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Equilibrium problem for elastic plate with thin rigid inclusion crossing an external boundary Full article

Journal Zeitschrift fur Angewandte Mathematik und Physik
ISSN: 0044-2275
Output data Year: 2021, Volume: 72, Pages: 121 Pages count : 11 DOI: 10.1007/s00033-021-01553-3
Tags Elastic plate, Thin rigid inclusion, Crack, Variational inequality, Free boundary problem, Inverse problem
Authors Khludnev Alexander 1,2,3 , Fankina Irina Vladimirovna 1,2,3
Affiliations
1 Lavrentyev Institute of Hydrodynamics
2 Sobolev Institute of Mathematics SB RAS
3 Novosibirsk State University

Abstract: The paper concerns an equilibrium problem for an elastic plate with a thin rigid inclusion. Both vertical and horizontal displacements of the plate are considered in the frame of the model. It is assumed that the inclusion crosses the external boundary of the plate. Moreover, the inclusion is delaminated from the plate which leads to appearance of a crack between the inclusion and the plate. To provide a mutual nonpenetration between crack faces, we consider nonlinear boundary conditions with unknown set of a contact. We prove a solution existence of the equilibrium problem and analyze an inverse problem with unknown elasticity tensor. To formulate the inverse problem, additional data are imposed to be determined from a boundary measurement. An existence of a solution to the inverse problem is proved, and stability properties are established.
Cite: Khludnev A. , Fankina I.V.
Equilibrium problem for elastic plate with thin rigid inclusion crossing an external boundary
Zeitschrift fur Angewandte Mathematik und Physik. 2021. V.72. P.121. DOI: 10.1007/s00033-021-01553-3 WOS Scopus РИНЦ OpenAlex
Identifiers:
Web of science: WOS:001054354700001
Scopus: 2-s2.0-85102321269
Elibrary: 46094075
OpenAlex: W3162102775
Citing:
DB Citing
Scopus 14
OpenAlex 13
Web of science 11
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