The wedge subjected to tractions proportional to rn: A paradox resolved

The classical two-dimensional solution for the stress distribution in an elastic wedge subjected to tractions proportional to r"(n/> 0) becomes infinite when the wedge angle 2c~ and the constant n satisfy the definite relations, this is a paradox. For n = 0 it was resolved by Dempsey [Journal of Elasticity l 1, 1-10 ( 1981 )] and Ting [Journal of Elasticity 14, 235-247 ( 1984)], for n > 0 and 2~ = it or 2~ it was resolved by Wang [Acta Mechanica Sinica 18(3), 242-252 (1986)]. However, the above investigations provided only a little resolution of it. In this paper all the cases of the paradox have been studied by employing the complex variable method, and the corresponding bounded solutions are obtained. Moreover, the secondary paradox is discovered in the problem, i.e.. the initial solution for the paradox is still infinite for some special values of (n, 7), and this is also resolved here. From the results obtained it can be observed that the stress distribution contains a/ʹ(In r) term for the paradox and a r"(ln r) 2 term more for the secondary paradox. © 1998 Elsevier Science Ltd. All rights reserved