Gadolin problem of assembling a prestressed two-layer pipe

This paper presents a solution to the Gadolin problem of the evolution of stressed states during the shrink-fit assembly of two cylindrical pipes. The materials of the assembly parts are described using the mathematical model of an ideal elastic-viscoplastic material. The friction law is specified on the contact surface of the materials of the assembly. The yield criterion is taken to be the condition of maximum octahedral stresses (Mises condition) in which the yield stress depends significantly on local temperature. Calculations of time-varying thermal stresses are performed in successive time steps, depending on the temperature distribution reached by that time. The results of calculations of the residual stress and fit interference in the assembly are compared with the values obtained from a numerical-analytical solution of the one-dimensional problem. It is noted that the calculations neglecting the singularity in the boundary conditions predict the different behavior of the fit interference in the near-end region of the structure.