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Boussinesq's problem for a flat-ended cylinder

  • Ian N. Sneddon (a1)

1. In a recent paper(1) expressions were found for the elastic stresses produced in a semi-infinite elastic medium when its boundary is deformed by the pressure against it of a perfectly rigid body. In deriving the solution of this problem—the ‘Boussinesq’ problem—it was assumed that the normal displacement of a point within the area of contact between the elastic medium and the rigid body is prescribed and that the distribution of pressure over that area is determined subsequently. The solutions for the special cases in which the free surface was indented by a cone, a sphere and a flat-ended cylindrical punch were derived, but no attempt was made to give a full account of the distribution of stress in the interior of the medium in any of these cases.

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(1)Harding, J. W. and Sneddon, I. N.Proc. Cambridge Phil. Soc. 41 (1945), 16.
(2)Krynine, D. F.Soil mechanics (New York, 1941), Chap. IV.
(3)Terzaghi, K.Theoretical soil mechanics (New York, 1943), p. 367.
(4)Love, A. E. H.Philos. Trans. A, 228 (1929), 377.
(5)Terezawa, K.J. Coll. Sci. Tokyo, 37 (1916), article 7.
(6)Watson, G. N.The theory of Bessel functions (Cambridge, 1922), p. 385.
(7)Nadai, A.Plasticity (New York, 1931), Fig. 313.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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