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The Stresses Around Holes in Plane Sheets

Published online by Cambridge University Press:  07 June 2016

I. C. Howard
Affiliation:
Department of Mathematics, Manchester University
L. S. D. Morley
Affiliation:
Royal Aircraft Establishment, Farnborough
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Summary

This paper describes the application of a previously published variational method to the solution of problems of holes in plane elastic sheets and is used to obtain numerical values for the specific case of an elliptic hole in an infinite sheet under tension at infinity. Two kinds of boundary condition at the hole are discussed. The first is that when the hole is unreinforced and stress free, and the second that when the hole is uniformly reinforced by a compact member. The results of the calculations are compared with those from known solutions to the problem, and the accuracy of the present method is investigated. These results provide a useful background to wider application of the method.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1967

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References

1. Mansfield, E. H. Neutral holes in plane sheet-reinforced holes which are elastically equivalent to the uncut sheet. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 6, p. 370, 1953.CrossRefGoogle Scholar
2. Muskhelishvili, N. I. Some basic problems of the mathematical theory of elasticity. Noordhoff, Groningen, 1953.Google Scholar
3. Sobey, A. J. The estimation of stresses around unreinforced holes in infinite elastic sheets. R & M 3354, 1962.Google Scholar
4. Morley, L. S. D. A variational method of solution for problems in plane elasticity. Journal of the Institute of Mathematics and its Applications, Vol. 1, p. 76, 1965.CrossRefGoogle Scholar
5. Chen, Lin-Si. In Problems of continuum mechanics, p. 69. Noordhoff, Groningen, 1961.Google Scholar
6. Wittrick, W. H. The stresses around reinforced elliptical holes in plane sheet Aeronautical Research Laboratories (Melbourne), Report SM 267, 1959.Google Scholar