Асимптотический анализ задачи о сопряжении включений Бернулли-Эйлера и Тимошенко в упругом теле

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Асимптотический анализ задачи о сопряжении включений Бернулли-Эйлера и Тимошенко в упругом теле. / Fankina, Irina Vladimirovna.

In: Siberian Electronic Mathematical Reports, Vol. 22, No. 1, 2025, p. 326-342.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2b05fa1917414043912a658a5a76bfc9,

title = "Асимптотический анализ задачи о сопряжении включений Бернулли-Эйлера и Тимошенко в упругом теле",

abstract = "We consider the equilibrium problem for a 2D elastic body with two thin elastic inclusions with a junction at a point. It is assumed that a crack exists between the inclusions and the body. Inequality-type boundary conditions are imposed at the crack faces to prevent mutual penetration. The problem depends on rigidity parameter of one of the inclusions: we are talking about family of problems. A weak convergence of solutions of the family of problems in suitable functional spaces is proved. By this convergence, we pass to the limit in the problems and establish the form of limit problem. Strong convergence of solutions of family of problems is also established. On its basis, the existence of a solution of the optimal control problem is proved. The optimal control problem is formulated in accordance with the Griffths failure criterion, the control parameter is the rigidity parameter of the inclusion.",

keywords = "crack, elastic body, junction conditions, non-penetration conditions, optimal control, rigidity parameter, thin inclusion, variational inequality",

author = "Fankina, {Irina Vladimirovna}",

note = "Фанкина И.В. Асимптотический анализ задачи о сопряжении включений Бернулли - Эйлера и Тимошенко в упругом теле // Сибирский электронный математический журнал. - 2025. - Т. 22. - № 1. - С. 326-342. DOI 10.33048/semi.2025.22.022 Работа выполнена при поддержке Математического Центра в Академгородке, соглашение № 075-15-2022-282 с Министерством науки и высшего образования Российской Федерации.",

year = "2025",

doi = "10.33048/semi.2025.22.022",

language = "русский",

volume = "22",

pages = "326--342",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

number = "1",

}

RIS

TY - JOUR

T1 - Асимптотический анализ задачи о сопряжении включений Бернулли-Эйлера и Тимошенко в упругом теле

AU - Fankina, Irina Vladimirovna

N1 - Фанкина И.В. Асимптотический анализ задачи о сопряжении включений Бернулли - Эйлера и Тимошенко в упругом теле // Сибирский электронный математический журнал. - 2025. - Т. 22. - № 1. - С. 326-342. DOI 10.33048/semi.2025.22.022 Работа выполнена при поддержке Математического Центра в Академгородке, соглашение № 075-15-2022-282 с Министерством науки и высшего образования Российской Федерации.

PY - 2025

Y1 - 2025

N2 - We consider the equilibrium problem for a 2D elastic body with two thin elastic inclusions with a junction at a point. It is assumed that a crack exists between the inclusions and the body. Inequality-type boundary conditions are imposed at the crack faces to prevent mutual penetration. The problem depends on rigidity parameter of one of the inclusions: we are talking about family of problems. A weak convergence of solutions of the family of problems in suitable functional spaces is proved. By this convergence, we pass to the limit in the problems and establish the form of limit problem. Strong convergence of solutions of family of problems is also established. On its basis, the existence of a solution of the optimal control problem is proved. The optimal control problem is formulated in accordance with the Griffths failure criterion, the control parameter is the rigidity parameter of the inclusion.

AB - We consider the equilibrium problem for a 2D elastic body with two thin elastic inclusions with a junction at a point. It is assumed that a crack exists between the inclusions and the body. Inequality-type boundary conditions are imposed at the crack faces to prevent mutual penetration. The problem depends on rigidity parameter of one of the inclusions: we are talking about family of problems. A weak convergence of solutions of the family of problems in suitable functional spaces is proved. By this convergence, we pass to the limit in the problems and establish the form of limit problem. Strong convergence of solutions of family of problems is also established. On its basis, the existence of a solution of the optimal control problem is proved. The optimal control problem is formulated in accordance with the Griffths failure criterion, the control parameter is the rigidity parameter of the inclusion.

KW - crack

KW - elastic body

KW - junction conditions

KW - non-penetration conditions

KW - optimal control

KW - rigidity parameter

KW - thin inclusion

KW - variational inequality

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105020401589&origin=inward

UR - https://www.mendeley.com/catalogue/8c42355b-6a2e-3727-8a75-8f833ecb9598/

U2 - 10.33048/semi.2025.22.022

DO - 10.33048/semi.2025.22.022

M3 - статья

VL - 22

SP - 326

EP - 342

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 71988499