Stress State of Two Glued Coaxial Tubes Under Nonuniform Axial Load

The deflected mode problem for the structure composed of two glued coaxial cylindrical tubes under nonuniform longitudinal load is considered. The purpose of the paper is to obtain a mathematical model of a stress state that allows us to find an analytic solution to the problem. Pipes are considered as thick-walled rods, which are joined by a non-zero thickness adhesive layer. The tangent stresses in the glue are considered constant by the thickness of the adhesive layer. The tangent stresses in the adhesive layer are proportional to the difference of the longitudinal shifts of the tube sides, which are faced to the adhesive layer. The stresses in the pipes are considered to be constant in thickness, that is, in radial direction and dependent on the axial and circumferential coordinates. It is considered that the structural elements only move in the axial direction, i.e. the effects related to Poisson deformations are neglected. The deflected mode problem for the joint is reduced to a system of two partial differential equations relatively to longitudinal shifts of layers. The solution is obtaining using the classical variable separation method in the form of Fourier series by circumferential coordinate. The convergence of the solutions is proved. The model problem is solved, results are compared to calculations produced by the finite element method. The tangent stresses in the glue reach maximum values at the edges of the adhesive line. The mathematical model of the joint under certain constraints has a sufficient accuracy for engineering problems and can be used to solve structural design problems.