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On inverse crack problems in elastostatics
Author(s) -
Ikehata Masaru,
Itou Hiromichi
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700642
Subject(s) - inverse problem , traction (geology) , boundary value problem , inverse , displacement (psychology) , displacement field , boundary (topology) , mathematical analysis , mathematics , nondestructive testing , point (geometry) , geometry , physics , structural engineering , engineering , finite element method , mechanical engineering , psychology , quantum mechanics , psychotherapist
In solid mechanics, nondestructive testing has been an important technique in gathering information about unknown cracks, or defects in material. From a mathematical point of view, this is described as an inverse problem of partial differential equations, that is, the problem is to extract information about the location and shape of an unknown crack from the surface displacement field and traction on the boundary of the elastic material. By using the enclosure method introduced by Prof. Ikehata we can derive the extraction formula of an unknown linear crack from a single set of measured boundary data. Then, we need to have precise properties of a solution of the corresponding boundary value problem; for instance, an expansion formula around the crack tip. In this paper we consider the inverse problem concentrating on this point. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)