An analytical solution for interfacial stresses of tapered-scarf joints under harmonic loads

Adhesively bonded tapered-scarf joints are widely employed in the repair of primary load-bearing composite structures owing to their superior stress transfer capability. However, despite their extensive engineering applications, analytical solutions for predicting the dynamic interfacial stress response of tapered-scarf joints under harmonic loading remain unavailable, and current analyses rely primarily on computationally expensive finite element simulations. To address this gap, a novel analytical model is proposed to predict the dynamic responses of interfacial shear and peel stresses in adhesively bonded tapered-scarf joints subjected to harmonic axial loads. By incorporating the dynamic equilibrium of the adherends in the through-thickness direction, the governing differential equations for the adhesive interfacial stresses are derived. The proposed model is validated against finite element simulations under four representative loading conditions. Furthermore, a comprehensive parametric study is conducted to investigate the effects of excitation frequency, adhesive thickness, taper angle, and material stiffness on the dynamic interfacial stress response. The results demonstrate that the proposed analytical model accurately captures the dynamic distributions of both shear and peel stresses while significantly improving computational efficiency compared with finite element analysis. The parametric results further show that, over the investigated frequency range, the maximum adhesive shear stress increases with excitation frequency and taper angle but decreases with adhesive-layer thickness. Increasing the adherend stiffness reduces the stress magnitude, whereas increasing the adhesive stiffness increases it.