On the three-dimensional stress field around a circular hole in a plate of arbitrary thickness

Abstract

An analytical solution for the three-dimensional stress field in a plate of an arbitrary thickness, 2h, and weakened by a cylindrical hole of radius a is presented. Far away from the hole, the plate is subjected to a uniform tensile load, σ0, in a direction parallel to the plane of the plate. The solution is shown to be derivable from a general 3D solution, which the first author constructed in a previous paper. The analysis shows the stress concentration factor to vary across the thickness and to be sensitive to the value of the radius to thickness ratio, a/h. Furthermore, it is shown that for ratios of (a/h)≧4, the results predicted by plane stress theory are more than adequate for engineering applications. Finally, the transition between plane stress and plane strain appears to occur at a/h=0.5.