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 OpenAlex
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 OpenAlex
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 OpenAlex
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 OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85104742847 |
| Elibrary: | 48151310 |
| OpenAlex: | W3157348201 |