Fully-Coupled Closed-Form Solution for Stresses in Adhesively Bonded Joints in Slender Reinforced Structures Subjected to Bending and Buckling

Abstract

An improved method is presented for the analysis of the stresses in adhesively bonded joints in slender reinforced structures subjected to bending and buckling. The method is based on a precise description of the kinematic equations in a reinforced beam cross-section under the assumption of isotropy and linear elasticity for both the adherends and adhesive. Second-order effects due to the member slenderness, as well as transverse deformation in the adhesive layer due to differential curvature between the two adherends, are taken into account. Governing equations for the shear and peel stresses in the adhesive layer are established in the form of two coupled differential equations. Here we take this interaction into account and propose a general solution for these two equations, which yields two fully-coupled closed-form equations for the stresses in the adhesive. These general equations can be adapted to any geometry and loading with appropriate boundary conditions. Exemplary calculations are worked out for a slender reinforced beam subjected to two different loadings. The theoretical results are found to be in good agreement with reference values obtained by means of a Finite Element Method analysis, especially at the adhesive edges where the stresses reach their critical values. It is concluded that the closed-form solution presented in this paper is suitable for a precise prediction of the adhesive stresses in bonded structural members subjected to bending and buckling.