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

Abstract

Many current materials and structural systems are layered. The structural performances of these multilayered systems are dependent on interfaces, the presence of which is inherent to them. A methodology for the simplified stress analysis of such structures under 1D-bar kinematics is presented. The macro-element technique is used to solve the set of ordinary differential equations involved. A dedicated macro-element is formulated through the approximation of displacements fields by Taylor expansion power series. The predictions of the simplified stress analysis are in close agreements with those obtained by FE analyses. Finally, the influence of adhesive thickness and of the overlap length on the adhesive stress peaks is presented.

Modelling load transfer in single-lap adhesively bonded and hybrid (bolted / bonded) joints

“…Applied to pure bonded joints, ME modelling is a semi-analytical method extending the scope of models belonging to the first family. It offers the advantage of providing a solution for geometrical, material and loading configurations for which there are no closed-form solutions [81][82][83][84][85][86][87][88][89][90][91][92][93]. As demonstrated in sections 4 and 5, ME modelling is an attractive approach to support the variation and associated growing complexity of simplifying hypotheses at low computational cost.…”

“…Finally, in the context of the shear-lag approach, the use of ME modelling does not seem relevant in the case on an elastic linear analysis due to the existence of closed-form and ready-to-use equations. Nevertheless, it can be of use in the analysis of more complex configurations such as nonlinear material behaviours, geometrical and/or mechanical properties graduation, multiple-lap joints or HBB joints [74,76,80,82,83,90,91].…”

“…To approximate the tested configuration, the 1D-beam ME is based on the Luo and Tong local equilibrium, in which the adhesive thickness is taken into account in the bending moment equation following Hart-Smith. Finally, in 2020, a formulation methodology based on TEPS was presented [90,91]. The unknown adherend displacements are expanded in power series.…”

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

“…The first one makes use of the Jordan form to solve the system of coupled ODEs, the unknown of which is the vector of displacements and their derivatives 26 . The second one is based on the use of Taylor expansion power series (TEPS), 27‐29 which has been applied on the graduation of adhesive properties and on the formulation of ME mass matrices. Following the previous path consisting in enriching the ME modeling, the objectives of this article are to present the formulation methodologies based a new methodology based on TEPS, (ii) on Fourier expansion series (FES) and (iii) to validate and compare their convergence performance.…”

“…First, the formulation methodology of ME stiffness matrix based on FES is described under membrane (Section 2) and under membrane plus bending (Section 3), but more rapidly as it follows exactly the same way but with additional complexity due to the higher number of variables. This methodology has already been presented in References 27 and 28 but in a different way. Furthermore, it is also given to introduce notations and to make easier the description of Fourier series methodology.…”