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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 49797, 12 pages

Reconstruction of round voids in the elastic half-space: Antiplane problem

1Faculty of Mechanics and Mathematics, Rostov State University, 5 Zorge Street, Rostov-on-Don 344090, Russia
2Dipartimento di Ingegneria dell' Informazione e Matematica Applicata, University of Salerno, Via Ponte don Melillo, Fisciano (SA) 84084, Italy

Received 15 February 2005; Revised 24 May 2005; Accepted 12 July 2005

Copyright © 2006 Mezhlum A. Sumbatyan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the reconstruction of geometry (position and size) of round voids located in the elastic half-space, in frames of antiplane two-dimensional problem. We assume that a known point force is applied to the boundary surface of the half-space, and we can measure the shape of the surface over a certain finite-length interval. Then, if the geometry of the defect is unknown, we construct an algorithm to restore its position and size. Some numerical examples demonstrate a good stability of the proposed algorithm.