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.

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

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