Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90 degree V-notch with Neumann boundary conditions

Abstract

This report presents explicit analytical expressions for the primal, primal shadows, dual and dual shadows functions for the Laplace equation in the vicinity of a circular singular edge with Neumann boundary conditions on the faces that intersect at the singular edge. Two configurations are investigated: a penny-shaped crack and a 90^o V-notch