Geodesic
Kirchhoff~--- Love plate with a flat rigid inclusion
Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 1, pp. 29-46

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An equilibrium problem for a plate under the action of external forces is studied. It is assumed that the plate has a flat rigid inclusion. We suppose that there is a throng crack along a fixed part of the inclusions boundary. To exclude a mutual penetration between crack faces, inequality type of boundary conditions are imposed. The problem is formulated as a variational inequality. The differential formulation of the problem is obtained provided that the solution is smooth. An equivalence of two settings is established: variational and differential. The contact problem for an elastic plate with a flat rigid inclusion is also considered. The differential and variational formulations of the problem are given. The unique solvability of the problem is substantiated.
Keywords: variational inequality, crack, non-penetration condition, Kirchhoff — Love plate. 
@article{CHFMJ_2023_8_1_a2,
     author = {N. A. Nikolaeva},
     title = {Kirchhoff~--- {Love} plate with a flat rigid inclusion},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {29--46},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_1_a2/}
}
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N. A. Nikolaeva. Kirchhoff~--- Love plate with a flat rigid inclusion. Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 1, pp. 29-46. http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_1_a2/