Calgary, Alberta, Canada T2N IN4
Communicated by Xavier J. R. Avula
(Received March 1984; revised November 1985)
Abstract-The paper presents the creep-stability analysis of viscoelastic cylindrical
shells under axial compression. The mechanical properties of the material are described

by the constitutive equations of the linear viscoelastic theory in terms of convolution
integral operators. The approximate analytical solution to the problem is obtained by
means of a modification of the quasi-elastic method. As a result, the instability condition
for the shell is formulated. It is shown that for viscoelastic materials with limited creep,
there is a safe load limit below which the structure is asymptotically stable. Any load
above the safe load limit leads to buckling at the corresponding critical time.
1. INTRODUCTION
Creep stability of circular cylindrical shells has been studied by numerous researchers
using various concepts and constitutive laws. A number of investigations utilize the initial
imperfection approach followed by the conclusion that under creep conditions initial imperfections
develop with time, leading eventually to collapse of the structure. The critical

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time in such analyses is usually defined in terms of infinite deformations or infinite deformation
rates. Comprehensive reviews of these studies are given by Hoffll, 21 and
Kurshin[3].
In recent years an increasing interest has been attracted by applications of the classical
bifurcation theory to the creep-stability research. In particular, creep stability of cylindrical
shells is treated in many publications[4-81 as an instantaneous process which involves
time-dependent constitutive terms and is characterized as branching into a different
equilibrium configuration. Respectively, the critical time is associated with the instant at
which bifurcation first becomes possible. The results from these studies depend upon the
basic assumptions as to the creep properties of the structure.
The present paper is concerned with the stability analysis of circular cylindrical shells
whose material properties are defined by the constitutive equations of the linear viscoelastic
theory. Using the concept of bifurcation the exact linear eigenvalue problem is
formulated in terms of two destabilizing parameters: the compressive load and time. The