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Axial symmetric stress distributions in aeolotropic hexagonal crystals. The problem of the plane and related problems

Published online by Cambridge University Press:  24 October 2008

H. A. Elliott
H. A. Elliott
Affiliation:
Department of MathematicsMcGill UniversityMontreal
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Extract

The method of transforms (7), (2) is shown to be directly applicable to the case of axial symmetric stress distributions in hexagonal crystals. It is shown that solutions for problems of indentation of the hexagonal plane by rigid punches can be found for punches of arbitrary axial symmetric shape. Solutions are given in full for the cases of spherical, conical and circularly cylindrical punches.

The same method is used to find the solutions for a material containing disk-shaped cracks between hexagonal planes and the results for the isotropic case deduced from the general solution.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 4 , October 1949 , pp. 621 - 630
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Busbridge, I.Proc. London Math. Soc. (2), 44 (1938), 115.CrossRefGoogle Scholar
(2)Elliott, H. A. and Sneddon, I. N.Quart. Appl. Math. 4 (1946), 262.Google Scholar
(3)Elliott, H. A.Proc. Phys. Soc. London, 59 (1947), 208.CrossRefGoogle Scholar
(4)Elliott, H. A.Proc. Cambridge Phil. Soc. 44 (1948), 522.CrossRefGoogle Scholar
(5)Green, A. E.Proc. Roy. Soc. A, 184 (1945), 231.Google Scholar
(6)Griffith, A. A.Philos. Trans. 221 (1921), 163.Google Scholar
(7)Harding, J. W. and Sneddon, I. N.Proc. Cambridge Phil. Soc. 41 (1945), 16.CrossRefGoogle Scholar
(8)Inglis, C. E.Trans. Instn Nav. Archit., London, 55 (1913), 219.Google Scholar
(9)Sack, R.Proc. Phys. Soc. London, 58 (1946), 729.CrossRefGoogle Scholar
(10)Titchmarsh, E. C.Theory of Fourier integrals (Oxford, 1937).Google Scholar
(11)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).Google Scholar
(12)Sneddon, I. N.Proc. Roy. Soc. A, 187 (1946), 229.Google Scholar