States of stress in multilayer spherical vessels, cylindrical tubes, and circular disks of linear viscoelastic material

Abstract

By using the properties of Abel operators and э_α-operators [3], unique implicit solutions for N-layer structures with alternating elastic and viscoelastic layers in the case where the viscoelastic operator corresponding to the Poisson ratio reduces to a constant. For an N-layer spherical vessel an analogous implicit solution is also obtained on the assumption that the viscoelastic medium is elastically compressible. Explicit expressions for the reaction pressures are written down for the case of all possible two- and three-layer structures with alternating elastic and viscoelastic layers and analyzed in detail. It is shown that the hypotheses in question lead to qualitatively different states of stress. The general results obtained are illustrated by an example.