Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T03:57:49.029Z Has data issue: false hasContentIssue false
  • English
  • Français

Boussinesq's problem for a rigid cone

Published online by Cambridge University Press:  24 October 2008

Ian N. Sneddon
Ian N. Sneddon
Affiliation:
The Department of Natural PhilosophyThe University of Glasgow
Get access Rights & Permissions [Opens in a new window]

Extract

1. The problem of determining the distribution of stress in a semi-infinite solid medium when its plane boundary is deformed by the pressure against it of a perfectly rigid cone is of considerable importance in various branches of applied mechanics. It arises in soil mechanics where the cone is the base of a conical-headed cylindrical pillar and the semi-infinite medium is the soil upon which it rests (1). In this instance the distribution of stress in the soil is known to be more or less similar to that calculated on the assumption that the soil is a perfectly elastic, isotropic and homogeneous medium, at least if the factor of safety of a mass of soil with respect to failure by plastic flow exceeds a value of about three (2). The same problem occurs in the theory of indentation tests in which a ductile material is indected by cylindrical punches with conical heads (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 4 , October 1948 , pp. 492 - 507
Copyright
Copyright © Cambridge Philosophical Society 1948

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Krynine, D. F.Soil mechanics (New York, 1941), Chap. iv.Google Scholar
(2)Terzaghi, K.Theoretical soil mechanics (New York, 1943), p. 367.CrossRefGoogle Scholar
(3)Bishop, R. F., Hill, R. and Mott, N. F.Proc. Phys. Soc. 57 (1945), 147.CrossRefGoogle Scholar
(4)v. Kármán, Th. and Duwez, P.Comptes rendus du 6econgres de mecan. appl. (in course of publication).Google Scholar
(5)Prandtl, L.Z. angew. Math. Mech. 3 (1923), 6, 401.CrossRefGoogle Scholar
(6)Hill, R., Lee, E. H. and Tupper, S. J.Proc. Roy. Soc. A, 188 (1947), 273.Google Scholar
(7)Boussinesq, J.Applications des potentiels (Paris, 1885).Google Scholar
(8)Love, A. E. H.Quart. J. Math. 10 (1939), 161.CrossRefGoogle Scholar
(9)Harding, J. W. and Sneddon, I. N.Proc. Cambridge Phil. Soc. 41 (1945), 16.CrossRefGoogle Scholar
(10)Sneddon, I. N.Proc. Cambridge Phil. Soc. 42 (1946), 29.CrossRefGoogle Scholar
(11)Watson, G. N.The theory of Bessel functions (2nd ed., Cambridge, 1944).Google Scholar
(12)Sneddon, I. N.Proc. Roy. Soc. A, 187 (1946), 229.Google Scholar
(13)Rayleigh, Lord. Phil. Mag. (6), 11 (1906), 283.CrossRefGoogle Scholar
(14)Hencky, H.Z. angew. Math. Mech. 4 (1924), 323.CrossRefGoogle Scholar
For further references see Nadai, A.Handbuch der Physik, 6, p. 470.Google Scholar