Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

Abstract We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacia...

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Autor principal:	Nyurgun Lazarev
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Variational inequality Inverse problem Nonpenetration Nonlinear boundary conditions Crack Rigid inclusion Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/162e1eb789ac4cedb1778ca2b3840932
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spelling	oai:doaj.org-article:162e1eb789ac4cedb1778ca2b38409322021-11-07T12:15:50ZInverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions10.1186/s13661-021-01565-y1687-2770https://doaj.org/article/162e1eb789ac4cedb1778ca2b38409322021-11-01T00:00:00Zhttps://doi.org/10.1186/s13661-021-01565-yhttps://doaj.org/toc/1687-2770Abstract We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.Nyurgun LazarevSpringerOpenarticleVariational inequalityInverse problemNonpenetrationNonlinear boundary conditionsCrackRigid inclusionAnalysisQA299.6-433ENBoundary Value Problems, Vol 2021, Iss 1, Pp 1-12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Variational inequality Inverse problem Nonpenetration Nonlinear boundary conditions Crack Rigid inclusion Analysis QA299.6-433
spellingShingle	Variational inequality Inverse problem Nonpenetration Nonlinear boundary conditions Crack Rigid inclusion Analysis QA299.6-433 Nyurgun Lazarev Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions
description	Abstract We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.
format	article
author	Nyurgun Lazarev
author_facet	Nyurgun Lazarev
author_sort	Nyurgun Lazarev
title	Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions
title_short	Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions
title_full	Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions
title_fullStr	Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions
title_full_unstemmed	Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions
title_sort	inverse problem for cracked inhomogeneous kirchhoff–love plate with two hinged rigid inclusions
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/162e1eb789ac4cedb1778ca2b3840932
work_keys_str_mv	AT nyurgunlazarev inverseproblemforcrackedinhomogeneouskirchhoffloveplatewithtwohingedrigidinclusions
_version_	1718443470663712768

Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

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