On Boussinesq's problem and penny-shaped cracks
- 1 April 1949
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 45 (2), 251-257
- https://doi.org/10.1017/s0305004100024804
Abstract
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.Keywords
This publication has 7 references indexed in Scilit:
- On the problem of the electrified discProceedings of the Edinburgh Mathematical Society, 1947
- Extension of Griffith's theory of rupture to three dimensionsProceedings of the Physical Society, 1946
- The distribution of stress in the neighbourhood of a crack in an elastic solidProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1946
- Boussinesq's problem for a flat-ended cylinderMathematical Proceedings of the Cambridge Philosophical Society, 1946
- The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punchMathematical Proceedings of the Cambridge Philosophical Society, 1945
- BOUSSINESQ'S PROBLEM FOR A RIGID CONEThe Quarterly Journal of Mathematics, 1939
- Dual Integral EquationsProceedings of the London Mathematical Society, 1938