Elastic stresses due to a semi-infinite band of hydrostatic pressure acting over a cylindrical hole in an infinite solid

Recently C. J. Tranter1 has presented expressions for the stresses due to a finite band of hydrostatic pressure acting over part of the length of a cylindrical hole which extends through an infinite elastic solid. By a similar analysis, expressions for the stresses due to a semi-infinite band of hydrostatic pressure acting over the cylindrical hole can be found. Referring to the analysis by Tranter, it is evident that the only change in boundary conditions is that involving ov at r — a. A semi-infinite band of hydrostatic pressure, p, is equivalent to the sum of