Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions
An equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion <inline-formula><math display="inline"><semant...
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MDPI AG
2020-10-01
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| Online Access: | https://www.mdpi.com/2227-7080/8/4/59 |
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| author | Evgeny Rudoy |
| author_facet | Evgeny Rudoy |
| author_sort | Evgeny Rudoy |
| collection | DOAJ |
| description | An equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion <inline-formula><math display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> as <inline-formula><math display="inline"><semantics><msup><mi>ε</mi><mi>N</mi></msup></semantics></math></inline-formula> with <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The passage to the limit as the parameter <inline-formula><math display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion (<inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo><</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>) and elastic inclusion (<inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>). The inhomogeneity disappears in the case of <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. |
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| language | English |
| last_indexed | 2024-03-10T15:16:15Z |
| publishDate | 2020-10-01 |
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| series | Technologies |
| spelling | doaj.art-d4bde812762f463b90d369e24a5ae4f82023-11-20T18:55:27ZengMDPI AGTechnologies2227-70802020-10-01845910.3390/technologies8040059Asymptotic Justification of Models of Plates Containing Inside Hard Thin InclusionsEvgeny Rudoy0Lavrentyev Institute of Hydrodynamics of SB RAS, 630090 Novosibirsk, RussiaAn equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion <inline-formula><math display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> as <inline-formula><math display="inline"><semantics><msup><mi>ε</mi><mi>N</mi></msup></semantics></math></inline-formula> with <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The passage to the limit as the parameter <inline-formula><math display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion (<inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo><</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>) and elastic inclusion (<inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>). The inhomogeneity disappears in the case of <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7080/8/4/59Kirchhoff-Love platecomposite materialthin inclusionasymptotic analysis |
| spellingShingle | Evgeny Rudoy Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions Technologies Kirchhoff-Love plate composite material thin inclusion asymptotic analysis |
| title | Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions |
| title_full | Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions |
| title_fullStr | Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions |
| title_full_unstemmed | Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions |
| title_short | Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions |
| title_sort | asymptotic justification of models of plates containing inside hard thin inclusions |
| topic | Kirchhoff-Love plate composite material thin inclusion asymptotic analysis |
| url | https://www.mdpi.com/2227-7080/8/4/59 |
| work_keys_str_mv | AT evgenyrudoy asymptoticjustificationofmodelsofplatescontaininginsidehardthininclusions |