Stress Concentration at a Nearly Circular Hole With Uncertain Irregularities

We study the stress concentration on the boundary of an uncertain nearly circular hole in an infinite elastic plane under uniform radial tension at infinity. 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 the form r = R + εh(θ), where R is the radius of the unperturbed circle and ε is a small parameter. First, we find an asymptotic solution for the stress concentration factor around the hole for any profile h(θ). Then we consider a certain set of bounded profiles, and we find the specific profile that yields the maximum stress concentration factor. 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.