Dynamic buckling of simple two-bar frames using catastrophe theory

Kounadis, AN

dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:17:45Z
dc.date.available	2014-03-01T01:17:45Z
dc.date.issued	2002	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14644
dc.subject	Catastrophe theory	en
dc.subject	Dynamic	en
dc.subject	Frames	en
dc.subject	Non-linear buckling	en
dc.subject.classification	Mechanics	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Buckling	en
dc.subject.other	Dynamics	en
dc.subject.other	Elasticity	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Potential energy	en
dc.subject.other	Structural loads	en
dc.subject.other	Catastrophe theory	en
dc.subject.other	Structural frames	en
dc.title	Dynamic buckling of simple two-bar frames using catastrophe theory	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0020-7462(01)00138-X	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0020-7462(01)00138-X	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	Non-linear static and dynamic elastic buckling of simple imperfect two-bar frames, treated as continuous systems, are analyzed with the aid of catastrophe theory using a comprehensive and readily employed procedure. Static catastrophes are extended to the corresponding dynamic catastrophes of undamped frames under step loading (autonomous systems) by properly determining the dynamic singularity and bifurcational sets. Attention is focused on fold and cusp catastrophes. A local analysis based on Taylor's expansion of the non-linear equilibrium equation of the frame allows us: (a) to classify the total potential energy function of the frames to the canonical form of the corresponding universal unfolding of the seven elementary Thom's catastrophes, and (b) to easily obtain static and dynamic buckling loads, critical points (singularity sets) and related imperfection sensitivities (bifurcational sets). An illustrative example associated with a static and dynamic fold catastrophe demonstrates the efficiency and reliability of the methodology proposed herein. (C) 2002 Elsevier Science 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/S0020-7462(01)00138-X	en
dc.identifier.isi	ISI:000175701800012	en
dc.identifier.volume	37	en
dc.identifier.issue	7	en
dc.identifier.spage	1249	en
dc.identifier.epage	1259	en