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Mathematical Problems of the Anisotropic Elasticity for Piece-wise Homogeneous Bodies

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Problems and Methods in Mathematical Physics

Part of the book series: TEUBNER-TEXTE zur Mathematik ((TTZM))

Abstract

The investigation deals with the problems of anisotropic elasticity for composed bodies i.e. for bodies which have piece-wise homogeneous structure. The most general case of the structure of the elastic body under consideration mathematically can be described by the following way.

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References

  1. Burchuladze, T.V., Gegelia, T.G.: The Development of the Potential Methods in the Elasticity Theory. Metsniereba, Tbilisi, 1985.

    Google Scholar 

  2. Costabel, M., Stephan, E.P.: An improved boundary element Galerkin method for three-dimensional crack problems. Integral Equations and Operator Theory. 10, 1987, 467–504.

    Article  MathSciNet  MATH  Google Scholar 

  3. Duduchava, R.: On multidimensional singular integral operators. I, II. J. Operator Theory, 11, 1984, 41–76.

    MathSciNet  MATH  Google Scholar 

  4. Duduchava, R., Natroshvili, D., Shargorodsky, E.: Boundary value problems of the mathematical theory of cracks. Proc. Inst. Appl. Math. Tbilisi Univ., 39, 1990, 68–84.

    MathSciNet  MATH  Google Scholar 

  5. Eskin, G.I.: Boundary Value Problems for Elliptic Pseudodifferential Equations. Transl. of Math. Monogr., AMS, V. 52. Providence, Rhode Island, 1981.

    Google Scholar 

  6. Jentsch, L.: Zur Existenz von regulren Lsungen der Elastostatik stckweise homogener Krper mit neuen Kontaktbedingungen an den Trennflehen zwischen zwei homogenen Teilen. Berlin: Akademie-Verlag, Abh. d. Schs. Akademie d. Wissenschaften zu Leipzig, Math. Naturw. Klasse. Bd. 53, H. 2, 1977.

    Google Scholar 

  7. Jentsch, L., Natroshvili, D.: Non-classical interface problems for piece-wise homogeneous anisotropic elastic bodies (to appear in Mathematical Methods in the Applied Sciences).

    Google Scholar 

  8. Kupradze, V.D.: Contact problems of the elasticity theory. Differential Equations, 16(2), 1980, 293–310.

    MathSciNet  MATH  Google Scholar 

  9. Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V.: Three-dimensional Problems of Mathematical Theory of Elasticity and Thermoelasticity. Nauka, Moscow, 1976.

    Google Scholar 

  10. Natroshvili, D.: Investigation of boundary value and initial boundary value problems of mathematical theory of elasticity and thermoelasticity for homogeneous anisotropic bodies by means of potential methods. Doct. thesis. Math. Inst. Acad. Sci. GSSR, 1984, 1-325.

    Google Scholar 

  11. Natroshvili, D., Chkadua, O., Shargorodsky, E.: Mixed boundary value problems of the anisotropic Elasticity. Proc. Inst. Appl. Math. Tbilisi Univ., 39, 1990, 133–181.

    MATH  Google Scholar 

  12. Shargorodsky, E.: Boundary value problems for elliptic pseudodifferential operators: the half space case. Proc. Tbilisi Mathem. Inst. Acad. Sci. GSSR, 99, 1993, 44–80.

    Google Scholar 

  13. Shargorodsky, E.: Boundary value problems for elliptic pseudodifferential operators on manifolds. Proc. Tbilisi Mathem. Inst. Acad. Sci GSSR, 104, 1993.

    Google Scholar 

  14. Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. VEB Deutscher Verlag der Wissenschaften Berlin, 1978.

    Google Scholar 

  15. Triebel, H.: Theory of Function Spaces. Leipzig Birkhuser Verlag, Basel-Boston Stuttgart, 1983.

    Book  Google Scholar 

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© 1994 Springer Fachmedien Wiesbaden

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Natroshvili, D. (1994). Mathematical Problems of the Anisotropic Elasticity for Piece-wise Homogeneous Bodies. In: Jentsch, L., Tröltzsch, F. (eds) Problems and Methods in Mathematical Physics. TEUBNER-TEXTE zur Mathematik. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85161-1_9

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  • DOI: https://doi.org/10.1007/978-3-322-85161-1_9

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-322-85162-8

  • Online ISBN: 978-3-322-85161-1

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