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

Abstract

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.

A simplified modal analysis of a single lap bonded joint using the macro-element technique

“…This method had been successfully used by Hart-Smith, in 1974, to address the stress distribution in a scarf joint (Hart-Smith, 1982). The use of TEPS led to the development of a ME dedicated to the static analysis of a joint with functionally graded properties (FGA) (Ordonneau et al, 2019). A single FGA ME represents the behaviour of a whole FGA bonded overlap and the shape functions can be easily computed to get the displacements of the adherends along the overlap.…”

“…In the present paper, the mass matrix associated with a ME, in 1D-bar and 1D-beam kinematics is presented. Its development follows the work (Ordonneau et al, 2019) in which the stiffness matrix of a ME is developed thanks to Taylor expansion power series (TEPS).…”

“…With the stiffness matrix from (Ordonneau et al, 2019) and the mass matrix presented here, modal analyses are performed on homogeneous and functionally graded adhesive (FGA) joints. The results given by the ME model are computed with MATLAB and compared with a PATRAN NASTRAN FE model.…”

Simplified stress analysis of multilayered bonded structure under 1D-bar kinematics

“…Sekmen et al provide a simplified stress analysis of multilayered bonded structure based on the semi-analytical resolution scheme called macroelement (ME) technique [7] under 1D-bar and 1D-beam kinematics. The ME technique is successfully used for the simplified stress analysis of single-lap bonded joints under mechanical and thermal loadings, eventually involving graded materials and geometrical properties along the overlap as well as nonlinear adhesive material behavior, while demanding low computational time [8][9][10][11]. Moreover, it is applied to the simulation of the delamination of composite laminated materials under pure mode I for a double cantilever beam test [12].…”

“…However, even for a linear computation, the results depend on the mesh refinement under 1D-beam kinematics. Besides, a new approach involving the Taylor expansion power series (TEPS) is introduced by Ordonneau et al [11] to formulate the ME stiffness matrix of two adherends bonded with one adhesive layer. The use of TEPS as a tool in the resolution process has already been employed for simplified stress analysis joints with graded properties [13][14][15][16].…”