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Rigidity Parameter Identification for Thin Inclusions Located Inside Elastic Bodies

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Abstract

The paper is concerned with an identification of a rigidity parameter for thin inclusions located inside elastic bodies. It is assumed that inclusions cross an external boundary of the elastic body. In addition to this, a delamination of the inclusions is assumed thus providing a crack between inclusions and the elastic body. To exclude a mutual penetration between crack faces, inequality-type boundary conditions are imposed. We consider elastic inclusions as well as rigid and rigid-elastic inclusions. To find a solution of the problem formulated, we solve an optimal control problem. A cost functional characterizes a displacement of the external part of the inclusion, and a rigidity parameter serves as a control function. We prove a solution existence of the problems formulated.

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Acknowledgments

This work was supported by Russian Science Foundation (15-11-10000).

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russia, 630090

    Alexander Khludnev

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  1. Alexander Khludnev
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Correspondence to Alexander Khludnev.

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Communicated by Emmanuel Trélat.

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Khludnev, A. Rigidity Parameter Identification for Thin Inclusions Located Inside Elastic Bodies. J Optim Theory Appl 172, 281–297 (2017). https://doi.org/10.1007/s10957-016-1025-8

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  • DOI: https://doi.org/10.1007/s10957-016-1025-8

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