- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (1)
- Authors
- Lazarev, Nyurgun P.; Semenova, Galina M.; Romanova, Natalya A.
- Contact information
- Lazarev, Nyurgun P.: North-Eastern Federal University Yakutsk, Russian Federation; ; OCRID: 0000-0002-7726-6742; Semenova, Galina M.: North-Eastern Federal University Yakutsk, Russian Federation; ; Romanova, Natalya A.: North-Eastern Federal University Yakutsk, Russian Federation;
- Keywords
- variational problem; crack; limit passage; nonpenetration condition; optimal control problem
- Abstract
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
- Pages
- 28–41
- DOI
- 10.17516/1997-1397-2021-14-1-28-41
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/137822
Journal of Siberian Federal University. Mathematics & Physics / 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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