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Doubly-periodic array of cracks in an infinite isotropic medium

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Abstract

The problem of a doubly-periodle array of 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 Cauchy-type singular integral equations and application of the Gauss or Lobatto-Chebyshev method of numerical solution of such equations.

Zusammenfassung

Das Problem einer zwei-periodischer Anordung gekrümmten Rissen in einem unendlichem isotropem Medium im allgemeinen ebener Spannung-bzw Dehnung-Zustand, unter Anwendung der Methode von komplexen Potentialen von Muskhelishvili [1], ist in einer Cauchyscher komplexer singulärer Integral-Gleichung auf einem der Rissen reduziert. Diese Gleichung kann weiter numerisch gelöst werden bei Transformation in einem System von zwei reelen Cauchyschen singulären Integral-Gleichungen und bei Anwendung der Methoden von Gauss oder Lobatto-Chebyshev für die numerische Resolution solcher Gleichungen.

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, The National Technical University, (625), 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. Doubly-periodic array of cracks in an infinite isotropic medium. J Elasticity 8, 157–169 (1978). https://doi.org/10.1007/BF00052479

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  • DOI: https://doi.org/10.1007/BF00052479

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