TY - JOUR

T1 - Optimal Control of Parameters for Elastic Body with Thin Inclusions

AU - Khludnev, Alexander

AU - Esposito, Antonio Corbo

AU - Faella, Luisa

N1 - Funding Information: The authors have been supported by the gruppo nazionale per l’analisi matematica, la probabilità e le loro applicazioni (GNAMPA) of the Istituto nazionale di alta matematica (INdAM). The first author was also supported by RFBR (19-51-50004). Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/1

Y1 - 2020/1

N2 - In this paper, an equilibrium problem for 2D non-homogeneous anisotropic elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. A connection between the inclusions at a given point is characterized by a junction stiffness parameter. The elastic inclusion is delaminated, thus forming an interfacial crack with the matrix. Inequality-type boundary conditions are imposed at the crack faces to prevent interpenetration. Existence of solutions is proved; different equivalent formulations of the problem are discussed; junction conditions at the connection point are found. A convergence of solutions as the junction stiffness parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is investigated. An analysis of limit models is provided. An optimal control problem is analyzed with the cost functional equal to the derivative of the energy functional with respect to the crack length. A solution existence of an inverse problem for finding the junction stiffness and rigidity parameters is proved.

AB - In this paper, an equilibrium problem for 2D non-homogeneous anisotropic elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. A connection between the inclusions at a given point is characterized by a junction stiffness parameter. The elastic inclusion is delaminated, thus forming an interfacial crack with the matrix. Inequality-type boundary conditions are imposed at the crack faces to prevent interpenetration. Existence of solutions is proved; different equivalent formulations of the problem are discussed; junction conditions at the connection point are found. A convergence of solutions as the junction stiffness parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is investigated. An analysis of limit models is provided. An optimal control problem is analyzed with the cost functional equal to the derivative of the energy functional with respect to the crack length. A solution existence of an inverse problem for finding the junction stiffness and rigidity parameters is proved.

KW - Crack

KW - Inverse problem

KW - Junction conditions

KW - Junction stiffness parameter

KW - Optimal control

KW - Rigidity parameter

KW - Thin inclusion

KW - Variational inequality

KW - JUNCTION PROBLEM

KW - CRACK

UR - http://www.scopus.com/inward/record.url?scp=85076929069&partnerID=8YFLogxK

U2 - 10.1007/s10957-019-01620-w

DO - 10.1007/s10957-019-01620-w

M3 - Article

AN - SCOPUS:85076929069

VL - 184

SP - 293

EP - 314

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 1

ER -