Non-linear buckling of simple models with tilted cusp catastrophe

Lignos, X; Ioannidis, G; Kounadis, AN

dc.contributor.author	Lignos, X	en
dc.contributor.author	Ioannidis, G	en
dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:19:19Z
dc.date.available	2014-03-01T01:19:19Z
dc.date.issued	2003	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15423
dc.subject	Catastrophe Theory	en
dc.subject	Degeneration	en
dc.subject	Discrete Model	en
dc.subject	Exact Results	en
dc.subject	Potential Energy	en
dc.subject.classification	Mechanics	en
dc.subject.other	Approximation theory	en
dc.subject.other	Mathematical models	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Potential energy	en
dc.subject.other	Non-linear buckling	en
dc.subject.other	Buckling	en
dc.title	Non-linear buckling of simple models with tilted cusp catastrophe	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0020-7462(02)00061-6	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0020-7462(02)00061-6	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	Non-linear buckling universal solutions of simple multiple-parameter discrete models are discussed via a comprehensive and readily employed procedure using Catastrophe Theory. Attention is focused on perfect models whose total potential energy (TPE) function, upon small disturbance breaking symmetry, reduces to the universal unfolding of the tilted cusp catastrophe. A local analysis based on simple approximations allows us to classify the TPE universal unfolding of any model to one of the seven elementary Thom's catastrophes by defining the corresponding control parameters. Subsequently, using global analyses one can obtain exact results for establishing the non-linear equilibrium paths: (a) of the ""perfect"" perturbed model (due to the small effect of an extra parameter) with the corresponding ""imperfect"" bifurcation and limit points(s), and (b) of the imperfect models (resulting after inclusion of the effect of normal imperfection parameters) together with the corresponding to each parameter limit points. Moreover, conditions for the direct evaluation of (non-degenerate) hysteresis points associated with a tilted cusp point in the control parameter plane, are established. Numerical results illustrate the methodology proposed herein. © 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(02)00061-6	en
dc.identifier.isi	ISI:000180906300003	en
dc.identifier.volume	38	en
dc.identifier.issue	8	en
dc.identifier.spage	1163	en
dc.identifier.epage	1172	en