A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method

[+] Author and Article Information
M. Guiggiani, A. Gigante

Dipartimento di Costruzioni Meccaniche e Nucleari, Universita degli Studi di Pisa, 56126 Pisa PI, Italy

J. Appl. Mech 57(4), 906-915 (Dec 01, 1990) (10 pages) doi:10.1115/1.2897660 History: Received May 05, 1989; Revised November 01, 1989; Online March 31, 2008


This paper presents a new general method for the direct evaluation of Cauchy principal value integrals in several dimensions, which is an issue of major concern in any boundary element method analysis in applied mechanics. It is shown that the original Cauchy principal value integral can be transformed into an element-by-element sum of regular integrals, each one expressed in terms of intrinsic (local) coordinates. The actual computation can be performed by standard quadrature formulae and can be easily included in any existing computer code. The numerical results demonstrate the accuracy and efficiency of the method, along with its insensitivity to the mesh pattern. This new method has full generality and, therefore, can be applied in any field of applied mechanics. Moreover, there are no restrictions on the numerical implementation, as the singular integrals may be defined on surface elements or internal cells of any order and type.

Copyright © 1990 by The American Society of Mechanical Engineers
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