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An Equilibrium Problem for a Kirchhoff–Love Plate, Contacting an Obstacle by Top and Bottom Edges

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Abstract

A new model describing the equilibrium of a Kirchhoff–Love plate which may come into mechanical contact with a rigid non-deformable obstacle is proposed. Unlike previous works, we consider the case when a contact is possible on curves located at the intersection of the side face of the plate and two obstacle surfaces that bound the plate from above and below. A boundary condition of Signorini’s type is imposed in the form of two inequalities restricting plate displacements. An equilibrium problem describing the contact of the plate with the rigid obstacle is formulated as a minimization problem for an energy functional over a suitable convex and closed set of admissible displacements. It is proved that the problem has a unique solution.

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Funding

The work is supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-02-2022-881, February 2, 2022.

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Authors and Affiliations

  1. North–Eastern Federal University, 677000, Yakutsk, Russia

    N. P. Lazarev, G. M. Semenova & E. D. Fedotov

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  1. N. P. Lazarev
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  2. G. M. Semenova
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  3. E. D. Fedotov
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Corresponding authors

Correspondence to N. P. Lazarev, G. M. Semenova or E. D. Fedotov.

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(Submitted by T. K. Yuldashev)

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Lazarev, N.P., Semenova, G.M. & Fedotov, E.D. An Equilibrium Problem for a Kirchhoff–Love Plate, Contacting an Obstacle by Top and Bottom Edges. Lobachevskii J Math 44, 614–619 (2023). https://doi.org/10.1134/S1995080223020245

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  • DOI: https://doi.org/10.1134/S1995080223020245

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