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

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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 http://hdl.handle.net/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

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