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TECHNICAL PAPERS

Collapse Tests on Externally Pressurized Toroids

[+] Author and Article Information
J. Błachut

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

J. Pressure Vessel Technol 125(1), 91-96 (Jan 31, 2003) (6 pages) doi:10.1115/1.1522417 History: Revised August 29, 2002; Revised September 29, 2002; Online January 31, 2003
Copyright © 2003 by ASME
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References

Błachut,  J., and Jaiswal,  O. R., 2000, “On Buckling of Toroidal Shells Under External Pressure,” Comput. Struct., 77, pp. 233–251.
Błachut, J., and Jaiswal, O. R., 1998, “Buckling of imperfect ellipsoids and closed toroids subjected to external pressure,” in “Analysis and Design of Composite, Process and Power Piping and Vessels,” ed., D. K. Williams, ASME, PVP-Vol. 368, pp. 121–128.
Błachut,  J., and Jaiswal,  O. R., 1999, “Instabilities in Torispheres and Toroids Under Suddenly Applied External Pressure,” J. Impact. Eng.,22, pp. 511–530.
Jordan,  P. F., 1973, “Buckling of Toroidal Shells Under Hydrostatic Pressure,” AIAA J., 11, pp. 1439–1441.
Gouliaev, V. I., Bazenov, V. A., Goculiak, E. A., and Gaidaicuk, V. V., 1990, “Analysis of Complex Shells,” Kiev, Budyvielnik (in Russian).
Fishlowitz, E. G., 1972, “Investigation of Elastic Stability of Circular Toroidal Shells Under Uniform External Pressure,” US Navy, NSRDC Report 3338, Washington DC.
Nordell, W. J., and Crawford, J. E., 1971, “Analysis of Behavior of Unstiffened Toroidal Shells,” Pacific Symp. Hydromechanically Loaded Shells, University of Hawaii, Honolulu, 1971, JASS, Paper 4-4.
Sobel,  L. H., and Flugge,  W., 1967, “Stability of Toroidal Shells Under Uniform External Pressure,” AIAA J., 5, pp. 425–431.
Fedosov,  Yu. A., 1969, “Experimental Investigations Into Stability of Toroidal Shells,” Izvestia VUZ, Aviatsionnyia Tekhnika, 12, pp. 154–157 (in Russian).
Fedosov,  Yu. A., 1971, “Stability of Toroidal Shell Under External Pressure,” Izvestia VUZ, Aviatsionnyia Tekhnika, 14, pp. 108–112 (in Russian).
Fedosov,  Yu. A., 1977, “Theoretical and Experimental Investigations Into Stability of Toroidal Shells Under External Pressure,” Izvestia VUZ, Aviatsionnyia Tekhnika, 20, pp. 98–102 (in Russian).
Galletly,  G. D., and Błachut,  J., 1995, “Stability of Complete Circular and Non-Circular Toroidal Shells,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 209, pp. 245–255.
Hibbitt, Karlsson, and Sorensen, Inc., ABAQUS User’s and Theory Manual, Ver. 6.2, RI 02860-4847, USA, 2001.
Bushnell, D., 1976, “Bosor5—Program for Buckling of Elastic-Plastic Complex Shells of Revolution Including Large Deflections and Creep,” Computers Struct. 6 , pp. 221–239.

Figures

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Section through spun toroid with top and bottom halves welded together (a); planar view of a toroid made by welding four, 90 deg, elbows (b,c)
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Typical stress-strain curve for mild steel (obtained from 1.97 mm thick flat test coupon)
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Bifurcation and collapse pressures for toroidal shell with circular cross section and r/t=18.74. The effect of two values of the yield point of mild steel, i.e., 194.8 and 400 MPa on the load-carrying capacity is shown.
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Deformed shape just prior to buckling and the corresponding eigenmode for R/r=5 (a,b), and for R/r=15 (c,d). Other values are: r/t=18.74,σyp=194.8 MPa. Note: Deformations are not to scale.
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Deformed shape at the collapse for R/r=5 (a), and for R/r=15 (b). Note: Deformations are not to scale.
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View of spun halves for TS1 shell
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Spun toroidal shell after welding and attachment of two nozzles
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Distribution of average, minimum and maximum values of the wall thickness in TS1, TS2, and TE1 toroidal shells
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View of stainless steel toroidal shell, TE1, being lowered to pressure tank for testing
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Toroidal shell, TE1, after collapse
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View of spun toroids, (a) TS1 and (b) TS2, after collapse
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Computed bifurcation buckling and collapse characteristics for two (r/t)-ratios

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