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The second fundamental crack problem and the rigid line inclusion problem in plane elasticity

Das zweite fundamentale Problem des Risses und das Problem des starren Linieneinschlusses der ebenen Elastizität

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Summary

The second fundamental problem of plane isotropic elasticity for a cracked infinite medium, that is the problem in which the displacement derivatives are given along the crack edges, as well as the closely related rigid line inclusion problem in plane elasticity are treated by using the method of complex potentials. Without restrictive assumptions on geometry and boundary conditions, these problems are reduced to a complex Cauchy type singular integral equation along the crack or the inclusion, the numerical solution of which can easily be obtained by using the Lobatto-Chebyshev method.

Zusammenfassung

Das zweite fundamentale Problem der ebenen Elastizität im unendlichen, isotropen Medium mit einem Riß, d. h. das Problem, in welchem die Ableitungen der Verschiebungen entlang der Rißkanten gegeben sind, wie auch das stark verwandte Problem des starren Linieneinschlusses der ebenen Elastizität, werden mit Hilfe der Methode der komplexen Potentiale behandelt. Diese Probleme werden ohne einschränkende Annahmen über die Geometrie und die Randbedingungen zu eine entlang des Risses oder des Einschlusses geltende komplexe singuläre Cauchysche Integralgleichung reduziert, deren numerische Lösung leicht mit Hilfe der Lobatto-Chebyshevschen Methode erhalten werden kann.

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, The National Technical University of Athens, 5 K. Zographou Street, Zographou, 624, Athens, Greece

    N. I. Ioakimidis &  P. S. Theocaris

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  1. N. I. Ioakimidis
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  2. P. S. Theocaris
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Ioakimidis, N.I., Theocaris, P.S. The second fundamental crack problem and the rigid line inclusion problem in plane elasticity. Acta Mechanica 34, 51–61 (1979). https://doi.org/10.1007/BF01176257

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