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Article

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

by
Evgeny Rudoy
* and
Sergey Sazhenkov
Lavrentyev Institute of Hydrodynamics of SB RAS, 630090 Novosibirsk, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(16), 3447; https://doi.org/10.3390/math11163447
Submission received: 6 July 2023 / Revised: 3 August 2023 / Accepted: 7 August 2023 / Published: 8 August 2023
(This article belongs to the Special Issue Variational Problems and Applications, 2nd Edition)
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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 asymptotic analysis; inhomogeneous elastic body; thin inclusion; rough boundary; interface condition

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MDPI and ACS Style

Rudoy, E.; Sazhenkov, S. Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion. Mathematics 2023, 11, 3447. https://doi.org/10.3390/math11163447

AMA Style

Rudoy E, Sazhenkov S. Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion. Mathematics. 2023; 11(16):3447. https://doi.org/10.3390/math11163447

Chicago/Turabian Style

Rudoy, Evgeny, and Sergey Sazhenkov. 2023. "Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion" Mathematics 11, no. 16: 3447. https://doi.org/10.3390/math11163447

APA Style

Rudoy, E., & Sazhenkov, S. (2023). Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion. Mathematics, 11(16), 3447. https://doi.org/10.3390/math11163447

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