Ah, the Inglis paper--the bane of my existence. I searched for years to find this paper. Many people referenced it, but didn't have the actual paper in their library (sounds almost unethical to reference a source you don't actually possess, but I guess that's just me). This Inst. of Naval Arch. journal was very hard to find. Finally, I located a marvelous reference published by SPIE--a compilation of several historically significant fracture mechanics papers. This particular compendium has the Inglis paper--my torment continues,as othere are other important references that I cannot get.
The SPIE book is MS137 "Selected Papers on the Foundations of Linear Elastic Fracture Mechanics"
There is also an MS138, "Selected Papers on Crack Tip Stress Fields"
These are both very good, and recommended if you work with cracks and other places where the stress concentrates.
The equation CoryPad gave is the stress concentration at the hole edge. The full equation for the circular hole in an infinite plate is from Timothy Michael O'Shenko's book, Theory of Elasticity. Let S be the far field stress, in the y direction. Let Syy be the normal stress in the y-direction. Then
Syy=(S/2)*(2+(a/r)^2+3*(a/r)^4), where 'a' is the radius of the hole, and 'r' is the distance from the center of the hole. Naturally, r<a makes no sense.
Note that this is for a centered, open hole in an infinite plate. Your FE solution naturally has a finite plate. Now what? You can just keep extending those boundaries of the plate until the ratio of the maximum stress Syy at the edge of the hole, divided by "S" is near 3.0 (say to within 5%, or to within 1% if you are ambitious). This raises the larger question, I believe, is how do you decide your solution is good if you don't have the exact solution. This is a much larger discussion, so I'll not start it here.
Anyway, hope the equation above helps. Good hunting.
lease see FAQ731-376 for tips on how to make the best use of Eng-Tips.