On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

Roman Chapko, B. Tomas Johansson, Oleh Sobeyko

Research output: Contribution to journalArticlepeer-review

Abstract

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.
Original languageEnglish
Pages (from-to)57-76
Number of pages19
JournalComputer Modeling in Engineering and Sciences
Volume62
Issue number1
DOIs
Publication statusPublished - 2010

Bibliographical note

Articles published by TSP are under an open access license, which means all articles published by TSP are accessible online free of charge and as free of technical and legal barriers to everyone. Published materials can be re-use if properly acknowledged

Keywords

  • alternating method
  • trigonometric interpolation
  • quadrature method
  • Green's function
  • elastostatics
  • Cauchy problem
  • boundary integral equations

Fingerprint

Dive into the research topics of 'On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion'. Together they form a unique fingerprint.

Cite this