Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On finite expansion of a hole in a thin infinite plate

Authors: P. G. Hodge Jr. and R. Sankaranarayanan
Journal: Quart. Appl. Math. 16 (1958), 73-80
MSC: Primary 73.00
DOI: https://doi.org/10.1090/qam/102974
MathSciNet review: 102974
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Abstract: A complete solution for all values of applied pressure is obtained for the expansion of a hole of zero radius in an initially uniform infinite sheet. The analysis is compared with those of previous investigators and found to be simpler and/or more complete. It is shown that the results are applicable to the expansion of a finite hole in a uniform sheet and to the expansion of a hole in a tapered sheet.

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  • [1] W. Prager, On the use of singular yield conditions and associated flow rules, J. Appl. Mech. 20, 317-320 (1953) MR 0059770
  • [2] P. G. Hodge, Jr., Plastic bending of an annular plate, J. Math. & Phys. 36, 130-137 (1957)
  • [3] G. I. Taylor, The formation and enlargement of a circular hole in a thin plastic sheet, Quart. J. Mech. Appl. Math. 1, 103-124 (1948) MR 0025923
  • [4] R. Hill, Plastic distortion of non-uniform sheets, Phil. Mag. Ser. 7, vol. xi, 971-983 (1949) MR 0032368
  • [5] J. M. Alexander and H. Ford, On expanding a hole from zero radius in a thin infinite plate, Proc. Roy. Soc. A226, 543-561 (1954) MR 0070414
  • [6] R. v. Mises, Mechanik der plastischen Formaenderung von Kristallen, ZAMM 8, 161-185 (1928)
  • [7] W. Prager, The theory of plasticity--a survey of recent achievements, James Clayton Lecture, Inst. Mech. Engrs., London, 1955
  • [8] P. G. Hodge, Jr., Minimum principles of piecewise linear isotropic plasticity, J. Ratl. Mech. and Anal. 5, 917-938 (1956) MR 0082289

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DOI: https://doi.org/10.1090/qam/102974
Article copyright: © Copyright 1958 American Mathematical Society

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