On a strain gradient elastic Timoshenko beam model

Lazopoulos, KA; Lazopoulos

dc.contributor.author	Lazopoulos, KA	en
dc.contributor.author	Lazopoulos	en
dc.date.accessioned	2014-03-01T01:36:32Z
dc.date.available	2014-03-01T01:36:32Z
dc.date.issued	2011	en
dc.identifier.issn	0044-2267	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21328
dc.subject	Gradient elastic theory	en
dc.subject	Stiffer	en
dc.subject	Timoshenko beam.	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	COUPLE STRESS THEORY	en
dc.subject.other	SCREW DISLOCATION	en
dc.subject.other	PLATES	en
dc.subject.other	STABILITY	en
dc.title	On a strain gradient elastic Timoshenko beam model	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/zamm.200900368	en
heal.identifier.secondary	http://dx.doi.org/10.1002/zamm.200900368	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	Considering the influence of the microstructure, the Timoshenko beam model is revisited, invoking Mindlin's strain gradient strain energy density function. The equations of motion are derived and the bending equilibrium equations are discussed. The adopted strain energy density function includes new terms. Those terms introduce the strong effect of the beam cross-section area. The influence of those terms is more evident in thin beams where the cross-section area is far bigger than its moment of inertia. Applications have been worked out exhibiting the difference of the present theory not only from the classical Timoshenko beam, but also from the existing variations including couple stresses. The solution of the static problem, for a simply supported beam loaded by a force at the middle of the beam, is defined and the first (least) eigen-frequency is found. The present model is proved to be stiffer. Considering the influence of the microstructure, the Timoshenko beam model is revisited, invoking Mindlin's strain gradient strain energy density function. The equations of motion are derived and the bending equilibrium equations are discussed. The adopted strain energy density function includes new terms. Those terms introduce the strong effect of the beam cross-section area. The influence of those terms is more evident in thin beams where the cross-section area is far bigger than its moment of inertia. Applications have been worked out exhibiting the difference of the present theory not only from the classical Timoshenko beam, but also from the existing variations including couple stresses. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.	en
heal.publisher	WILEY-BLACKWELL	en
heal.journalName	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik	en
dc.identifier.doi	10.1002/zamm.200900368	en
dc.identifier.isi	ISI:000297304300003	en
dc.identifier.volume	91	en
dc.identifier.issue	11	en
dc.identifier.spage	875	en
dc.identifier.epage	882	en