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Эта публикация цитируется в 11 научных статьях (всего в 11 статьях)
Дифференциальные уравнения, динамические системы и оптимальное управление
On modeling elastic bodies with defects
A. M. Khludnevab a Lavrentyev Institute of Hydrodynamics of SB RAS
pr. Lavrentieva, 15,
630090, Novosibirsk, Russia
b Novosibirsk State University,
Pirogova str., 1,
630090, Novosibirsk, Russia
Аннотация:
The paper concerns a mathematical analysis of equilibrium problems for 2D elastic bodies with thin defects. The defects are characterized with a damage parameter. A presence of defects implies that the problems are formulated in a nonsmooth domain with a cut. Nonlinear boundary conditions at the cut faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are analyzed. The paper provides an asymptotic analysis with respect to the damage parameter. We obtain invariant integrals over curves surrounding the defect tip. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.
Ключевые слова:
defect, damage parameter, non-penetration boundary conditions, variational inequality, optimal control, derivative of energy functional.
Поступила 29 декабря 2017 г., опубликована 15 февраля 2018 г.
Образец цитирования:
A. M. Khludnev, “On modeling elastic bodies with defects”, Сиб. электрон. матем. изв., 15 (2018), 153–166
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr906 https://www.mathnet.ru/rus/semr/v15/p153
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