Structures and Safety Reliability

Buckling of Unstiffened Steel Cones Subjected to Axial Compression and External Pressure

[+] Author and Article Information
J. Błachut1

 The University of Liverpool Mechanical Engineering, Liverpool, L69 3GH, UKem20@liverpool.ac.uk

O. Ifayefunmi

 The University of Liverpool Mechanical Engineering, Liverpool, L69 3GH, UKcathex@liverpool.ac.uk


Author to whom correspondence should be addressed.

J. Offshore Mech. Arct. Eng 134(3), 031603 (Feb 06, 2012) (9 pages) doi:10.1115/1.4004953 History: Received June 25, 2010; Revised November 20, 2010; Published February 06, 2012; Online February 06, 2012

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.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 2

Plot of axial compressive load against axial shortening for cones with different (r2 /t) values

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Figure 4

Plot of external hydrostatic pressure against axial shortening for cones with different (r2 /t) values

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Figure 5

Spread of plastic strain at collapse for cones with different (r2 /t) values under external hydrostatic pressure

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Figure 6

Spread of plastic strains through the wall as a proportion of total cross-sectional area, Atot , versus the (r2 /t) ratio. Plastic strains are recorded at the collapse loads.

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Figure 7

Combined stability plot in the case of external pressure and axial compression acting simultaneously

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Figure 8

Plot of external pressure against axial shortening at constant axial force, F (a). Also, the eigenshape corresponding to n = 11 circumferential waves (b).

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Figure 9

Domain of combined stability plot for r2 /t = 250

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Figure 10

Combined stability plot for r2 /t = 34 (to be verified experimentally)

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Figure 11

Spread of plastic strain within the combined stability domain for r2 /t = 34.3

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Figure 12

Illustration of possible numerical loading paths leading to the location of point 1

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Figure 13

Position of first yielding under combined loading for two distinct cases, i.e., A1 and B1 marked in Fig. 1

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Figure 14

Spread of plastic strains at collapse for two different combined loading paths. The magnitudes were recorded at points A2 and B2 marked in Fig. 1.

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Figure 15

Plot of the area of plastic strains within combined stability domain to the total area, as a function of the (r2 /t) ratio

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Figure 16

Schematic diagram of the experimental test rig for combined loading

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Figure 17

Photograph of the arrangements for combined loading (a), and view of the coupler between the top plate and tension bar (b, not to scale)

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Figure 18

Photographs of cones C5 and C6 after testing

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Figure 3

Spread of plastic strain at collapse for cones with different (r2 /t) values under axial compression

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Figure 1

Geometry of truncated conical shell




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