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 РИНЦ

Dates:

Submitted:	Apr 15, 2024
Published print:	Nov 8, 2024

Identifiers:

Elibrary:

79020073

Citing: Пока нет цитирований

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