This is the first study into elastic-plastic buckling of unstiffened truncated conical shells under simultaneously acting axial compression and an independent external pressure. This is both a numerical and experimental study. Domains of combined stability are obtained using the finite element method for a range of geometrical parameters. Cones are clamped at one end and free to move axially at the other end, where all the other degrees of freedom remain constrained. Shells are assumed to be from mild steel and the material is modeled as elastic perfectly plastic. The FE results indicate that the static stability domains remain convex. The failure mechanisms, i.e., asymmetric bifurcation and axisymmetric collapse are discussed together with the spread of plastic strains through the wall thickness. Also, the combined stability domains are examined for regions of purely elastic behavior and for regions where plastic straining exists. The latter is not convex and repercussions of that are discussed. The spread of plastic strain is computed for a range of the (radius-to-wall-thickness) ratios.

Experimental results are based on laboratory scale models. Here, a single geometry was chosen for validation of numerically predicted static stability domain. Parameters of this geometry were assumed as follows: the ratio of the bigger radius, r2, to the smaller radius, r1, was taken as (r2/r1) = 2.02; the ratio of radius-to-wall-thickness, (r2/t), was 33.0, and the cone semiangle was 26.56°, while the axial length-to-radius ratio was (h/r2) = 1.01. Shells were formed by computer numerically controlled machining from 252 mm diameter solid steel billet. They had heavy integral flanges at both ends and models were not stress relieved prior to testing. Details about the test arrangements are provided in the paper.

