mechanical behaviour of thick multilayered cylinders. The original contribution of this
work is to provide novel approximate analytical solutions to compute the timedependent
internal stress state throughout the pipe thickness within the framework of
nonlinear viscoelasticity theory. The structures considered are thick, multilayered

anisotropic infinitive long cylinders subjected to axisymmetric mechanical loading.
Under such conditions there is an exact elastic solution which naturally satisfies
equilibrium, strain-displacement, compatibility and boundary conditions for the stated
constitutive equations and loading. Due to the continuous stress variations throughout
the cylinder thickness, the proposed nonlinear viscoelastic solution assumes the
averaged stress state to calculate the nonlinear elastic and viscoelastic factors in each
3
layer. Furthermore the solution is obtained assuming that the creep strains, within each
layer, are constant through the thickness. The proposed algorithm converges to the exact
solution when the number of layers is artificially increased. For the linear viscoelastic
case the proposed solution proved to match the exact known solution for isotropic

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viscoelastic materials. Finally several invented cases are run to illustrate the importance
of the viscoelasticity phenomenon on the internal stress field throughout thick laminated
cylinders.
KEYWORDS: Polymer–matrix composites (PMCs); Creep; Elasticity; Analytical
modelling; Durability.
INTRODUCTION
The hollow cylinders or cylinders are very common structural elements, used in many
applications including trusses, hoses, piping systems and drive shafts. The effort to
improve oil production riser performance lead to the possible use of risers made of
polymer matrix composites to bring the oil to surface platforms in the offshore
exploration at waster depth of 2 km or more. Consequently the increasing use of
polymer matrix composites in civil engineering applications has renewed interest in
problems of stress analysis of cylindrical laminated composite structures.
Many analytical works about stress analysis of composite cylindrical shells have been

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.
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1331

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