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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Autores principales:	Miroslav Repka, Jan Sladek, Vladimir Sladek
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	von kármán large deformations flexoelectricity cantilever beam timoshenko model nonlinear system Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/4604a85724a1449eb41b00d80ff4b570
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spelling	oai:doaj.org-article:4604a85724a1449eb41b00d80ff4b5702021-11-25T18:32:38ZGeometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity10.3390/nano111131232079-4991https://doaj.org/article/4604a85724a1449eb41b00d80ff4b5702021-11-01T00:00:00Zhttps://www.mdpi.com/2079-4991/11/11/3123https://doaj.org/toc/2079-4991The 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.Miroslav RepkaJan SladekVladimir SladekMDPI AGarticlevon kármán large deformationsflexoelectricitycantilever beamtimoshenko modelnonlinear systemChemistryQD1-999ENNanomaterials, Vol 11, Iss 3123, p 3123 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	von kármán large deformations flexoelectricity cantilever beam timoshenko model nonlinear system Chemistry QD1-999
spellingShingle	von kármán large deformations flexoelectricity cantilever beam timoshenko model nonlinear system Chemistry QD1-999 Miroslav Repka Jan Sladek Vladimir Sladek Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity
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.
format	article
author	Miroslav Repka Jan Sladek Vladimir Sladek
author_facet	Miroslav Repka Jan Sladek Vladimir Sladek
author_sort	Miroslav Repka
title	Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity
title_short	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_sort	geometrical nonlinearity for a timoshenko beam with flexoelectricity
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4604a85724a1449eb41b00d80ff4b570
work_keys_str_mv	AT miroslavrepka geometricalnonlinearityforatimoshenkobeamwithflexoelectricity AT jansladek geometricalnonlinearityforatimoshenkobeamwithflexoelectricity AT vladimirsladek geometricalnonlinearityforatimoshenkobeamwithflexoelectricity
_version_	1718411011865706496

Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity

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