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The distribution of stress in the neighbourhood of a flat elliptical crack in an elastic solid

Published online by Cambridge University Press:  24 October 2008

A. E. Green  and
I. N. Sneddon
A. E. Green
Affiliation:
King's CollegeNewcastle-on-Tyne
I. N. Sneddon
Affiliation:
The UniversityGlasgow
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Extract

This paper is mainly concerned with the distribution of stress near a flat elliptical crack in a body of infinite extent under a uniform tension at infinity perpendicular to the plane of the crack. After an analytical solution of this problem was found the authors received a copy of a paper by Sadowsky and Sternberg (3) in which they solved the more general problem of the stress concentration around a tri-axial ellipsoidal cavity in an elastic body of infinite extent, the body at infinity being in a uniform state of stress whose principal axes are parallel to the axes of the cavity. The method of solution adopted by the present writers for the special case of the elliptical crack is somewhat different from the more general work of Sadowsky and Sternberg, and is, moreover, surprisingly simple, so it seems to be of value to present this solution here.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 1 , January 1950 , pp. 159 - 163
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

REFERENCES

(1)Green, A. E.Proc. Roy. Soc. A, 195 (1949), 533.Google Scholar
(2)Lamb, H.Hydrodynamics, 6th. edit. (Cambridge, 1932), pp. 151–2.Google Scholar
(3)Sadowsky, M. A. and Sternberg, E.J. Appl. Mech. 16 (1949), 149.CrossRefGoogle Scholar
(4)Whittaker, E. T. and Watson, G. N.A course of modern analysis (Cambridge, 1927), Ch. 23.Google Scholar