Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity
The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Kármán strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derive...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/11/11/3123 |
| _version_ | 1797508998882131968 |
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| author | Miroslav Repka Jan Sladek Vladimir Sladek |
| author_facet | Miroslav Repka Jan Sladek Vladimir Sladek |
| author_sort | Miroslav Repka |
| collection | DOAJ |
| description | The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Kármán strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derived. Moreover, this nonlinear system is linearized for each load increment, where it is solved iteratively. For the vanishing flexoelectric coefficient, the governing equations lead to the classical Timoshenko beam model. Furthermore, the influence of the flexoelectricity coefficient and the microstructural length-scale parameter on the beam deflection and the induced electric intensity is investigated. |
| first_indexed | 2024-03-10T05:11:46Z |
| format | Article |
| id | doaj.art-4604a85724a1449eb41b00d80ff4b570 |
| institution | Directory Open Access Journal |
| issn | 2079-4991 |
| language | English |
| last_indexed | 2024-03-10T05:11:46Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Nanomaterials |
| spelling | doaj.art-4604a85724a1449eb41b00d80ff4b5702023-11-23T00:43:32ZengMDPI AGNanomaterials2079-49912021-11-011111312310.3390/nano11113123Geometrical Nonlinearity for a Timoshenko Beam with FlexoelectricityMiroslav Repka0Jan Sladek1Vladimir Sladek2Institute of Construction and Architecture, Slovak Academy of Sciences, Dubravska Cesta 9, 84503 Bratislava, SlovakiaInstitute of Construction and Architecture, Slovak Academy of Sciences, Dubravska Cesta 9, 84503 Bratislava, SlovakiaInstitute of Construction and Architecture, Slovak Academy of Sciences, Dubravska Cesta 9, 84503 Bratislava, SlovakiaThe Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Kármán strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derived. Moreover, this nonlinear system is linearized for each load increment, where it is solved iteratively. For the vanishing flexoelectric coefficient, the governing equations lead to the classical Timoshenko beam model. Furthermore, the influence of the flexoelectricity coefficient and the microstructural length-scale parameter on the beam deflection and the induced electric intensity is investigated.https://www.mdpi.com/2079-4991/11/11/3123von kármán large deformationsflexoelectricitycantilever beamtimoshenko modelnonlinear system |
| spellingShingle | Miroslav Repka Jan Sladek Vladimir Sladek Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity Nanomaterials von kármán large deformations flexoelectricity cantilever beam timoshenko model nonlinear system |
| title | Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity |
| title_full | Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity |
| title_fullStr | Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity |
| title_full_unstemmed | Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity |
| title_short | Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity |
| title_sort | geometrical nonlinearity for a timoshenko beam with flexoelectricity |
| topic | von kármán large deformations flexoelectricity cantilever beam timoshenko model nonlinear system |
| url | https://www.mdpi.com/2079-4991/11/11/3123 |
| work_keys_str_mv | AT miroslavrepka geometricalnonlinearityforatimoshenkobeamwithflexoelectricity AT jansladek geometricalnonlinearityforatimoshenkobeamwithflexoelectricity AT vladimirsladek geometricalnonlinearityforatimoshenkobeamwithflexoelectricity |