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

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.