Stress concentrations around a pressurized hole close to a uniformly loaded boundary

The elastic stresses arising around a pressurized circular hole close to a free or uniformly loaded boundary are examined. The boundary near to the hole can represent the periphery of a circular disc, the straight edge of a half-plane, or the contour of a second circular hole. All three configurations are modelled with the same general geometry, described by means of bipolar coordinates, from which each particular shape is obtained by assigning a suitable value to the curvature of the adjacent boundary. An exact solution found in the literature, covering the cases of a pressurized hole cut in a disc or in a half-plane, is developed semi-analytically to solve the third case of two arbitrary, loaded, adjacent holes. For the three cases examined, closed-form expressions are derived for the stress distributions along the contour of the hole and along the nearby edge. These expressions hold true for any geometry and for arbitrary combinations of uniform loadings on the two boundaries. For the special case of a pressurized hole close to a free edge, readily accessible charts of stress concentration factors are also provided.