Abstract

The presence of imperfections significantly reduces the load carrying capacity of thin cylindrical shells due to the high sensitivity of thin shells to imperfections. To nullify this unfavorable characteristic, thin cylindrical shells are designed using a conservative knockdown factor method, which was developed by NASA in the late 1960s. Almost all the design codes, explicitly or implicitly, follow this approach. Recently, a new approach has emerged to significantly reduce the sensitivity of thin cylindrical shells. In this approach, wavy cross sections are used instead of circular cross sections for creating thin cylinders. Past studies have demonstrated the effectiveness of wavy cylinders to reduce imperfection sensitivity of thin cylinders under axial compression assuming linear elastic material behavior. These studies used eigenmode imperfections which do not represent realistic imperfections found in cylinders. In this paper, using a realistic dimple-like imperfection, new insights are presented into the response of wavy cylinders under uniform axial compression and bending. Furthermore, the effectiveness of the wavy cylinders to reduce imperfection sensitivity under bending load is investigated assuming a plastic Ramberg–Osgood material model. The effect of wave parameters, e.g., the amplitude and the number of waves, is also explored. This study reveals that wavy thin cylinders are insensitive to imperfections under bending in the inelastic range of the material. It is also found that the wave parameters play a decisive role in the response of thin wavy cylinders to imperfections under bending.

