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Some thermoelastic stress distributions in an infinite solid and a thick plate containing penny-shaped cracks

Published online by Cambridge University Press:  26 February 2010

R. Shail
R. Shail
Affiliation:
The Department of Applied Mathematics, The University of Liverpool.
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Extract

In engineering practice an important class of problems concerns the evaluation of the thermal stresses set up in a heated elastic solid containing cracks. The calculation of the thermal stresses in an infinite space, in which an axially symmetric heat flux across the faces of a penny-shaped crack is prescribed, was first carried out by Olesiak and Sneddon [1], using integral transform techniques. Their solution of the statical equations of thermoelasticity is appropriate to the case of a crack whose faces are stress free and gives zero shear stress on the plane containing the crack. Williams [2] has subsequently shown that the displacement vector in [1 ] can be written in terms of two harmonic functions, one of which is directly related to the temperature field, and has indicated how the analysis of [1] can be reduced to certain simple potential boundary value problems.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 2 , December 1964 , pp. 102 - 118
Copyright
Copyright © University College London 1964

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References

1. Olesiak, Z. and Sneddon, I. N., Arch. for Rat. Mech. and Annl., 4 (1960), 238.CrossRefGoogle Scholar
2. Williams, W. E., Zeit. ang. Math. Phy., 12 (1961), 452.CrossRefGoogle Scholar
3. Nowacki, W., Thermoelasticily (Pergamon, 1962).Google Scholar
4. Cooke, J. C., Quart. J. Mech. App. Math., 9 (1956), 103.CrossRefGoogle Scholar
5. Williams, W. E., Zeit. ang. Math. Phy., 13 (1962), 133.CrossRefGoogle Scholar
6. Collins, W. D., Proc. Edinburgh Math. Soc., 12 (1960), 95.CrossRefGoogle Scholar
7. Collins, W. D., Proc. Roy. Soc. (A), 266 (1962), 359.Google Scholar
8. Collins, W. D., Malhematika, 6 (1959), 120.CrossRefGoogle Scholar
9. Watson, G. N., Theory of Bessel functions (Cambridge, 1944).Google Scholar
10. Sneddon, I. N. and Tait, R. J., Int. J. Engng. Sci., 1 (1963), 391.CrossRefGoogle Scholar
11. Howland, R. C. J., Phil. Trans. Roy. Soc. (A), 229 (1930), 49.Google Scholar
12. Nelson, C. W., Math. of Comp., 15 (1961), 12.Google Scholar
13. Lebedev, N. N. and Ufliand, S. Ia., Appl. Math. Mech. Leningr., 22 (1958), 442.CrossRefGoogle Scholar