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Equilibrium Problem for an Inhomogeneous Kirchhoff–Love Plate Contacting with a Partially Delaminated Inclusion

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Abstract

A new mathematical model describing an equilibrium of an elastic Kirchhoff-Love plate is proposed. We suppose that the plate may come into contact on the side edge with a rigid obstacle. On a given part of the closed curve corresponding to the plate side edge we impose clam** conditions and on the rest part of the curve we consider a nonpenetration condition of the Signorini type. The rigid obstacle is defined by cylindrical surface with generators normal to the plate midplane. In addition, the plate has a flat rigid inclusion (stiffener) on the side edge. The inclusion also defined by a cylindrical surface. The peculiarity of the problem is related to the partial delamination of the inclusion on the contact surface. Boundary conditions of an inequality type ensure nonpenetration of the plate points and the obstacle as well as for points of an elastic matrix and inclusion points. Solvability of the problem is proved. Under the assumption that the solution of the variational problem is smooth enough, optimality conditions on the contact boundary are found.

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Funding

The work is supported by the Ministry of science and higher education of the Russian Federation, agreement no. 075-02-2023-947, February 16, 2023.

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Authors and Affiliations

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

    N. P. Lazarev, E. F. Sharin & E. S. Efimova

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  1. N. P. Lazarev
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  2. E. F. Sharin
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  3. E. S. Efimova
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Correspondence to N. P. Lazarev, E. F. Sharin or E. S. Efimova.

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Lazarev, N.P., Sharin, E.F. & Efimova, E.S. Equilibrium Problem for an Inhomogeneous Kirchhoff–Love Plate Contacting with a Partially Delaminated Inclusion. Lobachevskii J Math 44, 4127–4134 (2023). https://doi.org/10.1134/S1995080223100268

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  • DOI: https://doi.org/10.1134/S1995080223100268

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