysis. It is indicated that the present solution can provide a good prediction for the stress and in-plane loading distributions in the adhesive and adherends.