Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 |
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Output data | Year: 2021, Volume: 15, Number: 1, Pages: 129-140 Pages count : 12 DOI: 10.1134/s1990478921010117 | ||||||||
Tags | antiplane shear; asymptotic analysis; crack; inhomogeneous elastic body; thin elastic inclusion; thin rigid inclusion | ||||||||
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Abstract:
The equilibrium problem for an elastic body having an inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there is a power-law dependence of the shear modulus of the inclusion on a small parameter characterizing its width. We justify passage to the limit as the parameter vanishes and construct an asymptotic model of an elastic body containing a thin inclusion. We also show that, depending on the exponent of the parameter, there are the five types of thin inclusions: crack, rigid inclusion, ideal contact, elastic inclusion, and a crack with adhesive interaction of the faces. The strong convergence is established of the family of solutions of the original problem to the solution of the limiting one.
Cite:
Rudoy E.M.
, Itou H.
, Lazarev N.P.
Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem
Journal of Applied and Industrial Mathematics. 2021. V.15. N1. P.129-140. DOI: 10.1134/s1990478921010117 Scopus РИНЦ
Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem
Journal of Applied and Industrial Mathematics. 2021. V.15. N1. P.129-140. DOI: 10.1134/s1990478921010117 Scopus РИНЦ
Original:
Рудой Е.М.
, Itou H.
, Lazarev N.P.
Асимптотическое обоснование моделей тонких включений в упругом теле в рамках антиплоского сдвига
Сибирский журнал индустриальной математики. 2021. Т.24. №1. С.103-119. DOI: 10.33048/sibjim.2021.24.108 РИНЦ
Асимптотическое обоснование моделей тонких включений в упругом теле в рамках антиплоского сдвига
Сибирский журнал индустриальной математики. 2021. Т.24. №1. С.103-119. DOI: 10.33048/sibjim.2021.24.108 РИНЦ
Identifiers:
Scopus | 2-s2.0-85104742847 |
Elibrary | 48151310 |
OpenAlex | W3157348201 |