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A new method for the numerical solution of singular integral equations appearing in crack and other elasticity problems

Eine neue Methode numerischer Lösungen singulärer Integralgleichungen, die in Riß-und anderen Problemen der Elastizität vorkommen

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Summary

The solution of many elasticity problems and particularly crack problems can be reduced to the solution of a singular integral equation with a Cauchy type kernel (or a system of such equations). In this paper a new method of numerical solution of singular integral equations with Cauchy type kernels is proposed, based on the replacement of the unknown function by another function. This method presents some advantages over the previous methods under appropriate conditions. An application of the method to a crack problem in plane elasticity is also made.

Zusammenfassung

Die Lösung vieler Probleme der Elastizität und besonders der Rißprobleme kann in Form einer singulären Integralgleichung vom Cauchy-Typ (oder eines Systems solcher Gleichungen) gelöst werden. In dieser Arbeit empfiehlt sich eine neue Methode numerischer Lösungen singulärer Integralgleichungen des Cauchy-Typs, in der die unbekannte Funktion durch eine andere Funktion ersetzt wird. Diese Methode hat manche Vorteile gegenüber früheren Methoden unter entsprechenden Bedingungen. Diese Methode kann auch für ein ebenes, elastisches Rißproblem Verwendung finden.

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  1. Schoof of Engineering, University of Patras, P. O. Box 25B, Patras, Greece

    N. I. Ioakimidis (Chair of Mathematics B')

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  1. N. I. Ioakimidis
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Ioakimidis, N.I. A new method for the numerical solution of singular integral equations appearing in crack and other elasticity problems. Acta Mechanica 39, 117–125 (1981). https://doi.org/10.1007/BF01173197

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  • DOI: https://doi.org/10.1007/BF01173197

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