Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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.

References [Enhancements On Off] (What's this?)

  • [1] W. Prager, Discontinuous fields of plastic stress and flow, Proceedings, Second U.S. Congress of Applied Mechanics, Ann Arbor, Mich., 1954, pp. 21-32 MR 0079413
  • [2] Jaknke and Emde, Tables of functions, New York, 1938
  • [3] W. Freiberger, The uniform torsion of a perfectly plastic circular ring, Aeronaut. Research Labs. Rept. SM 213, Melbourne, Australia, 1953
  • [4] A. J. Wang and W. Prager, Plastic twisting of a circular ring sector, J. Mech. Phys. Solids 8, 169-175 (1955) MR 0069737
  • [5] W. Freiberger and W. Prager, Plastic twisting of thick-walled circular ring sectors, J. Appl. Mech. ASME Paper No. 55-A85 (1955) MR 0085787
  • [6] W. Prager and P. G. Hodge, Jr., Theory of perfectly plastic solids, John Wiley and Sons, New York, 1951, p. 73 MR 0051118
  • [7] W. Freiberger, The uniform torsion of an incomplete tore, Australian J. Sci. Research A, 2, 354-375 (1949) MR 0035622

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DOI: https://doi.org/10.1090/qam/81700
Article copyright: © Copyright 1956 American Mathematical Society

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