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Sib. Zh. Ind. Mat., 2017, Volume 20, Number 3, Pages 70–79 (Mi sjim970)  

The conjugation problem for thin elastic and rigid inclusions in an elastic body

V. A. Puris

Lavrentyev Institute of Hydrodynamics SB RAS, 15 Lavrentyev av., 630090 Novosibirsk

Abstract: We consider the problem of the conjugation of a thin elastic inclusion and a thin rigid inclusion that are in contact at one point and are placed in an elastic body. Depending on what kind of conjugation conditions are given at the contact point of the inclusions, we consider the two cases: the case of no fracture, where as the conjugation conditions we take the coincidence of the displacements at the contact point and the preservation of the angle between the inclusions, and the case with a fraction, where only the coincidence of the displacements is given. At the conjugation point, we obtain boundary conditions for a differential statement of the problem. Delamination happens at the positive face of the rigid inclusion. On the crack faces, inequality-type nonlinear boundary conditions are given to prevent the mutual penetration of the crack faces. Existence and uniqueness theorems for a solution to the equilibrium problem are proved for each of the cases.

Keywords: thin rigid inclusion, crack, nonlinear boundary conditions, Kirchhoff–Love beam, conjugation conditions.

Funding Agency Grant Number
Russian Science Foundation 15-11-10000


DOI: https://doi.org/10.17377/sibjim.2017.20.308

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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:3, 444–452

UDC: 539.3
Received: 06.06.2016
Revised: 13.02.2017

Citation: V. A. Puris, “The conjugation problem for thin elastic and rigid inclusions in an elastic body”, Sib. Zh. Ind. Mat., 20:3 (2017), 70–79; J. Appl. Industr. Math., 11:3 (2017), 444–452

Citation in format AMSBIB
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\by V.~A.~Puris
\paper The conjugation problem for thin elastic and rigid inclusions in an elastic body
\jour Sib. Zh. Ind. Mat.
\yr 2017
\vol 20
\issue 3
\pages 70--79
\mathnet{http://mi.mathnet.ru/sjim970}
\crossref{https://doi.org/10.17377/sibjim.2017.20.308}
\elib{https://elibrary.ru/item.asp?id=29775046}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 3
\pages 444--452
\crossref{https://doi.org/10.1134/S1990478917030152}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85028526446}


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