Motivated by practical engineering applications, the present paper examines the mechanical response of thin-walled cylinders surrounded by a rigid or deformable medium, subjected to uniform external pressure. Emphasis is given to structural stability in terms of buckling, postbuckling, and imperfection sensitivity. The present investigation is computational and employs a two-dimensional model, where the cylinder and the surrounding medium are simulated with nonlinear finite elements. The behavior of cylinders made of elastic material is examined first, and a successful comparison of the numerical results is conducted with available closed-form analytical solutions for rigidly confined cylinders. Subsequently, the response of confined thin-walled steel cylinders is examined. The numerical results show an unstable postbuckling response beyond the point of maximum pressure and indicate severe imperfection sensitivity on the value of the maximum pressure. A good comparison with limited available test data is also shown. Furthermore, the effects of the deformability of the surrounding medium are examined. In particular, soil embedment conditions are examined, with direct reference to the case of buried thin-walled steel pipelines. Finally, based on the numerical results, a comparison is attempted between the present buckling problem and the problem of “shrink buckling.” The differences between those two problems of confined cylinder buckling are pinpointed, emphasizing the issue of imperfection sensitivity.

References

References
1.
Watkins
,
R. K.
,
2004
, “
Buried Pipe Encased in Concrete
,”
International Conference on Pipeline Engineering and Construction
, San Diego, CA,
ASCE
.10.1061/40745(146)87
2.
Omara
,
A. M.
,
Guice
,
L. K.
,
Straughan
,
W. T.
, and
Akl
,
F. A.
,
1997
, “
Buckling Models of Thin Circular Pipes Encased in Rigid Cavity
,”
J. Eng. Mech.
,
123
(
12
), pp.
1294
1301
.10.1061/(ASCE)0733-9399(1997)123:12(1294)
3.
Ullman
,
F.
,
1964
, “
External Water Pressure Designs for Steel-Lined Pressure Shafts
,”
Water Pow.
,
16
, pp.
298
305
.
4.
Ahrens
,
T.
,
1970
, “
An In-Depth Analysis of Well Casings and Grouting: Basic Considerations of Well Design—Part II
,”
Water Well J.
, pp.
49
51
.
5.
Chicurel
,
R.
,
1968
, “
Shrink Buckling of Thin Circular Rings
,”
ASME J. Appl. Mech.
,
35
(
3
), pp.
608
610
.10.1115/1.3601259
6.
Burgess
,
I.
,
1971
, “
The Buckling of a Radially Constrained Imperfect Circular Ring
,”
Int. J. Mech. Sci.
,
13
(
9
), pp.
741
753
.10.1016/0020-7403(71)90043-9
7.
Bottega
,
W. J.
,
1989
, “
On the Behavior of an Elastic Ring Within a Contracting Cavity
,”
Int. J. Mech. Sci.
,
31
(
5
), pp.
349
357
.10.1016/0020-7403(89)90059-3
8.
Feodosyev
,
V. I.
,
1967
,
Selected Problems and Questions in Strength of Materials
,
Nauka Publishing House
,
Moscow
.
9.
Glock
,
D.
,
1977
, “
Überkritisches Verhalten eines Starr Ummantelten Kreisrohres bei Wasserdrunck von Aussen und Temperaturdehnung” (“Post-Critical Behavior of a Rigidly Encased Circular Pipe Subject to External Water Pressure and Thermal Extension”)
,
Der Stahlbau
,
7
, pp.
212
217
.
10.
Brush
,
D. O.
, and
Almroth
,
B. O.
,
1975
,
Buckling of Bars, Plates, and Shells
,
McGraw-Hill
,
New York
.
11.
El-Sawy
,
K.
, and
Moore
, I
. D.
,
1998
, “
Stability of Loosely Fitted Liners Used to Rehabilitate Rigid Pipes
,”
J. Struct. Eng.
,
124
(
11
), pp.
1350
1357
.10.1061/(ASCE)0733-9445(1998)124:11(1350)
12.
Aggarwal
,
S. C.
, and
Cooper
,
M. J.
,
1984
, “
External Pressure Testing of Insituform Lining
,” Coventry (Lanchester) Polytechnic, Coventry, UK, Internal Report.
13.