References

References
1.
Błachut
,
J.
, and
Ifayefunmi
,
O.
, 2010, “
Plastic Buckling of Conical Shells
,”
ASME J. Offshore Mech. Arctic Eng.
,
132
(
4
),
041401
.
2.
Singer
,
J.
,
Arbocz
,
J.
, and
Weller
,
T.
, 2002,
Buckling Experiments: Experimental Methods in Buckling of Thin-Walled Structures
, Vol.
2
,
John Wiley & Sons
,
New York
.
3.
Singer
,
J.
, 1965, “
On the Buckling of Unstiffened Orthotropic and Stiffened Conical Shells
,”
7th Congress of International Aeronautique
,
Paris
, June 14–16, pp.
1
22
.
4.
Singer
,
J.
,
Berkovits
,
A.
,
Weller
,
T.
,
Ishai
,
O.
,
Baruch
,
M.
, and
Harari
,
O.
, 1966, “
Experimental and Theoretical Studies on Buckling of Conical and Cylindrical Shells Under Combined Loading
,”
Technion Research and Development Foundation
,
Haifa
,
Israel
, TAE Rep. No. 48.
5.
Weller
,
T.
, and
Singer
,
J.
, 1967, “
Further Experimental Studies on Buckling of Ring Stiffened Conical Shells Under Axial Compression
,”
Technion Research and Development Foundation
,
Haifa
,
Israel
, TAE Rep. No. 70.
6.
Singer
,
J.
, 1967, “
The Influence of Stiffener Geometry and Spacing on the Buckling of Axially Compressed Cylindrical and Conical Shells, Theory of Thin Shells
,”
IUTAM 2nd Symposium Copenhagen
,
F.I.
Niordson
, ed.,
Springer-Verlag
,
Berlin
, pp.
234
263
.
7.
Weller
,
T.
, and
Singer
,
J.
, 1970, “
Experimental Studies on Buckling of Ring-Stiffened Conical Shells Under Axial Compression
,”
Exp. Mech.
,
10
, pp.
449
457
.
8.
Anderson
,
J. K.
, and
Davis
,
R. C.
, 1973, “
Buckling Tests of Two 4.6-Meter-Diameter
,
Magnesium Ring-Stiffened Conical Shells Loaded Under External Pressure
,” TN-D-7303,
NASA
,
Washington DC, USA
, pp.
1
68
.
9.
Williams
,
J. G.
, and
Davis
,
R. C.
, 1975, “
Buckling Experiments on Stiffened Cast-Epoxy Conical Shells
,”
Exp. Mech.
,
15
(
9
), pp.
329
338
.
10.
Ross
,
C. T. F.
, and
Johns
,
T.
, 1988, “
Buckling and Vibration of Ring-Stiffened Cones Under Uniform External Pressure
,”
Thin-Walled Struct.
,
6
(
4
), pp.
321
342
.
11.
Ross
,
C. T. F.
, 1995, “
Plastic Collapse of Thin-Walled Ring-Stiffened Conical Shells Under Uniform External Pressure
,”
J. Ship Res.
,
39
(
2
), pp.
166
175
.
12.
Spagnoli
,
A.
, 1997, “
Buckling of Conical Shells
,” Ph.D. thesis, Imperial College London.
13.
Ross
,
C. T. F.
, and
Johns
,
T.
, 1998, “
Plastic Axisymmetric Collapse of Thin-Walled Circular Cylinders and Cones Under Uniform External Pressure
,”
Thin-Walled Struct.
,
30
(
1–4
), pp.
35
54
.
14.
Ross
,
C. T. F.
,
Sawkins
,
D.
,
Thomas
,
J.
, and
Little
,
A. P. F.
, 1999, “
Plastic Collapse of Circular Conical Shells Under Uniform External Pressure
,”
Adv. Eng. Software
,
30
(
9–11
), pp.
631
647
.
15.
Ross
,
C. T. F.
,
Little
,
A. P. F.
, and
Adeniyi
,
K. A.
, 2005, “
Plastic Buckling of Ring-Stiffened Conical Shells Under External Hydrostatic Pressure
,”
Ocean Eng.
,
32
(
1
), pp.
21
36
.
16.
Ross
,
C. T. F.
, and
Little
,
A. P. F.
, 2007, “
Design Charts for the General Instability of Ring-Stiffened Conical Shells Under External Hydrostatic Pressure
,”
Thin-Walled Struct.
,
45
(
2
), pp.
199
208
.
17.
Ross
,
C. T. F.
,
Little
,
A. P. F.
,
Allsop
,
R.
,
Smith
,
C.
, and
Engelhardt
,
M.
, 2007, “
Plastic General Instability of Ring-Reinforced Conical Shells Under Uniform External Pressure
,”
Mar. Technol.
,
44
(
4
), pp.
268
277
.
18.
Ross
,
C. T. F.
, 2007, “
A Proposed Design Chart to Predict the Inelastic Buckling of Conical Shells Under Uniform External Pressure
,”
Mar. Technol.
,
44
(
2
), pp.
77
81
.
19.
Barkey
,
M. E.
,
Turgeon
,
M. C.
, and
Varun Nare
,
T.
, 2008, “
Buckling of Stiffened Thin-Walled Truncated Cones Subjected to External Pressure
,”
Exp. Mech.
,
48
(
3
), pp.
281
291
.
20.
Ross
,
C. T. F.
,
Andriosopoulos
,
G.
, and
Little
,
A. P. F.
2008, “
Plastic General Instability of Ring-Stiffened Conical Shells Under Eternal Pressure
,”
Appl. Mech. Mater.
,
13–14
, pp.
213
223
.
21.
Berkovits
,
A.
,
Singer
,
J.
, and
Weller
,
T.
, 1967, “
Buckling of Unstiffened Conical Shells Under Combined Loading
,”
Exp. Mech.
,
7
(
11
), pp.
458
467
.
22.
Sadr-Hashemi
,
F.
, 1987, “
Buckling of Conical Shells
,” Ph.D. thesis, University College London.
23.
Bose
,
M. R. S. C.
,
Thomas
,
G.
,
Palaninathan
,
R.
,
Damodaran
,
S. P.
, and
Chellapandi
,
P.
, 2001, “
Buckling Investigations on a Nuclear Reactor Inner Vessel Model
,”
Exp. Mech.
,
41
(
2
), pp.
144
150
.
24.
MacCalden
,
P. B.
, and
Matthiesen
,
R. B.
, 1967, “
Combination Torsion and Axial Compression Tests of Conical Shells
,”
AIAA J.
,
5
(
2
), pp.
305
309
.
25.
Radkowski
,
P. P.
, 1962, “
Elastic Instability of Conical Shells Under Combined Loading
,” NASA Rep. No. TN D-1510.
26.
Singer
,
J.
, and
Baruch
,
M.
, 1965, “
Buckling of Circular Conical Shells Under Combined Torsion and External Or Internal Pressure
,” in
Topics in Applied Mechanics
,
D.
Abir
,
F.
Ollendorff
, and
M.
Reiner
, eds.,
Elsevier Publishing Company
,
Amsterdam
, pp.
65
88
.
27.
Weingarten
,
V. I.
,
Morgan
,
E. J.
, and
Seide
,
P.
, 1965, “
Elastic Stability of Thin-Walled Cylindrical and Conical Shells Under Combined Internal Pressure and Axial Compression”
,
AIAA J.
,
3
(
6
), pp.
1118
1125
.
28.
Weingarten
,
V. I.
, 1964, “
Stability of Internally Pressurized Conical Shells Under Torsion
,”
AIAA J.
,
2
(
10
), pp.
1782
1788
.
29.
Weingarten
,
V. I.
, and
Seide
,
P.
, 1965, “
Elastic Stability of Thin-Walled Cylindrical and Conical Shells Under Combined External Pressure and Axial Compression
,”
AIAA J.
,
3
(
5
), pp.
913
920
.
30.
Ramsey
,
H.
, 1977, “
Plastic Buckling of Conical Shells Under Axial Compression
,”
Int. J. Mech. Sci.
,
19
(
5
), pp.
257
272
.
31.
Hibbitt, Karlsson, and Sorensen Inc., 2006, “abaqus—Theory and Standard User’s Manual” Version 6.4, ABAQUS, Pawtucket, RI.
32.
Błachut
,
J.
, and
Magnucki
,
K.
, 2008, “
Strength, Stability and Optimization of Pressure Vessels: Review of Selected Problems
,”
Appl. Mech. Rev.
,
61
(
6
),
060801
.
33.
Błachut
,
J.
, 1998, “
Buckling of Sharp Knuckle Torispheres Under External Pressure
,”
Thin-Walled Struct.
,
30
(
1–4
), pp.
55
77
.
34.
Ifayefunmi
,
O.
, 2011, “
Combined Stability of Conical Shells
,” Ph.D. thesis, The University of Liverpool, UK.
You do not currently have access to this content.