Cylindrically Orthotropic Medium with Lined Hole

Abstract

A solution for a thin elastic cylindrical lining embedded in an infinite, cylindrically orthotropic medium and subjected to a uniaxial stress field has been obtained. The solution, by separation of variables, is found by utilizing Lekhnitskii's stress function whereas the lining is analyzed using thin shell theory. Equilibrium and continuity are completely satisfied along the interface between the shell and the orthotropic medium. It is shown how the general solution provides insight into maximum stress and deformations that characterize cylindrical linings in an orthotropic medium where cylindrically orthotropic constants were transformed from orthotropic medium data. Since an orthotropic medium is more representative of a large class of glass‐fiber reinforced plastics, the results differ considerably with the picture obtained from calculations for an isotropic medium. The lining and the orthotropic medium are shown to greatly affect tangential stress distribution. These results represent only a concise example; any situation of interest can be computed since the general solutions are given.