On the solution for the elastic response of involute bodies

Abstract

A recent model to treat the elastic response of bodies of revolution possessing axisymmetric material structure, but otherwise arbitrary heterogeneous anisotropic elastic behavior, is examined in detail. Of particular interest is the derivation of the end conditions appropriate to the particular numerical solution technique employed (finite difference) because of the difference between the numbers of field equations and boundary conditions. It is felt that the procedure adopted may have much wider application than the present usage. The response of involute bodies is featured in this work as the illustrative problem of a frustrum of an involute cone under a constant temperature change is considered. A thorough comparison is made between the predictions given by the present model and those from the PATCHES-III finite element code, with generally favorable results.