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On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity

über eine neue, in der Elastizitätstheorie anwendbare Integrationsregel mit Benutzung der Gegenbauer-Polynome zur Lösung singulärer Integralgleichungen

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Summary

A new technique is proposed for the numerical solution of the Cauchy-type singular integral equations, by using the well known Gegenbauer polynomials. A large class of problems of mathematical physics, and especially several plane and antiplane elasticity problems, not possessing closed-form solutions, can be reduced to the solution of certain systems of such a type of singular integral equations. Also by using a certain method the new formula which is used for the numerical solution of the Cauchy-type integral equations can be extended for the general type of the finite-part singular integrals, too.

übersicht

Es wird eine neue Technik zur numerischen Lösung von Cauchyschen singulÄren Integralgleichungen unter Benutzung der bekannten Gegenbauer-Polynome vorgeschlagen. Eine gro\e Klasse von Problemen der mathematischen Physik und besonders verschiedene ebene und antiplanare Probleme der ElastizitÄtstheorie, welche keine geschlossenen Lösungen besitzen, können zur Lösung auf solche singulÄren Integralgleichungen zurückgeführt werden. Die für die numerische Lösung von Cauchyschen Integralgleichungen hergeleitete Methode kann für den allgemeinen Fall singulÄrer Integrale mit endlichem Anteil erweitert werden.

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  1. Dept. of Engineering Science Section of Mechanics, National Technical University of Athens, 5 Heroes of Polytechnion Av., GR-157 73, Athens, Greece

    E. G. Ladopoulos

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Ladopoulos, E.G. On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity. Ing. arch 58, 35–46 (1988). https://doi.org/10.1007/BF00537198

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