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
V. V. Sokolovskii,Statistics of a Free-Flowing Medium [in Russian], Gostekhizdat, Moscow (1954).
N. I. Muskhelishvili,Certain Basic Problems in the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
L. A. Galin,Elasoplastic Problems [in Russian], Nauka, Moscow (1984).
G. N. Savin,Distribution of Stresses near Holes [in Russian], Naukova Dumka, Kiev (1968).
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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