Rozszerzanie się Dwóch Lepko-sprężystych Walców Nałożonych na Siebie

In the paper an infinite cylinder is considered having an internal radius R0 and external R1, on which there was superposed freely by means of force a second cylinder (subsequently called the shell) having an internal radius R1, and external radius R2. The cylinder is subjected to an internal pressure p0. The external surface of the cylinder and the internal surface of the shell are constantly in exact contact with each other and mutually interact with pressure p1, equal in magnitude but oppositely directed. The external load of the shell is p2. The cylinder and the shell are made of different materials. For the so-formulated problem the expressions are given in the paper for the Laplace transforms of the components of the tensors of stress and deformation, assuming that the quantities p0, p1 and p2 are functions of the time and that the cylinder and shell are made of materials corresponding to the Zener model.

At first the solution was obtained for the elastic system. Next, utilizing the elasto-viscoelastic analogy formulated by Biot, the problem has been solved for the case when the cylinder and the shell possess rheological properties. Also included in the paper is a generalization of the problem of a «cylinder reinforced with an elastic shell» to the case when the cylinder constitutes a Zener body. Since a Zener body is rheologically complex, from the obtained formulae there follow solutions if the cylinder and shell are rheologically more simple media. The results derived here contain in them as particular cases already existing results [5, 6, 8, 12 and 13].