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Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem. / Rudoy, E. M.; Itou, H.; Lazarev, N. P.

In: Journal of Applied and Industrial Mathematics, Vol. 15, No. 1, 11, 02.2021, p. 129-140.

Research output: Contribution to journal › Article › peer-review

Harvard

Rudoy, EM, Itou, H & Lazarev, NP 2021, 'Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem', Journal of Applied and Industrial Mathematics, vol. 15, no. 1, 11, pp. 129-140. https://doi.org/10.1134/S1990478921010117

APA

Rudoy, E. M., Itou, H., & Lazarev, N. P. (2021). Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem. Journal of Applied and Industrial Mathematics, 15(1), 129-140. [11]. https://doi.org/10.1134/S1990478921010117

Vancouver

Rudoy EM, Itou H, Lazarev NP. Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem. Journal of Applied and Industrial Mathematics. 2021 Feb;15(1):129-140. 11. doi: 10.1134/S1990478921010117

Author

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. In: Journal of Applied and Industrial Mathematics. 2021 ; Vol. 15, No. 1. pp. 129-140.

BibTeX

@article{2ce22a09e04a4bb7af72376c913a7662,
title = "Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem",
abstract = "The equilibrium problem for an elastic body having an inhomogeneous inclusion withcurvilinear boundaries is considered within the framework of antiplane shear. We assume thatthere is a power-law dependence of the shear modulus of the inclusion on a small parametercharacterizing its width. We justify passage to the limit as the parameter vanishes and constructan asymptotic model of an elastic body containing a thin inclusion. We also show that, dependingon 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 strongconvergence is established of the family of solutions of the original problem to the solution of thelimiting one.",
keywords = "antiplane shear, asymptotic analysis, crack, inhomogeneous elastic body, thin elastic inclusion, thin rigid inclusion",
author = "Rudoy, {E. M.} and H. Itou and Lazarev, {N. P.}",
note = "Funding Information: The authors were supported by the Russian Foundation for Basic Research (projects nos. 18–41–140003 and 19–51–50004) and the Japan Society for the Promotion of Science (project no. J19–721). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = feb,
doi = "10.1134/S1990478921010117",
language = "English",
volume = "15",
pages = "129--140",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem

AU - Rudoy, E. M.

AU - Itou, H.

AU - Lazarev, N. P.

N1 - Funding Information: The authors were supported by the Russian Foundation for Basic Research (projects nos. 18–41–140003 and 19–51–50004) and the Japan Society for the Promotion of Science (project no. J19–721). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2

Y1 - 2021/2

N2 - The equilibrium problem for an elastic body having an inhomogeneous inclusion withcurvilinear boundaries is considered within the framework of antiplane shear. We assume thatthere is a power-law dependence of the shear modulus of the inclusion on a small parametercharacterizing its width. We justify passage to the limit as the parameter vanishes and constructan asymptotic model of an elastic body containing a thin inclusion. We also show that, dependingon 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 strongconvergence is established of the family of solutions of the original problem to the solution of thelimiting one.

AB - The equilibrium problem for an elastic body having an inhomogeneous inclusion withcurvilinear boundaries is considered within the framework of antiplane shear. We assume thatthere is a power-law dependence of the shear modulus of the inclusion on a small parametercharacterizing its width. We justify passage to the limit as the parameter vanishes and constructan asymptotic model of an elastic body containing a thin inclusion. We also show that, dependingon 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 strongconvergence is established of the family of solutions of the original problem to the solution of thelimiting one.

KW - antiplane shear

KW - asymptotic analysis

KW - crack

KW - inhomogeneous elastic body

KW - thin elastic inclusion

KW - thin rigid inclusion

UR - http://www.scopus.com/inward/record.url?scp=85104742847&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=46091547

U2 - 10.1134/S1990478921010117

DO - 10.1134/S1990478921010117

M3 - Article

AN - SCOPUS:85104742847

VL - 15

SP - 129

EP - 140

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

M1 - 11

ER -

ID: 28503025