MECHANICS RESEARCH ~ICATIONS Voi.15(2), 87-90, 1988. Printed in the USA. 0093-6413/88 $3.00 + .00 Copyright (c) 1988 Pergamon Press plc STRESS SINGULARITY AROUND TWO NEARBY HOLES Robert W. Zimmerman Department of Mechanical Engineering University of California Berkeley, CA 94720 USA (Received 20 July 1987; accepted for print 8 February 1988) Introduction The problem of determining the stresses in a plate containing a pair of circular holes has received much attention [1,2,3,4]. The most important feature of the solution of this problem is the value of the maximum stress concentration at the edges of the holes. For the case of transverse tension (i.e. load perpendicular to the line connect- ing the centers of the two holes), the maximum stress concentration, which occurs at the point on the boundary of the hole which is nearest to the neighboring hole, becomes unbounded as the distance between the holes decreases. Of particular interest is the form of the stress singularity in the limit as the holes become tangent to each other. It has recently been found numerically by Duan et al. [4] that this singularity seems to be of the form Ttt/Too = C/x/~, where Tt~ is the hoop stress, Too is the tension at infinity, ~ is the distance between the edges of the holes divided by the hole diameter, and C is some constant. Although an analytical solution to this problem has been found by Ling [l], it is in the form of an extremely complicated and slowly convergent infinite series whose behavior in the limiting case of t--~0 is not readily apparent. In this paper, a careful analysis of Ling's solution reveals that the order of the singularity is in fact 1/x/~, but the value of the numerical constant C is slightly different (1.94 instead of 2.13) than that found in [4]. Analysis We start with the observation that since longitudinal tension always leads to finite stresses at the hole boundaries, the singular part of the stress concentration for the case of transverse tension can be found by examining the solution for equal biaxial stresses (which is somewhat simpler in form). From [1], the hoop stresses at the edges of the hole are given by oo sinhnacosn~" ] T~t" - 2(cosha - cos0 Ksinha 1 + 4 ~ sinh2na + nsinh2a n=l where (1) 87