Mathematical Models of Mechanical Fields in Media with Inclusions and Holes

Marta Bryla, Andrei V. Krupoderov, Alexey A. Kushunin, Vladimir Mityushev () and Michail A. Zhuravkov ()
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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

A chapter in Handbook of Functional Equations, 2014, pp 15-42 from Springer

Abstract: 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.

Keywords: Alternating method of Schwarz; Functional equations for analytic functions; Superposition principle; Elastic half plane with cavities (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_2

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DOI: 10.1007/978-1-4939-1246-9_2

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