Abstract
The problem of detecting and localizing a cavity, a crack, or an inclusion in an elastic body by means of partially overdetermined data given on its outer boundary is considered. The input data can be obtained in a single static experiment. A new approach for solving this problem is proposed. The capabilities of the proposed approach are illustrated by the example of the problem for detecting a cavity in an elastic plate.
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Funding
The work цфы supported by the State Taskб state registration no. AAAA-A20-120011690132-4б and by the Russian Foundation for Basic Researchб project no. 19-01-00100.
Professor Efim Il’ich Shifrin, the renowned expert in the mechanics of deformable solids and in the fracture mechanics, the author of more than 200 papers in mechanics and applied mathematics, the member of the editorial board of the journal Prikladnaya Matematika i Mekhanika, and the active reviewer and author of the journal, turned 70 on April 14, 2020.
The editorial board and editorial staff of Prikladnaya Matematika i Mekhanika, colleagues, and disciples would like to thank him for his dedicated work, as well as wish him good health and further creative successes.
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Translated by E. Oborin
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Kasparova, E.A., Shifrin, E.I. Solution for the Geometric Elastostatic Inverse Problem by Means of Not Completely Overdetermined Boundary Data. Mech. Solids 55, 1298–1307 (2020). https://doi.org/10.3103/S0025654420080117
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DOI: https://doi.org/10.3103/S0025654420080117