Geodesic
On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 28-41

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The paper considers equilibrium models of Kirchhoff-Love plates with rigid inclusions of two types. The first type of inclusion is described by three-dimensional sets, the second one corresponds to a cylindrical rigid inclusion, which is perpendicular to the plate's median plane in the initial state. For both models, we suppose that there is a through crack along a fixed part of the inclusion's boundary. On the crack non-penetration conditions are prescribed which correspond to a certain known configuration bending near the crack. The uniqueness solvability of a new problems for a Kirchhoff-Love plate with a flat rigid inclusion is proved. It is proved that when a thickness parameter tends to zero, the problem for a flat rigid inclusion can be represented as a limiting task for a family of variational problems concerning the inclusions of the first type. A solvability of an optimal control problem with a control given by the size of inclusions is proved.
Keywords: variational problem, crack, nonpenetration condition, optimal control problem.
Mots-clés : limit passage 
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     title = {On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a {Kirchhoff-Love} plate with a crack},
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Nyurgun P. Lazarev; Galina M. Semenova; Natalya A. Romanova. On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 28-41. http://geodesic.mathdoc.fr/item/JSFU_2021_14_1_a3/