Simplified Finite Element Formulation of Unsymmetrical Adhesive Joints Based on Analytical Solutions

Abstract

A simplified finite element modelling approach is presented for the stiffness analysis of unsymmetrical structural adhesive joints, including a single-lap joint, an L-type joint and a T-type joint. The stiffness matrices for three simplified finite elements derive from the explicit analytical solution of the displacement theory developed. This theory takes the adherends of different materials and thicknesses in the adhesive joints into account, and is provided for any possible in-plane load acting on the adherends (tensile, shear and bending loads). The adhesive joint elements, which consider the adhesive layer's actual thickness and the continuous nature of load transfer between two adherends, are used to model the whole adhesive system of adherents and adhesive layer. The results obtained from the new approach were justified by comparing with Luo and Tong's analytical solution, four coarse finite element models and detailed two-dimensional linear elastic finite element results. It is indicated that the present approach can provide a good estimate of stiffness without increasing in total number of degrees of freedom of the model.