www.elsevier.com/locate/ijpvp
* Corresponding author. Tel.: C98 21 616 5510; fax: C98 21 600 0021.
E-mail address: mhkargar@sharif.edu (M.H. Kargarnovin).
the effect of convective heat transfer on the minimum

thickness of the vessel, and design graphs for several

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of a single-walled carbon nano-tube (SWCNT) conveying
viscous fluid embedded in an elastic medium. They revealed that
the frequency increased as the values of the viscosity parameter increased.
Soltani et al. [15] developed a transverse vibrational model
for a viscous fluid-conveying SWCNT embedded in biological soft
tissue. Their investigation determined that the structural instability
and the associated critical flow velocity could be affected by
the viscosity of the fluid and the nonlocal parameter. Khoddami
et al. [16] studied electro-thermo nonlinear vibration and instability
of embedded double-walled Boron Nitride nano-tubes

(DWBNNTs) conveying viscous fluid based on nonlocal piezoelasticity
theory. They reported that increasing the small scale parameter
decreased the real and imaginary parts of frequency and
critical fluid velocity. Furthermore, they concluded that the effect
of fluid viscosity on the vibration and instability of DWBNNTs
might be ignored. In many recent studies various size-dependent
continuum theories have been developed for vibration and stability
analysis of CNTs conveying fluid. Lee and Chang [17], Zhen
0927-0256/$ – see front matter  2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.commatsci.2013.04.047
⇑ Corresponding author. Tel.: +98 311 391 5248; fax: +98 311 391 2628.

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E-mail addresses: m.mirramezani@me.iut.ac.ir (M. Mirramezani), hrmirdamadi@
cc.iut.ac.ir (H.R. Mirdamadi), ghayour@cc.iut.ac.ir (M. Ghayour).
Computational Materials Science 77 (2013) 161–171
Contents lists available at SciVerse ScienceDirect
Computational Materials Science
journal homepage: www.elsevier.com/locate/commatsci
and Fang [18], Jannesari et al. [19] included the effect of small-size
into equations of motion by using nonlocal elasticity in their studies
and showed that increasing nonlocal parameter had the effect
of a decrease in the critical velocity of fluid. Ke and Wang [20]
investigated vibration and instability of fluid-conveying doublewalled
carbon nano-tubes based on modified couple stress theory.
They showed that the imaginary component of the frequency and
the critical flow velocity of the CNTs increased with an increase in

grouping are important phenomena in their own right:
we quickly and effortlessly perceive boundaries between
certain visual textures, perceive edges between coherent regions
in an image, and quickly detect unusual items that

seem to “pop out” from the background. Examples of perceptual
grouping phenomena are given in Figure 1.
Following the visual system’s “rules” of visual organization
makes interpretation of visual aspects of designs effortless:
a user easily sees which labels refer to which parts of a diaa
b
c
d
e
f
Figure 1: Perceptual grouping examples, including

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grouping by proximity & similarity (a, b), and grouping
by good continuation (c, d). (e) A user interface; what
is the percept? (f) A graph, from [5]. Will a user
perceive the trend of the data?
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specific permission and/or a fee.
CHI 2009, April 4–9, 2009, Boston, MA, USA.
Copyright 2009 ACM 978-1-60558-246-7/09/04…$5.00.
CHI 2009 ~ Cognitive Modeling and Assessment April 8th, 2009 ~ Boston, MA, USA
1331

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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