References

References
1.
Tsien
,
H.-S.
,
1942
, “
A Theory for the Buckling of Thin Shells
,”
J. Aeronaut. Sci.
,
9
(
10
), pp.
373
384
. 10.2514/8.10911
2.
Karman
,
T. V.
,
1941
, “
The Buckling of Thin Cylindrical Shells Under Axial Compression
,”
J. Aeronaut. Sci.
,
8
(
8
), pp.
303
312
. 10.2514/8.10722
3.
Karman
,
T. V.
, and
Tsien
,
H.-S.
,
1939
, “
The Buckling of Spherical Shells by External Pressure
,”
J. Aeronaut. Sci.
,
7
(
2
), pp.
43
50
. 10.2514/8.1019
4.
Koiter
,
W. T.
,
1945
, “
The Stability of Elastic Equilibrium
,”
Ph.D. thesis
,
Deft University of Technology
,
Delft, The Netherlands
(An English Translation Is Available in 1967)
.
5.
Hutchinson
,
J.
,
1965
, “
Axial Buckling of Pressurized Imperfect Cylindrical Shells
,”
AIAA J.
,
3
(
8
), pp.
1461
1466
. 10.2514/3.3169
6.
Hutchinson
,
J.
,
1965
, “
Buckling of Imperfect Cylindrical Shells Under Axial Compression Andexternal Pressure
,”
AIAA J.
,
3
(
10
), pp.
1968
1970
. 10.2514/3.3299
7.
Budiansky
,
B.
, and
Hutchinson
,
J. W.
,
1966
, “
A Survey of Some Buckling Problems
,”
AIAA J.
,
4
(
9
), pp.
1505
1510
. 10.2514/3.3727
8.
Hutchinson
,
J.
, and
Koiter
,
W.
,
1970
, “
Postbuckling Theory
,”
Appl. Mech. Rev.
,
23
(
12
), pp.
1353
1366
.
9.
Brush
,
D. O.
, and
Almroth
,
B. O.
,
1975
,
Buckling of Bars, Plates, and Shells
, Vol.
6
,
McGraw-Hill
,
New York
.
10.
Calladine
,
C. R.
,
1989
,
Theory of Shell Structures
,
Cambridge University Press
,
Cambridge
.
11.
Weingarten
,
V. I.
,
Seide
,
P.
, and
Peterson
,
J.
,
1968
, “
Buckling of Thin-Walled Circular Cylinders
,” U.S. Patent No. NASA SP-8007.
12.
EN 1993-1-6
,
2007
, “
Design of Steel Structures—Part-1-6: Strength and Stability of Shell Structures
,”
Technical Report
,
CEN (European Committee for Standardization)
,
Brussels, Belgium
.
13.
Seide
,
P.
,
Weingarten
,
V.
, and
Morgan
,
E.
,
1960
, “
The Development of Design Criteria for Elastic Stability of Thin Shell Structures
,”
Technical Report
,
TRW Space Technology Labs
,
Los Angeles, CA
.
14.
Ning
,
X.
, and
Pellegrino
,
S.
,
2015
, “
Imperfection-Insensitive Axially Loaded Thin Cylindrical Shells
,”
Int. J. Solids Struct.
,
62
, pp.
39
51
. 10.1016/j.ijsolstr.2014.12.030
15.
Ning
,
X.
, and
Pellegrino
,
S.
,
2017
, “
Experiments on Imperfection Insensitive Axially Loaded Cylindrical Shells
,”
Int. J. Solids Struct.
,
115–116
, pp.
73
86
. 10.1016/j.ijsolstr.2017.02.028
16.
Ning
,
X.
, and
Pellegrino
,
S.
,
2018
, “
Searching for Imperfection Insensitive Externally Pressurized Near-Spherical Thin Shells
,”
J. Mech. Phys. Solids
,
120
, pp.
49
67
(Special Issue in Honor of Ares J. Rosakis on the Occasion of His 60th Birthday)
. 10.1016/j.jmps.2018.06.008
17.
Yadav
,
K. K.
, and
Gerasimidis
,
S.
,
2018
, “
Imperfection Insensitivity of Wavy Cross-Sectional Thin Cylindrical Shells Under Bending
,”
Proceedings of IASS Annual Symposia, Vol. 25, International Association for Shell and Spatial Structures (IASS)
,
Boston, MA
, pp.
1
8
.
18.
Yadav
,
K. K.
, and
Gerasimidis
,
S.
,
2019
, “
Instability of Thin Steel Cylindrical Shells Under Bending
,”
Thin-Walled Struct.
,
137
, pp.
151
166
. 10.1016/j.tws.2018.12.043
19.
Brazier
,
L.
,
1927
, “
On the Flexure of Thin Cylindrical Shells and Other ‘Thin’ Sections
,”
Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci.
,
116
(
773
), pp.
104
114
. 10.1098/rspa.1927.0125
20.
Seide
,
P.
, and
Weingarten
,
V. I.
,
1961
, “
On the Buckling of Circular Cylindrical Shells Under Pure Bending
,”
ASME J. Appl. Mech.
,
28
(
1
), pp.
112
116
. 10.1115/1.3640420
21.
Ju
,
G.
, and
Kyriakides
,
S.
,
1992
, “
Bifurcation and Localization Instabilities in Cylindrical Shells Under Bending—II. Predictions
,”
Int. J. Solids Struct.
,
29
(
9
), pp.
1143
1171
. 10.1016/0020-7683(92)90140-O
22.
Kyriakides
,
S.
, and
Corona
,
E.
,
2007
,
Mechanics of Offshore Pipelines: Volume 1 Buckling and Collapse
, Vol.
1
,
Elsevier
,
New York
.
23.
Simulia
,
2014
,
ABAQUS Theory Manual
,
Dassault Systems Simulia Corporation
,
Providence, RI
.
24.
Riks
,
E.
,
1979
, “
An Incremental Approach to the Solution of Snapping and Buckling Problems
,”
Int. J. Solids Struct.
,
15
(
7
), pp.
529
551
. 10.1016/0020-7683(79)90081-7
25.
Gerasimidis
,
S.
,
Virot
,
E.
,
Hutchinson
,
J.
, and
Rubinstein
,
S.
,
2018
, “
On Establishing Buckling Knockdowns for Imperfection Sensitive Shell Structures
,”
ASME J. Appl. Mech.
,
85
(
9
), p.
091010
. 10.1115/1.4040455
26.
Hutchinson
,
J. W.
,
2016
, “
Buckling of Spherical Shells Revisited
,”
Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci.
,
472
(
2195
), p.
20160577
. 10.1098/rspa.2016.0577
27.
Lee
,
A.
,
Jiménez
,
F. L.
,
Marthelot
,
J.
,
Hutchinson
,
J. W.
, and
Reis
,
P. M.
,
2016
, “
The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells
,”
ASME J. Appl. Mech.
,
83
(
11
), p.
111005
. 10.1115/1.4034431
28.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
,
1961
,
Theory of Elastic Stability
,
McGraw-Hill
,
New York
.
29.
Jiménez
,
F. L.
,
Marthelot
,
J.
,
Lee
,
A.
,
Hutchinson
,
J. W.
, and
Reis
,
P. M.
,
2017
, “
Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects
,”
ASME J. Appl. Mech.
,
84
(
3
), p.
034501
. 10.1115/1.4035665
30.
Marthelot
,
J.
,
López Jiménez
,
F.
,
Lee
,
A.
,
Hutchinson
,
J. W.
, and
Reis
,
P. M.
,
2017
, “
Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force
,”
ASME J. Appl. Mech.
,
84
(
12
), p.
121005
. 10.1115/1.4038063
You do not currently have access to this content.