Stress state of adhesive joint of two coaxial cylindrical shells. General analytical model

This study presents a general analytical solution for the stress state in a lap adhesive joint between two concentric tubes subjected to arbitrary, not necessarily axisymmetric, boundary conditions. The joined tubes are modelled as orthotropic cylindrical shells, and the proposed mathematical formulation encompasses many previously known results as particular cases. The problem is reduced to a system of six partial differential equations governing the axial, circumferential, and radial displacements of the inner and outer shells. By expanding the displacements into a trigonometric Fourier series in the circumferential coordinate, the problem is further transformed into a set of ordinary differential equations. As a specific case, an analytical solution is obtained for the first time for the stress state in a cylindrical joint under bending. A model problem is solved, and the resulting stress distributions are validated against finite element analysis, demonstrating the high accuracy of the proposed model.