© 1985 by Oxford University Press
ELASTIC WEDGE SUBJECTED TO ANTIPLANE SHEAR TRACTIONS-A PARADOX EXPLAINED
( Department of Civil Engineering, Mechanics and Metallurgy, University of Illinois at Chicago P.O. Box 4348, Chicago, Illinois 60680, U.S.A. )
The elementary solution for the stress distribution near the apex of an elastic wedge subjected to a uniform antiplane shear traction on one side of the wedge becomes infinite for every point (r, 
) in the wedge when the wedge angle 2
approaches 
or . The paradox can be resolved by adding to the elementary solution a homogeneous solution which satisfies the traction-free boundary condition at the sides of the wedge. By letting the coefficient of the homogeneous solution depend on and approach infinity with opposite sign as 2 approaches or 2, one obtains a bounded solution. Similar procedures were used in resolving the paradoxes in other related problems. However, the addition of a homogeneous solution with its coefficient tending to infinity,though mathematically permissible, appears to have an arbitrariness which defies explanation. For the present problem, we are able to obtain an explicit solution for the wedge which is fixed at r=r0 ina form of infinite series. As 2 approaches or 2 , the first two terms of the solution have opposite signs and tend to infinity. Hence, the homogeneous solution with its coefficient tending to infinity as 2 tends to or2 exists. We also show that the infinite series can be reduced to integrals. For 2equal to or 2 the integrals yield a closed-form solution. Finally, for the wedge angle 2 subjected to non-symmetric tractions, thestresses have O(In r) as well as O(r1/2) singularities.