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Array of periodic curvilinear cracks in an infinite isotropic medium

Anordnung von periodisch gekrümmten Rissen in einem unendlichen, isotropen Medium.

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Summary

The problem of an array of periodic curvilinear cracks in an infinite isotropic medium under conditions of generalized plane stress or plane strain is reduced, by using the method of complex potentials of Muskhelishvili [1], to a complex Cauchy-type singular integral equation on one of the cracks, which can be further numerically solved by reduction to a system of two real Cauchytype singular integral equations and application of the Lobatto-Chebyshev method of numerical solution of such equations. Applications to the cases of arrays of straight or arc-shaped cracks are also given.

Zusammenfassung

Das Problem der Anordnung periodisch gekrümmter Risse in einem unendlichen, isotropen Medium wird untersucht. Der ebene Spannungs-bzw. Dehnungszustand wird für einen der Risse mit Hilfe komplexer Potentiale des Muskhelishvilischen Verfahrens in eine komplexe Cauchysche singuläre Integralgleichung reduziert. Die numerische Lösung des Problems erfolgt durch eine weitere Reduktion in ein System mit zwei Cauchyschen singulären Integralgleichungen unter Anwendung des Lobatto-Chebyshevschen Verfahrens. Beispiele für den Fall der Anordnung gerader wie auch bogenförmiger Risse werden angegeben.

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References

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, The National Technical University of Athens, 5 K. Zographou St., Zographou, 625, Athens, Greece

    N. I. Ioakmidis &  P. S. Theocaris

Authors
  1. N. I. Ioakmidis
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  2. P. S. Theocaris
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Ioakmidis, N.I., Theocaris, P.S. Array of periodic curvilinear cracks in an infinite isotropic medium. Acta Mechanica 28, 239–254 (1977). https://doi.org/10.1007/BF01208801

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  • DOI: https://doi.org/10.1007/BF01208801

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