Inverse problem for elastic body with thin elastic inclusion

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Abstract

An inverse problem for an elastic body with a thin elastic inclusion is investigated. It is assumed that the inclusion crosses the external boundary of the elastic body. A connection between the inclusion and the elastic body is characterized by the damage parameter. We study a dependence of the solutions on the damage parameter. In particular, passages to infinity and to zero of the damage parameter are investigated. Limit models are analyzed. Assuming that the damage and rigidity parameters of the model are unknown, inverse problems are formulated. Sufficient conditions for the inverse problems to have solutions are found. Estimates concerning solutions of the inverse problem are established.

Original languageEnglish
Pages (from-to)195-209
Number of pages15
JournalJournal of Inverse and Ill-Posed Problems
Volume28
Issue number2
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • crack
  • damage parameter
  • Inverse problem
  • nonlinear boundary conditions
  • thin inclusion
  • variational inequality
  • TIMOSHENKO
  • CRACK
  • SHAPE SENSITIVITY-ANALYSIS
  • FRACTURE
  • BODIES
  • BOUNDARY
  • PARAMETER-IDENTIFICATION
  • PLATE

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