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On Solvable Nonlocal Boundary-Value Problems

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Nonlocal Theory of Material Media

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 268))

Abstract

The nonlocal models which are being used in practice can be classified with respect to the form of their static equations into three categories: the volume-integral (VIM), the volume-surface integral (VSIM), and the integro-differential models (IDM). They will be discussed in more detail later. The general theory of nonlocal models for linear, homogeneous elastic media given by Rogula1 permits a systematic approach to the construction of such models. In this paper we shall not construct of them but only discuss the existing actually used class of models.

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References

  1. Rogula, D., On nonlocal continuum theories of elasticity, Anchives of Mechanics, 25, 233, 1973

    Google Scholar 

  2. Beals, R., Non-local elliptic boundary value problems, Bu.E’1etin o6 the Ametcan Ma-themaxcat Society, vol. 70, 693, 1964.

    MATH  MathSciNet  Google Scholar 

  3. Weissmann, A.M. and Kunin I.A., Boundary-value problems in nonlocal elasticity, PMM, 33, 5, 1965 (in Russian).

    Google Scholar 

  4. Rymarz, Cz., Boundary problems of the nonlocal theory, Pnoc. Van. Pnob!., 4, 1974.

    Google Scholar 

  5. Sztyren, M., On boundary forces in a solvable integral model of nonlocal elastic half-space, But. Acad. Pot. Sec., Sen. Sci. Techn., vol. 26, 299, 1978.

    MATH  Google Scholar 

  6. Sztyren, M., Boundary-value problems and surface forces for integral models of nonlocal elastic bodies, But. Acad. Pot. Set., Sen. ScL Techn., vol. 27, 327, 1979.

    Google Scholar 

  7. Sztyren, M., Boundary-value problems and surface forces for integro-differential models of nonlocal elastic bodies, Butt. Acad. Pot. Sc-.., Sen. ScL Techn., vol. 27, 335, 1979.

    Google Scholar 

  8. Kunin. I.A., Theory of elastic media with microstructure, NonLoca.E’.theory 06 eLa4t-Laj, (in Russian), Moscow, 1975.

    Google Scholar 

  9. Datta, B.K., and Kröner, E., Nichtlocale Elastostatic: Ableitung aus der Gittertheorie, Ze-Lt. Phy4., 196, 203, 1966.

    Google Scholar 

  10. Kröner, E., Elasticity theory of materials with loi:g-range cohesive forces, Int. J. Sotcd. Sxnuct., 33, 1967.

    Google Scholar 

  11. Edelen, D.G.B., Nonlocal variational mechanics, Int. J. Engng. ScL., 7, 269, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  12. Eringen, C., Nonlocal polar elastic continua, I’.t. J. Engng. Sci., 10, 1, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  13. Rogula, D., and Sztyren, M., On the one-dimensional models in nonlocal elasticity, LU.U. Acad. Pot. Sci. Sc Techn., 9, 341, 1978.

    Google Scholar 

  14. Rogula, D., and Sztyren, M., Fundamental one-dimensional solutions in nonlocal elasticity, Eatt. Acad. Pot Sc-.., Sen. Sc-.. Tech., 10, 417, 1978.

    MathSciNet  Google Scholar 

  15. Barnett D.M., On admissible solutions in nonlocal elasticity, Lattice dynam-.c.5, P. raamon Press, 1965.

    Google Scholar 

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© 1982 Springer-Verlag Wien

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Sztyren, M. (1982). On Solvable Nonlocal Boundary-Value Problems. In: Rogula, D. (eds) Nonlocal Theory of Material Media. International Centre for Mechanical Sciences, vol 268. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2890-9_4

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  • DOI: https://doi.org/10.1007/978-3-7091-2890-9_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81632-5

  • Online ISBN: 978-3-7091-2890-9

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