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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 3, Pages 561-574
http://dx.doi.org/10.1155/S0161171288000675

On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity

Department of Mathematics and Mechanics, The National Technical University of Athens, Athens GR - I57 73, Greece

Received 3 February 1987; Revised 11 October 1987

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the present report, we investigate the formulation, for the numerical evaluation of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity. Some simple formulas are given for the numerical solution of the general case of the multidimensional singular integrals. Moreover a numerical technique is also established for the numerical solution of some special cases of the multidimensional singular integrals like the two - and three - dimensional singular integrals. An application is given to the determination of the fracture behaviour of a thick, hollow circular cylinder of viscoelastic material restrained by an enclosing thin elastic ring and subjected to a uniform pressure.