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Mathematical Models of Mechanical Fields in Media with Inclusions and Holes

In: Handbook of Functional Equations

Author

Listed:
  • Marta Bryla

    (Pedagogical University)

  • Andrei V. Krupoderov

    (Belarusian State University)

  • Alexey A. Kushunin

    (Belarusian State University)

  • Vladimir Mityushev

    (Pedagogical University)

  • Michail A. Zhuravkov

    (Belarusian State University)

Abstract

Various problems of mechanics described by two-dimensional harmonic and biharmonic functions are investigated by application of the generalized alternating method of Schwarz (GMS). It is demonstrated that the GMS in zeroth approximation coincides with the principle of superposition. Iterative schemes for the $\mathbb R$ -linear problem on harmonic functions for multiply connected domains are constructed and compared to the GMS. The method is applied in symbolic form to the case when inclusions have elliptical shape. Two-dimensional problems for biharmonic functions by application of the Kolosov–Muskhelishvili formulae are considered by the principle of superposition to describe gas flows in rigid bodies. Viscoelastic problems in porous media are solved by use of the method of finite elements.

Suggested Citation

  • Marta Bryla & Andrei V. Krupoderov & Alexey A. Kushunin & Vladimir Mityushev & Michail A. Zhuravkov, 2014. "Mathematical Models of Mechanical Fields in Media with Inclusions and Holes," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 15-42, Springer.
    • Handle: RePEc:spr:spochp:978-1-4939-1246-9_2
    DOI: 10.1007/978-1-4939-1246-9_2
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