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

Roman Chapko1, B. Tomas Johansson2, Oleh Sobeyko1

Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Computer Modeling in Engineering & Sciences 2010, 62(1), 57-76. https://doi.org/10.3970/cmes.2010.062.057

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.

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Chapko, R., Johansson, B. T., Sobeyko, O. (2010). On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion. CMES-Computer Modeling in Engineering & Sciences, 62(1), 57–76.



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