Adhesive stresses in axially-loaded tubular bonded joints—Part II: Development of an explicit closed-form solution for the Lubkin and Reissner model

Abstract

The literature presents several analytical models and solutions for single-and double-lap bonded joints, whilst the joint between circular tubes is less common. For this geometry the pioneering model is that of Lubkin and Reissner (Trans. ASME 78, 1956), in which the tubes are treated as cylindrical thin shells subjected to membrane and bending loading, whilst the adhesive transmits shear and peel stresses which are a function of the axial coordinate only. Such assumptions are consistent with those usually adopted for the flat joints. A former investigation has shown that the L-R model agrees with FE results for many geometries and gives far better results than other models appeared later in the literature. The aim of the present work is to obtain and present an explicit closed-form solution, not reported by Lubkin and Reissner, which is achieved by solving the governing equations by means of the Laplace transform. The correctness of the findings, assessed by the comparison with the tabular results of Lubkin and Reissner, and the features of this solution are commented.

Adhesive stresses in axially-loaded tubular bonded joints – Part I: Critical review and finite element assessment of published models

“…Regarding the latter, it must be pointed out that in the case of joint 2 − for which 2c/t = 2, R = 0.1 and β = 4 according to Lubkin and Reissner − it has been noticed that the values published in [1] correspond in reality to β = 5. This finding has been made possible because the Lubkin and Reissner approach has been reconsidered and solved analytically with an alternative method, presented in detail in the part II of the present work [15].…”

“…By pointing out the limitations of the literature models, the disclosed results provide a useful reference for first-approximation designs and to establish a correct starting point for further, more refined, theories. These arguments point out the need for an explicit, closed-form solution, which is presented in the second part of this work [15].…”

Theoretical analysis and numerical simulation of axial tensile behavior of pipe joints based on bi-linear cohesive bond-slip model

“…The existing stress theoretical analysis mostly focuses on the bonding interface behavior in the elastic zone, and rarely involves the softening zone and debonding zone. Lubkin and Reissner (1956) studied the adhesive shear stress and normal stress by using the classical thin shell theory and later obtained the explicit closed-form solution by Laplace transform (Dragoni and Goglio, 2013; Goglio and Paolino, 2014). Shi and Cheng (1993) derived closed-form solutions by using the principle of minimal complementary energy.…”

Investigation of Functionally Graded Adherents on Failure of Socket Joint of FRP Composite Tubes

“…Using finite element findings on a variety of joint arrangements as mathematical milestones and expanding the investigations given in the literary works were also explored. Goglio and Paolino [ 10 ] re-examined Lubkin and Reissner’s [ 2 ] classic model for the tube junction under axial stress and developed a Laplace transform-based solution technique. Esmaeel and Taheri [ 11 ] investigated the impacts of erosion on the structural behavior of glued tube joints made of composite and aluminum adhesive layer, including the effects of two geometrical and loading parameters on the peel and shear stress variations in the epoxy matrix.…”