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A Punch Problem for a Transversely Isotropic Layer

Published online by Cambridge University Press:  24 October 2008

A. H. England
A. H. England
Affiliation:
King's CollegeNewcastle Upon Tyne
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Extract

In this note we consider the axially symmetric indentation of a transversely isotropic layer resting on a rigid foundation. The corresponding half-space problems both for isotropic and transversely isotropic materials have been solved previously (see (l), (2), (3), p. 455) and, more recently, the present problem has been solved for isotropic materials in (4) and (5) using methods different from that given in this paper. In § 2 the problem is reduced to the solution of a Fredholm integral equation of the second kind. In § 3 and subsequently the case of incomplete penetration by the punch, when the radius of the circle of contact is less than that of the end face of the punch, is considered. Finally, in §4 the results are illustrated by considering a hemispherically ended punch.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 3 , July 1962 , pp. 539 - 547
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Green, A. E., and Zerna, W., Theoretical elasticity (Oxford, 1954).Google Scholar
(2)Elliott, H. A., Proc. Cambridge Philos. Soc. 45 (1949), 621.CrossRefGoogle Scholar
(3)Sneddon, I. N., Fourier transforms (McGraw-Hill; New York, 1951).Google Scholar
(4)Lebedev, N. N. and Ufliand, Ia. S., Appl. Math. Mech. 22 (1958), 442.CrossRefGoogle Scholar
(5)Vorovich, I. I. and Ustinov, Iu. A., Appl. Math. Mech. 23 (1959), 637.CrossRefGoogle Scholar
(6)Collins, W. D., Proc. Edinburgh Math. Soc. 12 (1960), 95.CrossRefGoogle Scholar
(7)Segedin, C. M., Mathematika, 4 (1957), 156.CrossRefGoogle Scholar
(8)Sneddon, I. N., Mathematika, 6 (1959), 118.CrossRefGoogle Scholar