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Equilibrium problem for elastic plate with thin rigid inclusion crossing an external boundary

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Abstract

The paper concerns an equilibrium problem for an elastic plate with a thin rigid inclusion. Both vertical and horizontal displacements of the plate are considered in the frame of the model. It is assumed that the inclusion crosses the external boundary of the plate. Moreover, the inclusion is delaminated from the plate which leads to appearance of a crack between the inclusion and the plate. To provide a mutual nonpenetration between crack faces, we consider nonlinear boundary conditions with unknown set of a contact. We prove a solution existence of the equilibrium problem and analyze an inverse problem with unknown elasticity tensor. To formulate the inverse problem, additional data are imposed to be determined from a boundary measurement. An existence of a solution to the inverse problem is proved, and stability properties are established.

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Acknowledgements

This work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.

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  1. Lavrentyev Institute of Hydrodynamics of RAS, Sobolev Institute of Mathematics of RAS, Novosibirsk State University, Novosibirsk, Russia, 630090

    Alexander Khludnev & Irina Fankina

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  1. Alexander Khludnev
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  2. Irina Fankina
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Correspondence to Alexander Khludnev.

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Khludnev, A., Fankina, I. Equilibrium problem for elastic plate with thin rigid inclusion crossing an external boundary. Z. Angew. Math. Phys. 72, 121 (2021). https://doi.org/10.1007/s00033-021-01553-3

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  • DOI: https://doi.org/10.1007/s00033-021-01553-3

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