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 | ||
| Tags | ASYMPTOTIC ANALYSIS, INHOMOGENEOUS ELASTIC BODY, THIN INCLUSION, ROUGH BOUNDARY, INTERFACE CONDITION | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2022-0001 |
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.
Cite:
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
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
Dates:
| Submitted: | Jul 6, 2023 |
| Accepted: | Aug 7, 2023 |
| Published print: | Aug 8, 2023 |
Identifiers:
| Web of science: | WOS:001056508200001 |
| Scopus: | 2-s2.0-85199330107 |
| Elibrary: | 61500201 |
| OpenAlex: | W4385650486 |