Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Axial displacement dislocations for the hollow cone and the hollow sphere

Authors: J. N. Goodier and J. C. Wilhoit Jr.
Journal: Quart. Appl. Math. 13 (1955), 263-269
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/72656
MathSciNet review: 72656
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Abstract: Simple solutions in closed form are given for the dislocational states of stress in a hollow cone (Fig. 3) or a hollow sphere (Fig. 5) induced by making an axial cut, and imposing a rigid-body displacement of one face of the cut relative to the other, in the axial direction. The problems are solved by adaptations of the Saint-Venant torsion theory, and of J. H. Michell's theory of torsion of non-uniform shafts.

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

  • [1] V. Volterra, Sur l'equilibre des corps élastiques multiplement connexés, Ann. Sci. de l'Ecole Normale Supérieure, Ser. 3, 24, 401 (1907)
  • [2] J. C. Wilhoit, Jr., An addition to Poritsky's solution of a differential equation of torsion, Quart. Appl. Math. 11, 499 (1954) MR 0058426
  • [3] S. Ghosh, On some many-valued solutions of the equations of elastic equilibrium, in polar co-ordinates, Z. angew. Math. u. Mech. 12, 188 (1932)

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DOI: https://doi.org/10.1090/qam/72656
Article copyright: © Copyright 1955 American Mathematical Society

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