THE WEDGE PARADOX AND A CORRESPONDENCE PRINCIPLE

The wedge paradox for stress-free boundaries is the wedge loaded by a concentrated moment at the vertex (Carothers problem). The paradox con sists of the fact the for wedges smaller than a half-space the solutio n exists, while for wedges bigger than a half-space as shown by Sternb erg-Koiter the solution does not exist. We examine the possiblity of a paradox for clamped-clamped boundary conditions. We obtain the soluti on for a clamped-clamped wedge loaded by a concentrated couple at an i nterior point and show that for wedges smaller than a half-space the l imit is zero as the moment approaches the vertex (i.e. the clamped wed ge absorbs the concentrated couple), for a half-space it is a constant , and for angles bigger than a half-space the limit does not exist (pa radox). Moreover, from the solution for the clamped wedge, taking the limit as Poisson's ratio tends to one, the solution for the stress-fre e wedge is retrieved (Carothers) according to the correspondence betwe en cavities and rigid inclusions established by Dundurs (1989) and Mar kenscoff (1993).