Gadolin’s Theory in Elastoplastic Formulation

The Gadolin’s theory, or the problem of two shrink-fitted cylinders, is usually considered in the statement when the stresses stay within the applicability area of the elastic model. The generalization of this theory to the case when plastic strains appear in the inner cylinder is presented. The solution of the Lamé problem in the elastoplastic formulation is given as the first stage of solving the general problem. The resolving equations for estimating the plastic zone radius and the contact pressure at a specified tightness are derived. Some examples of the application of the results for the calculation of a stress-strain state of disk specimens with an initial level of stresses close to the ultimate yield point are considered. The normal displacements of the surface of elastoplastic rings are found.