Far Eastern Mathematical Journal

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Noneuclidean structure of internal stress in continuum


M. A. Guzev, V. P. Myasnikov

2001, issue 2, Ń. 29–44


Abstract
It is shown that the choice in determination of internal stress in continuum is defined by the noneuclidean geometric objects charactirizing defects of internal material structure.

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References

[1] S. K. Godunov, E. I. Romenskij, E'lementy mexaniki sploshnoj sredy, Nauchnaya kniga, Novosibirsk, 1998, 268 s.
[2] K. Kondo, “On the geometrical and physical foundations of the theory of yielding”, Proc. 2nd Japan Nat. Congr. Appl. Mech., Tokyo, 1953, 41–47.
[3] B. A. Bilby, R. Bullough, E. Smith, “Continuos distributions of dislocations: a new application of the methods of non-Reimannian geometry”, Proc. Roy. Soc. A, 231, 1955, 263–273.
[4] A. Kadich, D. E'delen, Kalibrovochnaya teoriya dislokacij i disklinacij, Mir, M., 1987, 168 s.
[5] Fizicheskaya mezomexanika i komp'yuternoe konstruirovanie materialov, t. 1, red. V. E. Panin, Nauka, Novosibirsk, 1995, 297 s.
[6] Fizicheskaya mezomexanika i komp'yuternoe konstruirovanie materialov, t. 2, red. V. E. Panin, Nauka, Novosibirsk, 1995, 320 s.
[7] V. P. Myasnikov, M. A. Guzev, “Neevklidova model' deformirovaniya materialov na razlichnyx strukturnyx urovnyax”, Fizicheskaya mezomexanika, 3:1 (2000), 5–16.
[8] G. N. Chernyshov, A. L. Popov, V. M. Kozincev, I. I. Ponomarev, Ostatochnye napryazheniya v deformiruemyx tverdyx telax, Nauka, M., 1996, 240 s.
[9] L. D. Landau, E. M. Lifshic, Teoriya uprugosti, Nauka, M., 1987, 248 s.
[10] N. I. Ostrosablin, “Ob uravneniyax Bel'trami-Michella i operatore Sen-Venana”, Dinamika sploshnoj sredy. Sbornik nauchnyx trudov, 116 (2000), 211–217, Novosibirsk.
[11] L. D. Landau, E. M. Lifshic, Teoriya polya, Nauka, M., 1988, 512 s.
[12] B. A. Dubrovin, S. P. Novikov, L. T. Fomenko, Sovremennaya geometriya: Metody i prilozheniya, Nauka, M., 1986, 760 s.

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