Optimal Control of Parameters for Elastic Body with Thin Inclusions

Alexander Khludnev (), Antonio Corbo Esposito () and Luisa Faella ()
Additional contact information
Alexander Khludnev: Novosibirsk State University
Antonio Corbo Esposito: Universita di Cassino e del Lazio Meridionale
Luisa Faella: Universita di Cassino e del Lazio Meridionale

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 1, No 15, 293-314

Abstract: Abstract 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.

Keywords: Thin inclusion; Junction stiffness parameter; Rigidity parameter; Crack; Variational inequality; Junction conditions; Optimal control; Inverse problem; 35J88; 49J20 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01620-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:184:y:2020:i:1:d:10.1007_s10957-019-01620-w

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01620-w

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().