A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations

[+] Author and Article Information
M. Guiggiani

Dipartimento di Costruzioni Meccaniche e Nucleari, Universita di Pisa, 56126 Pisa, Italy

G. Krishnasamy, T. J. Rudolphi

Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, Ames, IA 50011

F. J. Rizzo

Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Appl. Mech 59(3), 604-614 (Sep 01, 1992) (11 pages) doi:10.1115/1.2893766 History: Received April 27, 1990; Revised February 11, 1991; Online March 31, 2008


The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.

Copyright © 1992 by The American Society of Mechanical Engineers
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