Singular Shear-Force States in Elementary Plate Theory

Abstract

We show that the most classical Kirchhoff-Love theory of thin plates is compatible with the occurrence of a specific singular shear-force state in the interior of the body. It is well-known from Kirchhoff that, on the edge boundary of the plate, the specific shear-forces and the curve-gradient of the specific twisting-moments, measured per unit length, are statically inter-related. We observe and prove that a similar static equivalence holds for the edge boundary of any sub-body, and this allows many interpretations of the contact interactions that may take place between the parts of the plate. In particular, a specific shear-force acting on a smooth part of the edge boundary of a sub-body may depend upon its curvature, tending to a concentrated force at a sharp corner. The possibility of developing concentrated contact interactions is a general characteristic of non-simple continua, of which the theory of thin plates is but one representative example.