On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack

Nyurgun P. Lazarev ; Galina M. Semenova ; Natalya A. Romanova

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 28-41.

Résumé

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.

Détail

Keywords: variational problem, crack, nonpenetration condition, optimal control problem.
Mots-clés : limit passage

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