Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Zone estimates in the elastic-plastic torsion problem


Author: Wan Lee Yin
Journal: Quart. Appl. Math. 35 (1977), 410-414
MSC: Primary 73.35
DOI: https://doi.org/10.1090/qam/462082
MathSciNet review: 462082
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Abstract | References | Similar Articles | Additional Information

Abstract: Using continuity and jump conditions across the elastic-plastic interface, we show that the curvature of the shearing stress lines in the plastic zone of a simply connected bar under torsion is bounded above by a number proportionate to the twisting angle. For sufficiently large torsion the above geometrical condition defines a region in the cross-section which is a priori elastic. This lower bound for the elastic zone in the sense of set inclusion is supplemented by an upper bound for the zone area.


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

  • [1] R. Hill, The Mathematical Theory of Plasticity, Oxford, at the Clarendon Press, 1950. MR 0037721
  • [2] W. Prager and P. G. Hodge, Jr., Theory of perfectly plastic solids, Wiley, New York, 1951, p. 68
  • [3] Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers John Wiley & Sons, Inc. New York-London-Sydney, 1964. MR 0163043

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DOI: https://doi.org/10.1090/qam/462082
Article copyright: © Copyright 1977 American Mathematical Society


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