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Гомогенизация статической модели антиплоского сдвига армированного композита Full article

Journal Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304
Output data Year: 2024, Volume: 21, Number: 2, Pages: 1042-1063 Pages count : 22 DOI: 10.33048/semi.2024.21.069
Tags composite material, thin inclusion, anti-plane shear, homogenization, numerical experiment.
Authors Леонова Э.И. 1,2
Affiliations
1 Lavrentyev Institute of Hydrodynamics
2 Novosibirsk State University

Abstract: The static problem of anti-plane shear of a thermoelastic composite, stitched with reinforcing threads, is considered. The original formulation contains a small positive parameter ε, which characterizes the distance between neighboring threads. It is also assumed that the thermomechanical characteristics of the composite body depend on ε. The asymptotic behavior of solutions as the parameter ε tends to zero is investigated. The limiting transition as ε → 0+ is mathematically rigorously justi ed and represents a homogenization procedure. This transition is based on the application of the standard Allaire Nguetseng two-scale convergence method and its version by G. Allaire, A. Damlamian, U. Hornung for homogenization on thin inclusions. The result consists of the construction of a limit averaged model of anti-plane shear of the composite material. Using the newly obtained model, numerical experiments are performed, which show consistency of the theoretical conclusions.
Cite: Леонова Э.И.
Гомогенизация статической модели антиплоского сдвига армированного композита
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2024. Т.21. №2. С.1042-1063. DOI: 10.33048/semi.2024.21.069 WOS Scopus РИНЦ
Dates:
Submitted: Apr 15, 2024
Published print: Nov 8, 2024
Identifiers:
Web of science: WOS:001396421100011
Scopus: 2-s2.0-85212340149
Elibrary: 79020073
Citing:
DB Citing
Elibrary 1
Web of science 1
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