General formulation of macro-elements for the simulation of multi-layered bonded structures

Sébastien Schwartz (1, 2) , Eric Paroissien (2) , Frederic Lachaud (2)

1 Sogeti (FRANCE)
2 ICA - Institut Clément Ader

Adhesively bonded joints are often addressed through Finite Element (FE). However, analyses based on FE models are computationally expensive, especially when the number of adherends increases. Simplified approaches are suitable for intensive parametric studies. Firstly, a resolution approach for a 1D-beam simplified model of bonded joint stress analysis under linear elastic material is presented. This approach, named the macro-element (ME) technique, is presented and solved through two different methodologies. Secondly, a new methodology for the formulation of ME stiffness matrices is presented. This methodology offers the ability to easily take into account for the modification of simplifying hypotheses while providing the shape of solutions, which reduced then the computational time. It is illustrated with the 1D-beam ME resolution and compared with the previous ones. Perfect agreement is shown. Thirdly, a 1D-beam multi-layered ME formulation involving various local equilibrium equations and constitutive equations is described. It is able to address the stress analysis of multi-layered structures. It is illustrated on a double lap joint (DLJ) with the presented method.

Mots clés: Macro-element -Multi-layered; Ordinary differential equation procedure; Analytical models- Stress analysis; Aeronautical

Domaines: Mécanique des structures [physics.class-ph]

Sébastien Schwartz, Eric Paroissien, Frederic Lachaud. General formulation of macro-elements for the simulation of multi-layered bonded structures. The Journal of Adhesion, 2020, 96 (6), pp.602-632. ⟨10.1080/00218464.2019.1622420⟩. ⟨hal-02882394⟩