Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion

Evgeny Rudoy () and Sergey Sazhenkov
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Evgeny Rudoy: Lavrentyev Institute of Hydrodynamics of SB RAS, 630090 Novosibirsk, Russia
Sergey Sazhenkov: Lavrentyev Institute of Hydrodynamics of SB RAS, 630090 Novosibirsk, Russia

Mathematics, 2023, vol. 11, issue 16, 1-14

Abstract: In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter δ characterizing its width and are assumed to be proportional to δ − 1 . Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as δ tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on δ .

Keywords: asymptotic analysis; inhomogeneous elastic body; thin inclusion; rough boundary; interface condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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