Optimal Control of Parameters for Elastic Body with Thin Inclusions

Alexander Khludnev, Antonio Corbo Esposito, Luisa Faella

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)293-314
Number of pages22
JournalJournal of Optimization Theory and Applications
Volume184
Issue number1
DOIs
Publication statusPublished - Jan 2020

Keywords

  • Crack
  • Inverse problem
  • Junction conditions
  • Junction stiffness parameter
  • Optimal control
  • Rigidity parameter
  • Thin inclusion
  • Variational inequality
  • JUNCTION PROBLEM
  • CRACK

OECD FOS+WOS

  • 5.02.PE OPERATIONS RESEARCH & MANAGEMENT SCIENCE
  • 1.01.PN MATHEMATICS, APPLIED

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