Materials Technology

Plastic Buckling of Conical Shells

[+] Author and Article Information
J. Błachut, O. Ifayefunmi

Department of Mechanical Engineering, University of Liverpool, Liverpool L69 3GH, UK

J. Offshore Mech. Arct. Eng 132(4), 041401 (Sep 24, 2010) (11 pages) doi:10.1115/1.4001437 History: Received June 18, 2009; Revised February 01, 2010; Published September 24, 2010; Online September 24, 2010

This paper studies the static stability of metal cones subjected to combined, simultaneous action of the external pressure and axial compression. Cones are relatively thick; hence, their buckling performance remains within the elastic-plastic range. The literature review shows that there are very few results within this range and none on combined stability. The current paper aims to fill this gap. Combined stability plot, sometimes called interactive stability plot, is obtained for mild steel models. Most attention is given to buckling caused by a single type of loading, i.e., by hydrostatic external pressure and by axial compression. Asymmetric bifurcation bucklings, collapse load in addition to the first yield pressure and first yield force, are computed using two independent proprietory codes in order to compare predictions given by them. Finally, selected cone configurations are used to verify numerical findings. To this end four cones were computer numerically controlled-machined from a solid steel billet of 252 mm in diameter. All cones had integral top and bottom flanges in order to mimic realistic boundary conditions. Computed predictions of buckling loads, caused by external hydrostatic pressure, were close to the experimental values. But similar comparisons for axially compressed cones are not so good. Possible reasons for this disparity are discussed in the paper.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Geometry of the truncated conical shell

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Figure 2

Plot of the external hydrostatic pressure versus axial shortening of the cone. Geometry of the cone is given by r2/r1=2.02, r2/t=34.3, h/r2=1.01, and β=26.56 deg.

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Figure 3

View of the initial FE model (Fig. 3) and of the deformed shape under external hydrostatic pressure at p=6.78 MPa (Fig. 3)

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Figure 4

Spread of the plastic strains through the wall thickness at different pressure levels indicated in Fig. 2. Cone is loaded by external, hydrostatic pressure.

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Figure 5

View of the cone just prior to bifurcation buckling (Fig. 5, with a magnification factor of 150) and of the associated eigenshape with n=4 circumferential lobes (Fig. 5), pbif=8.27 MPa

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Figure 6

Plot of the axial compressive force F versus dimensionless axial shortening of the cone

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Figure 7

Spread of the plastic strains in axially compressed cone

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Figure 8

Domain of the combined stability for a cone subjected to the simultaneous action of the external pressure and axial compression (results from BOSOR5 )

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Figure 9

Cutting pattern for cones C1, C2, C3, and C4. Also, dimensions of the round tensile test specimens and directions of their cutting. All dimensions are given in mm.

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Figure 10

Section through conical shell (Fig. 1). The insert illustrates the transition from the shell wall to the flange, Fig. 1. Photograph of the manufactured cone (Fig. 1). Note the difference between r2 (internal radius) and r¯2 (mid-surface radius).

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Figure 11

Stress-strain curve for mild steel specimen S1. The insert shows the region between 0% and 1.2% uni-axial strain.

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Figure 12

Scatter of the wall thickness in the hoop direction for cones C1, C2, and C3

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Figure 13

Arrangements for measuring (r,z)-coordinates of the internal surface of a cone

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Figure 14

Arrangements for fixing the top and bottom covering plates (Fig. 1), and photograph of the same is shown in Fig. 1

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Figure 15

Section through the test tank with a cone filled with transformer oil

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Figure 16

Plot of the external pressure versus the amount of expelled oil for cone C2; comparison of the experimental and numerical results

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Figure 17

Photograph of cones C1 and C2 after testing

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Figure 18

Test arrangements for the case of the axial compression (Fig. 1), and photograph of the tested cones C3 and C4 (Figs.  1818)



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