Stress concentration at a nearly circular hole with uncertain irregularities

The stress concentration on the boundary of an uncertain nearly circular hole in an infinite elastic plane under uniform radial tension at infinity is studied. The uncertainty in the deviation of the hole profile from an ideal circle is modeled deterministically. The shape of the hole boundary in polar coordinates is assumed to have form r = R + epsilon-h (theta), where R is the radius of the unperturbed circle and epsilon is a small parameter. First, an asymptotic solution is found for the stress concentration factor around the hole for any profile h (theta). Then a certain set of bounded profiles is considered and the specific profile that yields the maximum stress concentration factor is found. This may provide the designer with a useful "worst case" information regarding the influence of the uncertainty of the hole shape on the uncertainty of the resulting stress concentration factor.