Asymptotic solutions to the non-linear cantilever elastica

Stampouloglou, IH; Theotokoglou, EE; Andriotaki, PN

dc.contributor.author	Stampouloglou, IH	en
dc.contributor.author	Theotokoglou, EE	en
dc.contributor.author	Andriotaki, PN	en
dc.date.accessioned	2014-03-01T01:21:53Z
dc.date.available	2014-03-01T01:21:53Z
dc.date.issued	2005	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16406
dc.subject	Approximate analytic solutions	en
dc.subject	Asymptotic analysis	en
dc.subject	Elastica of cantilevers	en
dc.subject	Non-linear ODEs	en
dc.subject	Uniformly distributed loading	en
dc.subject.classification	Mechanics	en
dc.subject.other	Asymptotic solutions	en
dc.subject.other	Non-linear differential equations	en
dc.subject.other	Uniformly distributed loadings	en
dc.subject.other	Differential equations	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Nonlinear systems	en
dc.title	Asymptotic solutions to the non-linear cantilever elastica	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijnonlinmec.2005.05.003	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijnonlinmec.2005.05.003	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	In this work it is shown that by a series of admissible functional transformations the constructed higher-order strongly nonlinear differential equation (ODE), describing the elastica of a cantilever due to a terminal generalized concentrated, as well as to a lateral uniformly distributed loading, is reduced to a first-order non-linear integrodifferential equation consisting of the first intermediate integral of the original equation. The absence of exact analytic solutions in terms of known (tabulated) functions of the above reduced equation leads to the conclusion that there are no exact analytic solutions of this complicated elastica problem. In the limits of small values of the slope parameter of the deflected elastica, we expand asymptotically the above integrodifferential equation to non-linear ODEs of the generalized Emden-Fowler types, exact analytic solutions of which are constructed in parametric form. (c) 2005 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.doi	10.1016/j.ijnonlinmec.2005.05.003	en
dc.identifier.isi	ISI:000233098200003	en
dc.identifier.volume	40	en
dc.identifier.issue	10	en
dc.identifier.spage	1252	en
dc.identifier.epage	1262	en