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On Boussinesq's problem and penny-shaped cracks

Published online by Cambridge University Press:  24 October 2008

A. E. Green
A. E. Green
Affiliation:
King's CollegeNewcastle-on-Tyne
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Extract

Harding and Sneddon(3) and Sneddon(6) have shown that the systematic application of Hankel transforms to the problem of the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch, reduces the problem essentially to one of solving a pair of integral equations belonging to a class which has been studied by Titchmarsh(8) and Busbridge(1). The same method has also been applied by Sneddon(7) to the problem of the distribution of stress in the neighbourhood of a circular crack in an elastic solid. In both types of problem the results are expressed in quite simple forms independent of Bessel functions and this suggests that there should be an alternative method of solution. It is now possible to supply such a method with the help of a recent paper by Copson(2) on the problem of the electrified disk. In addition, some generalization of the stress systems considered by Harding and Sneddon can be made since they confined their analysis to stresses which were symmetrical about an axis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 251 - 257
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Busbridge, I. W.Proc. London Math. Soc. (2), 44 (1938), 115.CrossRefGoogle Scholar
(2)Copson, E. T.Proc. Edinburgh Math. Soc. 8 (1947), 14.CrossRefGoogle Scholar
(3)Harding, J. W. and Sneddon, I. N.Proc. Cambridge Phil. Soc. 41 (1945), 16.CrossRefGoogle Scholar
(4)Love, A. E. H.Quart. J. Math. 10 (1939), 161.CrossRefGoogle Scholar
(5)Sack, R.Proc. Phys. Soc. London, 58 (1946), 729.CrossRefGoogle Scholar
(6)Sneddon, I. N.Proc. Cambridge Phil. Soc. 42 (1946), 29.CrossRefGoogle Scholar
(7)Sneddon, I. N.Proc. Roy. Soc. A, 187 (1946), 229.Google Scholar
(8)Titchmarsh, E. C.An Introduction to the Theory of Fourier Integrals (Oxford, 1937), p. 334.Google Scholar