A Novel Double Beam Element with Continuously Distributed Elastic Springs for Modelling De-bonds in Adhesively Bonded Joints

Abstract

A defect proof joint is not guaranteed by even the most sophisticated manufacturing techniques. Hence, health monitoring of joints is of utmost significance. Use of guided waves for non-destructive testing of adhesively bonded lap joints is addressed in this work. A double beam element is developed to model the adhesively bonded region. A double beam element is constituted of two parallel Timoshenko beam-rod elements connected to each other by continuously distributed vertical elastic springs. Only a single spectral element is sufficient to model joints having varying levels of adhesion provided the adherands are crack free. Alongside, a superconvergent finite element is also formulated to model the bonded region. The superconvergent finite element developed in this work uses a combination of polynomial and exponential functions as shape functions, which results in exact stiffness matrix, and thus reduces the approximation errors significantly in comparison to conventional finite element formulation. The superconvergent double beam element is also free of shear locking as the order of interpolating function of transverse displacement is one order higher than that of the beam slope. Further, responses of single lap joint samples with varying levels of adhesion subjected to ultrasonic loading are obtained. Thus, the numerical models developed here can be used to conduct preliminary studies on adhesively bonded joints with a wide range of loading frequencies, and aid in selection of probing frequencies for conducting experiments.