Problems for plates with rigid inclusions contacting with flat and pointwise obstacles on the front surfaces
https://doi.org/10.25587/2411-9326-2025-3-15-27
Abstract
Two nonlinear mathematical models on equilibrium of plates in contact with obstacles of two types are studied. It is assumed that the plate contains a bulk rigid inclusion that touches the obstacle in the initial state. The first type of obstacle limits displacements of the plates to a square-shaped section lying on the front surface. The second type of obstacle also restricts displacements on the front surface, but has a pointwise character, i.e. Signorini-type conditions are specified at one given point. The convergence of solutions of a family of variational problems is proved as the parameter that determines the area of the contact zone tends to zero. It is shown that a limit function is the solution to the problem describing the pointwise contact of the plate.
About the Authors
N. P. Lazarev
North-Eastern Federal University (NEFU), Scientific Research Institute of Mathematics
Russian Federation
Russian Federation
Nyurgun P. Lazarev
58 Belinsky Street, Yakutsk 677891
D. Ya. Nikiforov
Institute of Mathematics and Information Science, North-Eastern Federal University
Russian Federation
Russian Federation
Djulustan Ya. Nikiforov
58 Belinsky Street, Yakutsk 677000
S. V. Safonov
Republican Lyceum Boarding School
Russian Federation
Russian Federation
Stepan V. Safonov
37 Oyunsky Street, Yakutsk 677891
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Review
For citations:
Lazarev N.P., Nikiforov D.Ya., Safonov S.V. Problems for plates with rigid inclusions contacting with flat and pointwise obstacles on the front surfaces. Mathematical notes of NEFU. 2025;32(3):15-27. (In Russ.) https://doi.org/10.25587/2411-9326-2025-3-15-27
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