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

Author

Listed:
  • Evgeny Rudoy

    (Lavrentyev Institute of Hydrodynamics of SB RAS, 630090 Novosibirsk, Russia)

  • Sergey Sazhenkov

    (Lavrentyev Institute of Hydrodynamics of SB RAS, 630090 Novosibirsk, Russia)

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 .

Suggested Citation

  • Evgeny Rudoy & Sergey Sazhenkov, 2023. "Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3447-:d:1213122
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    References listed on IDEAS

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    1. Nyurgun P. Lazarev & Victor A. Kovtunenko, 2022. "Signorini-Type Problems over Non-Convex Sets for Composite Bodies Contacting by Sharp Edges of Rigid Inclusions," Mathematics, MDPI, vol. 10(2), pages 1-11, January.
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