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Conditions of existence of univalently stressed contours in the first main problem of the theory of elasticity for a plane with cut

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Abstract

A definition of a univalently stressed contour in a compressible isotropic plane with a curvilinear cut is given, which extends the notion of an equiresistant contour. Conditions for elliptic and square contours to be univalently stressed are formulated and proved.

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References

  1. 1.

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

  2. 2.

    A. S. Kosmodamianskii,Plane Problems in the Theory of Elasticity for Plates with Holes, Cuts, and Protuberances [in Russian], Vyshcha Shkola, Kiev (1975).

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 295–296, February, 1995.

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Lozhkin, V.N. Conditions of existence of univalently stressed contours in the first main problem of the theory of elasticity for a plane with cut. Ukr Math J 47, 347–350 (1995). https://doi.org/10.1007/BF01056726

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Keywords

  • Isotropic Plane
  • Stressed Contour