Hypersingular formulation for boundary stress evaluation revisited. Part 1: Smooth boundaries.

Abstract

This work focuses on the (HBIE) hypersingular boundary integral equation,
also called traction equation, and on its use to evaluate the stress tensor
in linear elasticity. When the field point is moved to the boundary, by means
of a limit process, free terms come into play. As a common belief, they are
due to the strongly singular kernel: indeed it is proved that the hypersingular
kernel does not cause any free term when tractions are evaluated on
smooth boundaries with respect to the boundary surface normal (when the
concept of normal makes sense). The stress tensor along the boundary involves
surfaces with normal differing from the boundary normal, too. In this
case, free terms are proved to be generated also by the hypersingular kernel,
aside from the regularity of the boundary: their analysis is the main goal of
the present work.