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Solution of some periodic elastoplastic problems

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The article considers an elastoplastic problem for a plane weakened by an infinite number of round openings. It is assumed that the level of the stresses and the distance between the openings are such that the round openings are completely enveloped by the corresponding plastic zone; under these circumstances, the adjacent plastic regions do not coalesce. The article also considers the inverse elastoplastic problem under conditions of plane strain for an unbounded plane, weakened by a periodic series of openings. A number of communications have been devoted to periodic problems in the theory of elasticity and plasticity with an unknown boundary [1–8]. In distinction from [1–8], in which the method of perturbations was used, another method is used to solve periodic elastoplastic problems, making it possible to obtain a solution with any arbitrary relative dimensions of the region.

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Literature cited

  1. 1.

    A. S. Kosmodamianskii, “The elastoplastic problem for an isotropic solid, weakened by an infinite number of openings,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Mekh. Mashinostr., No. 4 (1961).

  2. 2.

    I. Yu. Khoma, “Stress concentration in a thin plate, weakened by an infinite number of round openings, with elastoplastic strains,” in: Proceedings of the Fourth All-Union Conference on the Theory of Shells and Plates [in Russian], Erevan (1964).

  3. 3.

    B. D. Annin, Two-Dimensional Elastoplastic Problems [in Russian], Izd. Novosibirsk Univ., Novosibirsk (1968).

  4. 4.

    V. M. Mirsalimov, “Solutions of elastoplastic problems for a plane with a single-period system of round openings,” Dokl. Akad. Nauk AzerbSSR, No. 5 (1973).

  5. 5.

    V. M. Mirsalimov, “An elastoplastic problem for a solid, weakened by openings,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6 (1974).

  6. 6.

    V. M. Mirsalimov and É. M. Mekhti-zade, “An elastoplastic problem for a thin plate, weakened by an infinite number of round openings,” in: Investigation of Some Questions in the Constructional Theory of Functions and Differential Equations [in Russian], Izd. AzINSFTEKhIMA, Baku (1973).

  7. 7.

    G. M. Ivanov and A. S. Kosmodamianskii, “An inverse periodic elastoplastic problem,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10 (1971).

  8. 8.

    V. M. Mirsalimov, “Inverse problems in the theory of elasticity,” Dep. No. 3998-72, Baku (1971).

  9. 9.

    L. A. Galin, “The plane elastoplastic problem,” Prikl. Mat. Mekh.,10, No. 3 (1946).

  10. 10.

    N. I. Muskhelishvili, Basic Problems in the Mathematical Theory of Elasticity [in Russian], 5th ed., Izd. Nauka, Moscow (1966).

  11. 11.

    É. I. Grigolyuk and A. A. Fil'shtinskii, Perforated Plates and Shells [in Russian], Izd. Nauka, Moscow (1970).

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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–121, November–December, 1975.

The author thanks G. P. Cherepanov for his interest in the work.

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Mirsalimov, V.M. Solution of some periodic elastoplastic problems. J Appl Mech Tech Phys 16, 933–937 (1975). https://doi.org/10.1007/BF00852824

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  • Mathematical Modeling
  • Mechanical Engineer
  • Industrial Mathematic
  • Plane Strain
  • Plastic Zone