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Stresses in a Plate Pierced by two Unequal Circular Holes

Published online by Cambridge University Press:  04 July 2016

G. A. O. Davies  and
J. R. Hoddinott
G. A. O. Davies
Affiliation:
Department of Aeronautical Engineering, Sydney University
J. R. Hoddinott
Affiliation:
Department of Aeronautical Engineering, Sydney University
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Extract

The problem of two identical circular holes in an infinite sheet has been solved by Ling using bipolar co-ordinates and taking advantage of the double symmetry.

The case of any two unequal holes is of interest in that one common situation is that of a small circular hole close to a relatively larger one. In this case it is tempting merely to use the classical single hole solution, first for the larger hole and then for the small hole situated in the “uniform” stress field produced by the larger one. The accuracy of this simple method of superposition is examined.

The notation of Muskhelishvili is followed where the problem consists of finding two functions of the complex variable z=x+iy which are analytic in the region and satisfy the boundary conditions on both holes and at infinity.

Type
Technical notes
Information
The Aeronautical Journal , Volume 67 , Issue 631 , July 1963 , pp. 451 - 452
Copyright
Copyright © Royal Aeronautical Society 1963

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References

1.Ling, C. B.On the Stresses in a Plate Containing Two Circular Holes. Journal of Applied Physics, 19, 77, 1948.CrossRefGoogle Scholar
2.Muskhelishvili, N. I.Some Basic Problems of the Mathematical Theory of Elasticity. P. Noordhoff, 1953.Google Scholar
3.Buchwald, V. T. and Davies, G. A. O. Plane Elastostatic Boundary Value Problems of Doubly Connected Regions. Quart. Journal of Mechanics and Applied Mathematics. (To be published).Google Scholar