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ЖУРНАЛЫ // Сибирские электронные математические известия // Архив

Сиб. электрон. матем. изв., 2020, том 17, страницы 615–625 (Mi semr1235)

Эта публикация цитируется в 3 статьях

Дифференциальные уравнения, динамические системы и оптимальное управление

Asymptotic modelling of bonded plates by a soft thin adhesive layer

E. M. Rudoyab

a Lavrentyev Institute of Hydrodynamics of SB RAS, 15, Lavrenyeva ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogov str., Novosibirsk, 630090, Russia

Аннотация: In the present paper, a composite structure is considered. The structure is made of three homogeneous plates: two linear elastic adherents and a thin adhesive. It is assumed that elastic properties of the adhesive layer depend on its thickness $\varepsilon$ as $\varepsilon$ to the power of $3$. Passage to the limit as $\varepsilon$ goes to zero is justified and a limit model is found in which the influence of the thin adhesive layer is replaced by an interface condition between adherents. As a result, we have analog of the spring type condition in the plate theory. Moreover, a representation formula of the solution in the adhesive layer has been obtained.

Ключевые слова: bonded structure, Kirchhoff-Love's plate, composite material, spring type interface condition, biharmonic equation.

УДК: 517.9

MSC: 74K20

Поступила 21 января 2020 г., опубликована 17 апреля 2020 г.

Язык публикации: английский

DOI: 10.33048/semi.2020.17.040



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