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

Abstract

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