A methodology for the computation of the macro-element stiffness matrix for the stress analysis of a lap joint with functionally graded adhesive properties

The interest of functionally graded adhesives (FGA) is growing as it is a mean to increase a bonded joint strength without any modification of the initial design of the adherends. The behaviour of bonded joints with variable adhesive properties along the overlap can be predicted with a potentially time-costly Finite Element (FE) analysis. Dedicated numerical procedures and design tools for FGA bonded joints would increase. The objective of this paper is to offer a mesh-free method for the analysis of functionally graded joints. The technique is based on the macro-element (ME) method and Taylor expansion in power series (TEPS) are used to approach the shape functions of the ME. The method has been developed so far for 1D-bar and 1D-beam kinematics frameworks. This mesh-free_method and a Finite-Element analysis give similar results.