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

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

Journal

Mathematics
ISSN: 2227-7390

Output data

Year: 2023, Volume: 11, Number: 16, Article number : 3447, Pages count : 14 DOI: 10.3390/math11163447

Funding (1)

Министерство науки и высшего образования Российской Федерации

FWGG-2022-0001

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.

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. V.11. N16. 3447 :1-14. DOI: 10.3390/math11163447 WOS Scopus РИНЦ OpenAlex

Submitted:	Jul 6, 2023
Accepted:	Aug 7, 2023
Published print:	Aug 8, 2023

Web of science:	WOS:001056508200001
Scopus:	2-s2.0-85199330107
Elibrary:	61500201
OpenAlex:	W4385650486

Пока нет цитирований