Analysis of centrifugal stresses in anisotropic viscoelastic cylinder.

Abstract

HE stress analysis for anisotropic viscoelastic materials has become the subject of increasing concern in the past few years. The ever increasing use of composites and oriented plastics as structural members has made it necessary to study the effect of anisotropy as well as viscoelasticity on the performance of these components. Problems in linear isotropic viscoelasticity have been analyzed by many authors, such as Lee, 1 Hilton,2 and Bland,3 under various loading conditions. However, similar attempts in the analysis of anisotropic viscoelasticity have been frustrating because of the difficulties faced in the use of Laplace transform, particularly in the inversion of solutions. As a result, even the simple problems which can be solved explicitly, become important in understanding the interaction of anisotropy and the viscoelastic behavior of materials.4 ~ 6 In this paper, some elementary solutions of stress analysis problems for an anisotropic viscoelastic cylinder are given. Specifically, analysis for a long hollow cylinder, rotating about its axis, is considered. In the course of the analysis, the constitutive equations of the theory of infinitesimal viscoelasticity exhibiting a general anisotropic behavior are assumed. These are expressed in terms of different time-dependent modulus functions. A particular type of spacial nonhomogeneity, where the material moduli are assumed to be representable as a production of functions of time and coordinates, is considered. Through the application of integral (Laplace) transform the problem is then solved. Although the analysis is made for a general linear viscoelastic medium, for simplicity, numerical results are presented for a material having simple viscoelastic behavior. Anisotropic Viscoelasticity The basic problem in quasi-static linear viscoelastic stress analysis is to determine a stress field atj(xk, t) and the displacement field wf(xfc, t) as functions of space variables xk and time t. The governing equilibrium equations, which are independent of material constitution, are the displacement-strain relations and the principles of linear momentum and moment of momentum. They are in the usual notation