Summary
Discretization of various integral equations of the second kind in elastostatic boundary value problems leads to singular or almost singular systems of algebraic equations, i.e. the determinants of the coefficient matrices vanish or are extremely small. The reason for this lies in the fact that the integral operators have isolated zero eigenvalues. In this paper a method of removing the zero eigenvalues is developed which is based mainly on mechanical aspects.
The results of the investigations are presented in such a way that it is possible to apply the method without understanding all details of its deduction.
Section 1 contains an extensive survey of the paper.
Zusammenfassung
Die Diskretisierung zahlreicher Integralgleichungen zweiter Art für Randwertprobleme der Elastostatik liefert singuläre oder fast singuläre Systeme algebraischer Gleichungen, d.h., die Determinanten der Koeffizientenmatrizen verschwinden oder sind sehr klein. Der Grund dafür liegt darin, daß die Integraloperatoren isolierte Nulleigenwerte besitzen. In diesem Aufsatz wird eine hauptsächlich auf mechanischen Gesichtspunkten basierende Methode zur Beseitigung der Nulleigenwerte entwickelt.
Die Ergebnisse der Untersuchungen werden so dargestellt, daß die Methode auch angewendet werden kann, ohne alle Details ihrer Herleitung zu verstehen.
Kapitel 1 enthält einen ausführlichen Überblick über den Aufsatz.
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Heise, U. Removal of the zero eigenvalues of integral operators in elastostatic boundary value problems. Acta Mechanica 41, 41–61 (1981). https://doi.org/10.1007/BF01246903
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DOI: https://doi.org/10.1007/BF01246903