Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90 degree V-notch with Neumann boundary conditions
Provides analytical tools for solving Laplace problems with singular edges, relevant for fracture mechanics and stress analysis, but is an incremental extension of existing mathematical frameworks.
This report derives explicit analytical expressions for primal, shadow, dual, and dual-shadow functions for Laplace equation near a circular crack and a 90° V-notch with Neumann boundary conditions, providing closed-form solutions for these singular geometries.
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.