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Converse problem of elasticity theory for an anisotropic medium

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To prevent stress concentration it is of considerable interest that the body contour be found whose portions show no preference to brittle failure or plastic deformation. Such contours are called by us “equally rigid.” Two-dimensional problems are considered for finding the “equally rigid” form of the hole in an anisotropic medium. The lack of stress concentration on the coutour of the hole is the criterion which decides whether or not the hole is “equally rigid.” For an isotropic medium this converse problem of elasticity theory was solved in [1].

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Literature cited

  1. 1.

    G. P. Cherepanov, “Some problems of elasticity and plasticity theory with unknown boundary,” in: Applications of the Theory of Functions to the Mechanics of Continuous Media [in Russian], Vol. 1, Nauka, Moscow (1965).

  2. 2.

    S. G. Lekhnitskii, Anisotropic Plates [in Russian], Gostekhizdat, Moscow (1957).

  3. 3.

    G. N. Savin, Stress Distribution close to Holes [in Russian], Naukova Dumka, Kiev (1968).

  4. 4.

    G. P. Cherepanov, “Boundary-value problems with analytic coefficients,” Dokl. Akad. Nauk SSSR,161, No. 2 (1965).

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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 190–193, July–August 1975.

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Mirsalimov, V.M. Converse problem of elasticity theory for an anisotropic medium. J Appl Mech Tech Phys 16, 645–648 (1975). https://doi.org/10.1007/BF00858311

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  • Mathematical Modeling
  • Mechanical Engineer
  • Brittle
  • Plastic Deformation
  • Stress Concentration