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Limiting equilibrium of a plane with a circular hole

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Ukrainian Mathematical Journal Aims and scope

Abstract

The elastoplastic state of a compressible isotropic plane with a circular hole is studied by the method of a small parameter. An unknown boundary separating the domain of limiting equilibrium and the elastic domain is determined. We construct the complex Kolosov-Muskhelishvili functions that describe the elastic state of a plane and compare these with the solutions of Galin's problem.

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References

  1. V. V. Sokolovskii,Statistics of a Free-Flowing Medium [in Russian], Gostekhizdat, Moscow (1954).

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  2. N. I. Muskhelishvili,Certain Basic Problems in the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).

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  3. L. A. Galin,Elasoplastic Problems [in Russian], Nauka, Moscow (1984).

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  4. G. N. Savin,Distribution of Stresses near Holes [in Russian], Naukova Dumka, Kiev (1968).

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. N. Lozhkin

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  1. V. N. Lozhkin
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 980–981. July, 1993.

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Lozhkin, V.N. Limiting equilibrium of a plane with a circular hole. Ukr Math J 45, 1086–1088 (1993). https://doi.org/10.1007/BF01057455

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  • DOI: https://doi.org/10.1007/BF01057455

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