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.
The first author's work was supported by the Russian Foundation for Basic
Research (grant no. 18-29-10007-mk), the 2nd author's work was supported
the Ministry of science and higher education of the Russian Federation,
supplementary agreement no. 075-02-2020-1543/1, April 29, 2020.
Received: 10.05.2020 Received in revised form: 10.07.2020 Accepted: 20.09.2020
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
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”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 28–41
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\paper On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 1
\pages 28--41
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\crossref{https://doi.org/10.17516/1997-1397-2021-14-1-28-41}
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This publication is cited in the following 11 articles:
N. Lazarev, G. Semenova, E. Efimova, “Equilibrium problem for an inhomogeneous two-dimensional elastic body with two interacting thin rigid inclusions”, Journal of Computational and Applied Mathematics, 438 (2024), 115539
Victor A. Kovtunenko, Nyurgun P. Lazarev, “Variational inequality for a Timoshenko plate contacting at the boundary with an inclined obstacle”, Phil. Trans. R. Soc. A., 382:2277 (2024)
Oksana V. Germider, Vasily N. Popov, “On calculation of bending of a thin orthotropic plate using Legendre and Chebyshev polynomials of the first kind”, Zhurn. SFU. Ser. Matem. i fiz., 17:5 (2024), 586–598
N. A. Nikolaeva, “Plastina Kirkhgofa — Lyava s ploskim zhestkim vklyucheniem”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 29–46
N. P. Lazarev, V. A. Kovtunenko, “Zadacha o ravnovesii dvumernogo uprugogo tela s dvumya kontaktiruyuschimi tonkimi zhestkimi vklyucheniyami”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 227, VINITI RAN, M., 2023, 51–60
N. P. Lazarev, E. F. Sharin, E. S. Efimova, “Equilibrium Problem for an Inhomogeneous Kirchhoff–Love Plate Contacting with a Partially Delaminated Inclusion”, Lobachevskii J Math, 44:10 (2023), 4127
N. P. Lazarev, E. D. Fedotov, “Trekhmernaya zadacha tipa Sinorini dlya kompozitnykh tel, kontaktiruyuschikh ostrymi granyami zhestkikh vklyuchenii”, Chelyab. fiz.-matem. zhurn., 7:4 (2022), 412–423
Nyurgun P. Lazarev, “Equilibrium problem for a thermoelastic Kirchhoff–Love plate with a delaminated flat rigid inclusion”, Phil. Trans. R. Soc. A., 380:2236 (2022)
Nyurgun Lazarev, Galina Semenova, Evgenii Sharin, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020002
N. P. Lazarev, E. F. Sharin, G. M. Semenova, “Optimalnoe upravlenie raspolozheniem tochki sharnirnogo soedineniya zhestkikh vklyuchenii v zadache o ravnovesii plastiny Timoshenko”, Chelyab. fiz.-matem. zhurn., 6:3 (2021), 278–288
Lazarev N., “Inverse Problem For Cracked Inhomogeneous Kirchhoff-Love Plate With Two Hinged Rigid Inclusions”, Bound. Value Probl., 2021:1 (2021), 88
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