Dynamic buckling of a simple geometrically imperfect frame using Catastrophe Theory

Raftoyiannis, IG; Constantakopoulos, TG; Michaltsos, GT; Kounadis, AN

dc.contributor.author	Raftoyiannis, IG	en
dc.contributor.author	Constantakopoulos, TG	en
dc.contributor.author	Michaltsos, GT	en
dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:24:02Z
dc.date.available	2014-03-01T01:24:02Z
dc.date.issued	2006	en
dc.identifier.issn	0020-7403	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17174
dc.subject	Catastrophe theory	en
dc.subject	Dynamic buckling	en
dc.subject	Fold catastrophes	en
dc.subject	Inperfect frames	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Materials science	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Potential energy	en
dc.subject.other	Set theory	en
dc.subject.other	Structural frames	en
dc.subject.other	Catastrophe theory	en
dc.subject.other	Dynamic buckling	en
dc.subject.other	Fold catastrophes	en
dc.subject.other	Inperfect frames	en
dc.subject.other	Total potential energy (TPE)	en
dc.subject.other	Buckling	en
dc.title	Dynamic buckling of a simple geometrically imperfect frame using Catastrophe Theory	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijmecsci.2006.05.010	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijmecsci.2006.05.010	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	This paper deals with nonlinear static and dynamic buckling of a geometrically imperfect two-bar frame due to initially crooked bars, which is subjected to an eccentrically applied load at its joint. The analysis is facilitated by considering the frame (being a continuous system) as one degree-of-freedom (1-DOF) system with generalized coordinate unknown the column axial force and then by employing catastrophe theory. Through a local analysis via Taylor's expansion of the nonlinear equilibrium equation of the frame, one can classify the total potential energy (TPE) function of the frame to the canonical form of the corresponding TPE function of the seven elementary Thom's catastrophes. Using energy criteria static catastrophes are extended to the corresponding dynamic catastrophes of undamped frames under step loading (autonomous systems) by conveniently determining the dynamic singularity and bifurcational sets. Numerical examples associated with static and dynamic fold catastrophes demonstrate the efficiency and reliability of the present approach. (C) 2006 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Mechanical Sciences	en
dc.identifier.doi	10.1016/j.ijmecsci.2006.05.010	en
dc.identifier.isi	ISI:000240702800001	en
dc.identifier.volume	48	en
dc.identifier.issue	10	en
dc.identifier.spage	1021	en
dc.identifier.epage	1030	en