Simplified Modeling of Adhesively Bonded Flat and Slended Structures

Assemblies remain an essential part of structural design. Their main function is to enable the existence of a structure, itself made up of structural elements. There are many different assembly technologies, such as mechanical fastening, welding or bonding. In service, a structure is generally subjected to a set of external loads, which it must resist in order to perform its functions. These loads are distributed to the structural elements in the form of forces, the nature of which depends on the initial design choices. The structural elements are then dimensioned to resist these loads. For example, a wing-like structure has a geometric shape that enables it to generate lift from the reaction to aerodynamic pressure on its surface. This aerodynamic load generates shear forces, bending moments and torsional moments in the structure. The spar is the structural element capable of absorbing the bending moment, which it transmits to the fuselage, enabling the aircraft to fly. The connections then ensure that the structural elements are balanced under the resulting forces. The connecting elements, such as the adhesive layer, are subject to the reactions of the resulting forces. As a result, the connecting elements deform, generating stresses that counteract these deformations. These stresses then balance the resulting forces. The deformation of the connecting elements thus ensures the balance of the structural elements or, in other words, the transfer of forces.

This article deals with the connection of two slender flat structures (single shear) by bonding under quasi-static loading. This type of structure can be used, for example, by the transportation (automotive, rail, naval, aerospace) or civil construction industries. Slender planar structures offer the possibility of making sufficiently simplifying assumptions to lead to the writing of ready-to-use predictive analytical equations, while still being relevant to physical reality. However, the scope of application of these formulas can sometimes be restrictive. This may require the use of semi-analytical solution methods, which are numerical solution methods applied to a set of sufficiently simplifying assumptions. On the basis of existing theories in the literature, often developed for aeronautical applications but also in civil construction or electronics, the aim of this article is to explain the modeling and solving approaches and their associated limitations. In addition, an application to a more complex configuration, hybrid assemblies (bolted/glued), is presented to illustrate the interest of a particular semi-analytical approach: macro-element modeling (ME). Finally, the paper concludes with a discussion of the use of these calculations in the design of slender, planar structures.