Boot
,
J. C.
,
1997
, “
Elastic Buckling of Cylindrical Pipe Linings With Small Imperfections Subject to External Pressure
,”
Tunnel. Undergr. Sp. Tech.
,
12
(
Suppl 1
), pp.
3
15
.10.1016/S0886-7798(98)00018-2
14.
Bottega
,
W. J.
,
1993
, “
On the Separation of Concentric Elastic Rings
,”
Int. J. Mech. Sci.
,
35
(
10
), pp.
851
866
.10.1016/0020-7403(93)90044-U
15.
Li
,
F. S.
, and
Kyriakides
,
S.
,
1991
, “
On the Response and Stability of Two Concentric, Contracting Rings Under External Pressure
,”
Int. J. Solid. Struct.
,
27
(
1
), pp.
1
14
.10.1016/0020-7683(91)90141-2
16.
Li
,
F. S.
, and
Kyriakides
,
S.
,
1990
, “
On the Propagation Pressure of Buckles in Cylindrical Confined Shells
,”
ASME J. Appl. Mech.
,
57
(4), pp.
1091
1094
.10.1115/1.2897636
17.
Montel
,
R.
,
1960
, “
Formule Semi-Empirique pour la Détermination de la Pression Extérieure Limite d’Instabilité des Conduits Métalliques Lisses Noyées dans du Béton
,”
La Houille Blanche
,
15
(
5
), pp.
560
568
.10.1051/lhb/1960048
18.
Timoshenko
,
S.
, and
Gere
,
J. M.
,
1961
,
Theory of Elastic Stability
,
2nd ed.
,
McGraw-Hill
,
New York
.
19.
Borot
,
H.
,
1957
, “
Flambage d'un Cylindre à Paroi Mince, Placé dans une Enveloppe Rigide et Soumis à une Pression Extérieure
,”
La Houille Blanche
,
12
(
6
), pp.
881
887
.10.1051/lhb/1957061
20.
Amstutz
,
E.
,
1969
, “
Das Einbeulen von Schacht – und Stollenpanzerungen
,”
Schweizerische Bauzeitung
,
87
, pp.
541
549
(U.S. Dept. of the Interior, Translation No. 825).
21.
Jacobsen
,
S.
,
1974
, “
Buckling of Circular Rings and Cylindrical Tubes Restrained Against Radial Displacement Under External Pressure
,”
Water Pow.
,
26
, pp.
400
407
.
22.
Taras
,
A.
, and
Greiner
,
R.
,
2007
, “
Zum Gültigkeitsbereich der Bemessungsformeln für Druckschachtpanzerungen Unter Außendruck” (“Scope of the Design Assumption for Pressure Tunnel Steel Linings Under External Pressure”)
,
Stahlbau
,
76
(
10
), pp.
730
738
.10.1002/stab.200710078
23.
Yamamoto
,
Y.
, and
Matsubara
,
N.
,
1982
, “
Buckling of a Cylindrical Shell Under External Pressure Restrained by an Outer Rigid Wall
,”
Proceedings, Symposium on Collapse and Buckling, Structures; Theory and Practice
,
Cambridge University Press
,
London
, pp.
493
504
.
24.
Kyriakides
,
S.
, and
Youn
,
S. K.
,
1984
, “
On the Collapse of Circular Confined Rings Under External Pressure
,”
Int. J. Solid. Struct.
,
20
(
7
), pp.
699
713
.10.1016/0020-7683(84)90025-8
25.
Kyriakides
,
S.
,
1986
, “
Propagating Buckles in Long Confined Cylindrical Shells
,”
Int. J. Solid. Struct.
,
22
(
12
), pp.
1579
1597
.10.1016/0020-7683(86)90064-8
26.
El-Sawy
,
K.
,
2001
, “
Inelastic Stability of Tightly Fitted Cylindrical Liners Subjected to External Uniform Pressure
,”
Thin Wall. Struct.
,
39
(
9
), pp.
731
744
.10.1016/S0263-8231(01)00026-X
27.
El-Sawy
,
K.
,
2002
, “
Inelastic Stability of Loosely Fitted Cylindrical Liners
,”
J. Struct. Eng.
,
128
(
7
), pp.
