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Mathematical notes of NEFU, 2021, Volume 28, Issue 1, Pages 51–66
DOI: https://doi.org/10.25587/SVFU.2021.12.25.005
(Mi svfu310)
 

Mathematics

Numerical solution of the equilibrium problem for a two-dimensional elastic body with a thin semirigid inclusion

T. S. Popova

Ammosov North-Eastern Federal University, 48 Kulakovsky Street, Yakutsk 677000, Russia
Abstract: The equilibrium problem for a two-dimensional elastic body containing a thin semirigid inclusion is considered. The inclusion delaminates from the elastic matrix, forming a crack; therefore, the problem is posed in a nonsmooth domain with a cut. The mathematical model of the delaminated thin semirigid inclusion was developed on the assumption that the rigidity of the material differs in different directions. The problem statement is presented both in the form of a variational inequality and in the form of a boundary value problem. The boundary condition on the crack faces has a form of inequality and, as a result, the problem is non-linear. Consequently, the construction of an algorithm for the numerical solution of the problem requires the use of additional analytical methods. The methods of domain decomposition, the method of Lagrange multipliers, and the finite element method are used. An algorithm for the numerical solution of the problem is constructed and a computational example is provided.
Keywords: variational inequality, semirigid inclusion, thin inclusion, crack, non-penetration conditions, nonlinear boundary conditions, domain decomposition, Uzawa algorithm.
Received: 14.01.2021
Revised: 26.02.2021
Accepted: 26.02.2021
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: T. S. Popova, “Numerical solution of the equilibrium problem for a two-dimensional elastic body with a thin semirigid inclusion”, Mathematical notes of NEFU, 28:1 (2021), 51–66
Citation in format AMSBIB
\Bibitem{Pop21}
\by T.~S.~Popova
\paper Numerical solution of the equilibrium problem for a two-dimensional elastic body with a thin semirigid inclusion
\jour Mathematical notes of NEFU
\yr 2021
\vol 28
\issue 1
\pages 51--66
\mathnet{http://mi.mathnet.ru/svfu310}
\crossref{https://doi.org/10.25587/SVFU.2021.12.25.005}
\elib{https://elibrary.ru/item.asp?id=45658540}
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