Hybrid (Bolted/Bonded) Joints Applied to Aeronautic Parts: Analytical One-Dimensional Models of a Single-Lap Joint

Abstract

Abstract:The load transfer in hybrid (bolted/bonded)

A comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints

“…A JE is a 4-nodes brick element allowing for the modelling of two bonded adherends [15][16][17]. Over a similar period of time, the first and third authors of the present papers and co-workers have been working on the development of the macro-element (ME) technique for the simplified stress analysis of bonded, bolted and hybrid (bonded/bolted) joints made of dissimilar and possibly laminated beams [18][19][20][21][22][23][24]. The JE and ME are based on the same modelling approach.…”

“…The ME technique can be regarded as a mathematical procedure allowing for the resolution of the system of ODEs, under a less restricted application field of simplifying hypotheses, in terms of geometry, material behaviours, kinematics, boundary conditions and loads. Dedicated 4-nodes bonded-bars (BBa) and bonded-beams (BBe) have been formulated [18][19][20][21][22][23][24]. Once the stiffness matrix of the complete structure is assembled from the elementary stiffness matrices and the boundary conditions are applied, the minimization of the potential energy provides the solution, in terms of adhesive stress distributions along the overlap, internal forces and displacements in the adherends at any abscissa along the joint.…”

“…In the case of the 1D-bar kinematics, the closed-form expressions for the components of K BBa can be determined analytically [18][19][20], such as:…”

On the Potential Static Strength of Hybrid (Bolted/Bonded) Lap Joints with Functionally Graded Adhesives

“…Even if the ME elementary stiffness matrix has already been described in details in [7,22,[27][28], the main steps are provided for the comfort of the reader. The length of the ME is quoted .…”

Analytical Two-Dimensional Model of a Hybrid (Bolted/Bonded) Single-Lap Joint

“…The presented approach in this paper can be applied in the one-dimensional case and provide the same results as the method based on the direct integration of the local equilibrium equations. 19 Moreover the use of the FEM is flexible since different boundaries conditions can be applied easily. That's why the FEM approach is chosen for this twodimensional derivation.…”