Mathematical models of mechanical fields in media with inclusions and holes

Marta Bryla; Andrei V. Krupoderov; Alexey A. Kushunin; Vladimir Mityushev; Michail A. Zhuravkov

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

Mathematical models of mechanical fields in media with inclusions and holes

Marta Bryla
, Andrei V. Krupoderov
, Alexey A. Kushunin
, Vladimir Mityushev^*
, Michail A. Zhuravkov

^*Corresponding author for this work

Pedagogical University of Cracow
Belarusian State University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

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 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.

Original language	English
Title of host publication	Springer Optimization and Its Applications
Publisher	Springer International Publishing
Pages	15-42
Number of pages	28
DOIs	https://doi.org/10.1007/978-1-4939-1246-9_2
State	Published - 2014
Externally published	Yes

Publication series

Name	Springer Optimization and Its Applications
Volume	95
ISSN (Print)	1931-6828
ISSN (Electronic)	1931-6836

Keywords

Alternating method of Schwarz
Elastic half plane with cavities
Functional equations for analytic functions
Superposition principle

Access to Document

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

Cite this

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title = "Mathematical models of mechanical fields in media with inclusions and holes",

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 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, Elastic half plane with cavities, Functional equations for analytic functions, Superposition principle",

author = "Marta Bryla and Krupoderov, \{Andrei V.\} and Kushunin, \{Alexey A.\} and Vladimir Mityushev and Zhuravkov, \{Michail A.\}",

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doi = "10.1007/978-1-4939-1246-9\_2",

language = "英语",

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Mathematical models of mechanical fields in media with inclusions and holes. / Bryla, Marta; Krupoderov, Andrei V.; Kushunin, Alexey A. et al.
Springer Optimization and Its Applications. Springer International Publishing, 2014. p. 15-42 (Springer Optimization and Its Applications; Vol. 95).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Mathematical models of mechanical fields in media with inclusions and holes

AU - Bryla, Marta

AU - Krupoderov, Andrei V.

AU - Kushunin, Alexey A.

AU - Mityushev, Vladimir

AU - Zhuravkov, Michail A.

PY - 2014

Y1 - 2014

N2 - 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 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.

AB - 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 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.

KW - Alternating method of Schwarz

KW - Elastic half plane with cavities

KW - Functional equations for analytic functions

KW - Superposition principle

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DO - 10.1007/978-1-4939-1246-9_2

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T3 - Springer Optimization and Its Applications

SP - 15

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BT - Springer Optimization and Its Applications

PB - Springer International Publishing

ER -

Mathematical models of mechanical fields in media with inclusions and holes

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