Decay rates for the compound circular cylinder

Abstract

An exact linear elasticity solution developed by the author for the decay of self-equilibrating end loads applied to a hollow circular cylinder is extended here to determine decay rates for a compound circular cylinder of two materials having different stiffness; only axisymmetric loads are considered. The results are of interest not only as a quantification of Saint-Venant's Principle (SVP), but also because the minimum decay rate indicates the rate of load transfer and hence the maximum extent of a transition region where load is transferred from one cylinder to another. As with the semi-infinite plane strain sandwich, one of the few other geometries amenable to mathematical analysis, rates of decay can be so slow that routine invocation of SVP is not justified. The rate of load transfer from a stiff inner cylinder to a more flexible concentric cylinder is affected by the ratio of the elastic properties and also the diameter ratio. For load transfer to be effected over minimum distance the difference in stiffness should be small; when the difference in stiffness is large, rapid load transfer can be achieved by keeping the diameter ratio small.