An asymptotic approach in problems of crack identification |
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| Affiliation: | 2. Kaly-Cell, 20A Rue du Général Leclerc, Plobsheim, France;3. UNISTRA, 4 Rue Blaise Pascal, Strasbourg, France;4. CiToxLAB France, B.P. 563, Evreux, France;5. Centre de Chirurgie Viscérale et de Transplantation, Hôpital de Hautepierre, 67098 Strasbourg, France;6. PEPITE EA4267, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France;1. Department of Mechanical, Faculty of Engineering, University of Malaya, Kuala Lumpur, 50603, Malaysia;2. Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD, UK;3. Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, 50603, Malaysia;1. Henan Eye Institute, Henan Eye Hospital, No. 7 Weiwu Road, Zhengzhou 450003, China;2. School of Pharmaceutical Science, Zhengzhou University, No. 100 Science Avenue, Zhengzhou 450001, China |
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| Abstract: | An asymptotic approach to solving problems of the identification of a rectilinear crack of small relative size is presented. The solution of the direct problem is reduced to solving a boundary integral equation. Using the proposed approach, its kernel is investigated, and the main part of the asymptotic form is singled out. The inverse problem of determining the crack parameters from prescribed information on the amplitudes of the displacement on the boundary of a layer is solved. Transcendental equations are obtained, from which the characteristics of a crack are determined in stages. Numerical results of the solution of the inverse problem are presented. |
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