Elastic-plastic torsion of circular ring sectors
Author:
W. Freiberger
Journal:
Quart. Appl. Math. 14 (1956), 259-265
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/81700
MathSciNet review:
81700
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Abstract: The solution is presented to the problem of uniform torsion of circular ring sectors with circular cross section under the assumption of perfect plasticity. The elastic-plastic problem is solved by a semi-inverse method. When the entire ring is plastic a discontinuity of stress appears which may be regarded as the limiting case of an elastic core; such discontinuities have recently been discussed in the literature [1]. The solution for the discontinuous fully plastic stress distribution is exact, that for the elastic-plastic case approximate in the sense that it is found exactly for cross sections differing slightly from the circular. This difference is negligible for ratios of ring radius $R$ to cross section radius $\rho$ occurring in practical applications to helical springs of small pitch.
- William Prager, Discontinuous fields of plastic stress and flow, Proceedings of the Second U. S. National Congress of Applied Mechanics, Ann Arbor, 1954, American Society of Mechanical Engineers, New York, 1955, pp. 21–32. MR 0079413
Jaknke and Emde, Tables of functions, New York, 1938
W. Freiberger, The uniform torsion of a perfectly plastic circular ring, Aeronaut. Research Labs. Rept. SM 213, Melbourne, Australia, 1953
- A. J. Wang and W. Prager, Plastic twisting of a circular ring sector, J. Mech. Phys. Solids 3 (1955), 169–175. MR 69737, DOI https://doi.org/10.1016/0022-5096%2855%2990008-9
- W. Freiberger and W. Prager, Plastic twisting of thick-walled circular ring sectors, J. Appl. Mech. 23 (1956), 461–463. MR 0085787
- William Prager and Philip G. Hodge Jr., Theory of perfectly plastic solids, John Wiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951. MR 0051118
- W. Freiberger, The uniform torsion of an incomplete tore, Australian J. Sci. Res. Ser. A 2 (1949), 354–375. MR 35622
W. Prager, Discontinuous fields of plastic stress and flow, Proceedings, Second U.S. Congress of Applied Mechanics, Ann Arbor, Mich., 1954, pp. 21-32
Jaknke and Emde, Tables of functions, New York, 1938
W. Freiberger, The uniform torsion of a perfectly plastic circular ring, Aeronaut. Research Labs. Rept. SM 213, Melbourne, Australia, 1953
A. J. Wang and W. Prager, Plastic twisting of a circular ring sector, J. Mech. Phys. Solids 8, 169-175 (1955)
W. Freiberger and W. Prager, Plastic twisting of thick-walled circular ring sectors, J. Appl. Mech. ASME Paper No. 55-A85 (1955)
W. Prager and P. G. Hodge, Jr., Theory of perfectly plastic solids, John Wiley and Sons, New York, 1951, p. 73
W. Freiberger, The uniform torsion of an incomplete tore, Australian J. Sci. Research A, 2, 354-375 (1949)
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Article copyright:
© Copyright 1956
American Mathematical Society