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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 959–974 (Mi semr1107)

Differentical equations, dynamical systems and optimal control

On equilibrium problem for a two-layer structure in the presence of a defect

I. V. Frankina

Lavrentyev Institute of Hydrodynamics, 15, Lavrentyeva àve., Novosibirsk, 630090, Russia

Abstract: The equilibrium problem of the structure, which consists of two elastic plates, is considered. It is assumed that the plates are flatly deformed, and the layers are modeled as elastic bodies. Plates are glued along a given line. In addition there is a defect along the gluing line in one of the layers. On the defect faces, nonlinear boundary conditions containing the damage parameter are established. Using the variational approach, the solvability of this problem is proved. In the problem, the passage to the limit is carried out when the damage parameter tends to zero and to infinity. Differential formulations for the corresponding limit problems are obtained. The case of the rigidity of one of the layers tends to infinity is considered; the obtained limit problem is analyzed.

Keywords: two-layer structure, nonpenetration condition, damage parameter, defect, variational inequality.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-29-10007_ìê

DOI: https://doi.org/10.33048/semi.2019.16.065

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Bibliographic databases:

UDC: 539.311,517.958
MSC: 35Q74,74G65
Received April 9, 2019, published July 31, 2019

Citation: I. V. Frankina, “On equilibrium problem for a two-layer structure in the presence of a defect”, Sib. Èlektron. Mat. Izv., 16 (2019), 959–974

Citation in format AMSBIB
\Bibitem{Fra19} \by I.~V.~Frankina \paper On equilibrium problem for a two-layer structure in the presence of a defect \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 959--974 \mathnet{http://mi.mathnet.ru/semr1107} \crossref{https://doi.org/10.33048/semi.2019.16.065} `