Stresses in a Plate Pierced by two Unequal Circular Holes

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Abstract
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.

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