Further Paradoxes in Generalized Levy Problems

The classical solution of Levy's plate problem breaks down for a critical plate angle, with both stress and displacement fields becoming unbounded throughout the plate. The same sort of paradoxical response occurs in traditional solutions for other critical angles if the pressure in Levy's original problem is replaced by a constant shear traction. These breakdowns can be rectified by suitably supplementing classical fields. In this note, a further generalization of Levy's problem is considered. This entails clamping the plate edge without applied tractions. Critical angles for which traditional analysis breaks down are identified, and new solutions are developed for these angles. This revised version was published online in July 2006 with corrections to the Cover Date.