Gadolin Problem of Assembling a Prestressed Two-Layer Pipe

This paper presents a solution to the Gadolin problem of the evolution of stressed states in 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 maximum octahedral stress criterion (von Mises criterion) in which the yield stress depends significantly on the local temperature. Time-varying thermal stresses are calculated in successive time steps, depending on the temperature distribution reached by that time. The calculated residual stress and fit interference in the assembly are compared with the values obtained from a numerical-analytical solution of the one-dimensional problem. Differences in the behavior of the fit interference in the near-end region of the structure due to the neglect of the singularity in the boundary conditions are noted.