On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics

Summary.  In this paper, we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper also includes two examples taken from fracture mechanics and acoustics: a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen. Received July 15, 2002; revised November 13, 2002 Published online: May 8, 2003 The paper has been supported by Italian Ministry for Instructions, University and Research (M.I.U.R.) through its national and local projects.