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RESEARCH PAPERS

Plastic Loads for Internally Pressurized Toroidal Shells

[+] Author and Article Information
J. Błachut

The University of Liverpool, Mechanical Engineering, Liverpool L69 3GH, U.K.

J. Pressure Vessel Technol 127(2), 151-156 (May 27, 2005) (6 pages) doi:10.1115/1.1858925 History: Received September 02, 2004; Revised November 24, 2004; Online May 27, 2005
Copyright © 2005 by ASME
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References

Gerdeen,  J. C., 1979, “A Critical Evaluation of Plastic Behavior Data and a United Definition of Plastic Loads for Pressure Components,” Weld. Res. Counc. Bull., 254, pp. 1–64.
Galletly,  G. D., and Błachut,  J., 1985, “Torispherical Shells Under Internal Pressure: Failure due to Asymmetric Plastic Buckling or Axisymmetric Yielding,” Proc. IMechE,199, pp. 225–238.
Kalnins,  A., and Updike,  D. P., 1991, “New Design Curves for Torispherical Heads,” Weld. Res. Counc. Bull., 364, pp. 1–59.
Błachut,  J., 1995, “Plastic Loads for Internally Pressurized Torispheres,” Int. J. Pressure Vessels Piping, 64, pp. 91–100.
Błachut,  J., and Ramachandra,  L. S., 1996, “The Failure of Internally Pressurized Vessel Heads due to Yielding,” in ICPVT-8, Design and Analysis, A. Chaaban, ed., ASME,2, pp. 207–216.
Turner,  H. M., 1962, “Design Parameters for Elliptical Toroidal Pressure Vessels,” Aerospace Eng,21, pp. 33–38.
Marketos,  J. D., 1963, “Optimum Toroidal Pressure Vessel Filament Wound Along Geodesic Lines,” AIAA J., 1, pp. 1942–1945.
Koppert,  J. J., and Beukers,  A., 2000, “Full Composite Intensoid Pressure Vessels or How Composites Can Compete With Steel,” SAMPE J., 36, pp. 8–15.
Li,  S., and Cook,  J., 2002, “An Analysis of Filament Overwound Toroidal Pressure Vessels and Optimum Design of Such Structures,” JPVT, Trans. ASME, 124, pp. 215–222.
Ren,  W., Liu,  W., Zhang,  W., Reimerdes,  H. G., and Oery,  H., 1999, “A Survey of Works on the Theory of Toroidal Shells and Curved Tubes,” Acta Mech. Sin., 15, pp. 225–234.
Skrzypek,  J., and Muc,  A., 1988, “Limit States of Geometrically Nonlinear Elastic–Plastic Toroidal Shells Under Pressure With Bending,” Int. J. Mech. Sci.,30, pp. 347–363.
Jones,  D. P., Holiday,  J. E., and Larson,  L. D., 1999, “Elastic–Plastic Failure Analysis of Pressure Burst Tests on Thin Toroidal Shells,” JPVT, Trans. ASME, 121, pp. 149–153.
Błachut,  J., 2003, “Collapse Tests on Externally Pressurized Toroids,” ASME J. of Pressure Vessel, 125, pp. 91–96.
Hibbitt, Karlsson, and Sorensen, Inc., 2002, ABAQUS User’s and Theory Manual, Ver. 6.2, RI 02860-4847, USA.
Brookfield,  D. J., Moreton,  D. N., and Moffat,  D. G., 1986, “Shakedown and Cold Creep of Stainless Steel Type 316 Torispherical Drumheads Subjected to Internal Pressure,” JPVT, Trans. ASME, 108, 289–296.

Figures

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Geometry of closed toroidal shell with circular cross-section
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Distribution of the Huber–Mises–Hencky effective stress around the tube in a closed, toroidal shell with circular cross-section and constant wall thickness
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Tube’s deformed cross-section at pressure, pyp, for selected geometries
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Typical variation of wall thickness in a spun toroid [Fig. 4(a)]. Also, typical wall thickness variation in toroids made from welded elbows [Fig. 4(b)—schedule ‘10’ elbows, model TWE1].
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Sketch illustrating the definition of plastic loads, pV1 and pV2 [Fig. 5(a)]. Also, view of toroidal shell after welding of elbows and attachment of two nozzles [Fig. 5(b)].
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Testing arrangements for volume measurements of expanding toroidal shell
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Plot of pressure versus ΔV/Vo curve for shell TWE1. Also, illustration how pV1 and pV2 were derived graphically from the experiment [Fig. 7(a)]. View of TWE1 after test and TWE2 prior to test [Fig. 7(b)].
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Relative position of the first yield pressure, pyp, and two plastic loads pV1 and pV2 for internally pressurised torispherical shells
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Position of first yield [Fig. 9(a)], and spread of plastic strains through the wall thickness at the level of two plastic loads, pV1 and pV2 [Figs. 9(b) and 9(c)]
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Position of first yield, and spread of plastic strains trough the wall thickness at pressures pV1 and pV2. Nominal geometry of TWE1 was used.

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