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

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

Journal

Сибирские электронные математические известия / Siberian Electronic Mathematical Reports
ISSN: 1813-3304

Output data

Year: 2025, Volume: 22, Number: 1, Pages: 326-342 Pages count : 17 DOI: 10.33048/semi.2025.22.022

Tags

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

Authors

Фанкина И.В. ^1,2

Affiliations

1	Novosibirsk State University
2	Lavrentyev Institute of Hydrodynamics

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 Griffiths failure criterion, the control parameter is the rigidity parameter of the inclusion.

Фанкина И.В.
Асимптотический анализ задачи о сопряжении включений Бернулли -- Эйлера и Тимошенко в упругом теле
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2025. Т.22. №1. С.326-342. DOI: 10.33048/semi.2025.22.022 WOS Scopus

Published online:

Apr 15, 2025

Web of science:	WOS:001473623500019
Scopus:	2-s2.0-105020401589

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