Nonlinear asymptotic analysis in elastica of straight bars-analytical parametric solutions

Andriotaki, PN; Stampouloglou, IH; Theotokoglou, EE

dc.contributor.author	Andriotaki, PN	en
dc.contributor.author	Stampouloglou, IH	en
dc.contributor.author	Theotokoglou, EE	en
dc.date.accessioned	2014-03-01T01:24:45Z
dc.date.available	2014-03-01T01:24:45Z
dc.date.issued	2006	en
dc.identifier.issn	0939-1533	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17416
dc.subject	Asymptotic analysis	en
dc.subject	Buckling analysis	en
dc.subject	Elastica of bars	en
dc.subject	Nonlinear ODEs	en
dc.subject	Parametric solutions	en
dc.subject.classification	Mechanics	en
dc.subject.other	Asymptotic stability	en
dc.subject.other	Buckling	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Buckling analysis	en
dc.subject.other	Elastica of bars	en
dc.subject.other	Parametric solutions	en
dc.subject.other	Bars (metal)	en
dc.title	Nonlinear asymptotic analysis in elastica of straight bars-analytical parametric solutions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00419-006-0054-4	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00419-006-0054-4	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	It is shown that by a series of admissible functional transformations the already derived (third-order) strongly nonlinear ordinary differential equation (ODE), describing the elastica buckling analysis of a straight bar under its own weight [Int.J.Solids Struct.24(12), 1179-1192, 1988, The Theory of Elastic Stability, McGraw-Hill, New York, 1961], is reduced to a first-order nonlinear integrodifferential equation. The absence of exact analytic solutions of the reduced equation leads to the conclusion that there are no exact analytic solutions in terms of known (tabulated) functions of this elastica buckling problem. In the limits of large or small values of the slope of the deflected elastica, we expand asymptotically the above integrodifferential equation to nonlinear ODEs of the Emden-Fowler or Abel nonlinear type. In these cases, using the solution methodology recently developed in Panayotounakos [Appl. Math. Lett. 18:155-162, 2005] and Panayotounakos and Kravvaritis [Nonlin. Anal. Real World Appl., 7(2):634-650, 2006], we construct exact implicit analytic solutions in parametric form of these types of equations and thus approximate implicit analytic solutions of the original elastica buckling nonlinear ODE. © Springer-Verlag 2006.	en
heal.publisher	SPRINGER	en
heal.journalName	Archive of Applied Mechanics	en
dc.identifier.doi	10.1007/s00419-006-0054-4	en
dc.identifier.isi	ISI:000241839000003	en
dc.identifier.volume	76	en
dc.identifier.issue	9-10	en
dc.identifier.spage	525	en
dc.identifier.epage	536	en