934
941
.10.1061/(ASCE)0733-9445(2002)128:7(934)
28.
El-Sawy
,
K.
,
2013
, “
Inelastic Stability of Liners of Cylindrical Conduits With Local Imperfection Under External Pressure
,”
Tunnel. Undergr. Sp. Tech.
,
33
, pp.
98
110
.10.1016/j.tust.2012.09.004
29.
Estrada
,
C. F.
,
Godoy
,
L. A.
, and
Flores
,
F. G.
,
2012
, “
Buckling of Vertical Sandwich Cylinders Embedded in Soil
,”
Thin Wall. Struct.
,
61
, pp.
188
195
.10.1016/j.tws.2012.05.010
30.
Vasilikis
,
D.
, and
Karamanos
,
S. A.
,
2009
, “
Stability of Confined Thin-Walled Steel Cylinders Under External Pressure
,”
Int. J. Mech. Sci.
,
51
(
1
), pp.
21
32
.10.1016/j.ijmecsci.2008.11.006
31.
Vasilikis
,
D.
, and
Karamanos
,
S. A.
,
2011
, “
Buckling Design of Confined Steel Cylinders Under External Pressure
,”
ASME J. Press. Vess. Tech.
,
133
(
1
), p.
011205
.10.1115/1.4002540
32.
Comité Européen de Normalization
,
2007
,
Strength and Stability of Shell Structures, EN 1993-1-6
, Eurocode 3, Part 1–6,
Brussels
,
Belgium
.
33.
European Convention for Constructional Steelwork
,
2008
,
Buckling of Steel Shells, European Design Recommendations
,
5th ed.
, J. M. Rotter, and H. Schmidt, eds.,
Brussels
,
Belgium
, ECCS Publication No. 125.
34.
Hibbit
,
H. D.
,
Karlsson
,
B. I.
, and
Sorensen
,
P.
,
2007
,
Theory Manual
, Version 6.7, ABAQUS,
Providence, RI
.
35.
Koiter
,
W. T.
,
1963
,
Elastic Stability and Post-Buckling Behaviour, Proceedings of the Symposium in Nonlinear Problems
,
University of Wisconsin Press
,
Madison
, WI, pp.
257
275
.
36.
Budiansky
,
B.
,
1965
, “
Dynamic Buckling of Elastic Structures: Criteria and Estimates
,”
Proceedings of the International Conference in Dynamic Stability of Structures
, pp.
83
106
.
37.
Jeyapalan
,
J. K.
, and
Watkins
,
R. K.
,
2004
, “
Modulus of Soil Reaction (E') Values for Pipeline Design
,”
J. Transp. Eng.
,
130
(
1
), pp.
43
48
.10.1061/(ASCE)0733-947X(2004)130:1(43)
38.
Hsu
,
P. T.
,
Elkon
,
J.
, and
Pian
,
T. H. H.
,
1964
, “
Note on the Instability of Circular Rings Confined to a Rigid Boundary
,”
ASME J. Appl. Mech.
,
31
(
3
), pp.
559
562
.10.1115/1.3629687
39.
Bucciarelli
,
L. L.
, Jr., and
Pian
,
T. H. H.
,
1967
, “
Effect of Initial Imperfections on the Instability of a Ring Confined in an Imperfect Rigid Boundary
,”
ASME J. Appl. Mech.
,
34
(
4
), pp.
979
984
.10.1115/1.3607866
40.
El-Bayoumy
,
L.
,
1972
, “
Buckling of a Circular Elastic Ring Confined to a Uniformly Contracting Circular Boundary
,”
ASME J. Appl. Mech.
,
39
(
3
), pp.
758
766
.10.1115/1.3422785
41.
Soong
,
T. C.
, and
Choi
,
I.
,
1985
, “
Bucking of an Elastic Elliptical Ring Inside a Rigid Boundary
,”
ASME J. Appl. Mech.
,
52
(
3
), pp.
523
528
.10.1115/1.3169094
42.
Sun
,
C.
,
Shaw
,
W. J. D.
, and
Vinogradov
,
A. M.
,
1995
, “
Instability of Confined Rings: An Experimental Approach
,”
Exper. Mech.
,
35
(
2
), pp.
97
103
.10.1007/BF02326466
You do not currently have access to this content.