Formulation methodologies based on Taylor expansion power and Fourier expansion series for the macro-element resolution scheme of enriched models for the stress analysis of adhesively bonded joints

In recent years, interest in adhesive bonding has grown as it can be considered an efficient solution in terms of strength-to-mass ratio when applied to lightweight structures or an interesting solution to complement conventional technologies. The study of bonded adhered joints is carried out using a technique based on the macro-element method (ME), the ME shape functions are modeled using Taylor expansion power and Fourier expansion series. The purpose of this work is to compare the stiffness matrix obtained first from the entire Taylor series and then with the entire Fourier series. The method has been developed so far for 1D-bar and 1D-beam kinematics frameworks.