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

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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
problem is treated by means of the quasi-elastic solution technique which utilizes the
concept of a time-dependent elastic material as a model of the actual viscoelastic response.