Approximate dynamic buckling loads of discrete systems via geometric considerations of their energy surface

Gantes, CJ; Kounadis, AN; Mallis, J

dc.contributor.author	Gantes, CJ	en
dc.contributor.author	Kounadis, AN	en
dc.contributor.author	Mallis, J	en
dc.date.accessioned	2014-03-01T01:13:35Z
dc.date.available	2014-03-01T01:13:35Z
dc.date.issued	1998	en
dc.identifier.issn	0178-7675	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12592
dc.subject	Discrete System	en
dc.subject	Dissipative Structure	en
dc.subject	Equilibrium Point	en
dc.subject	Nonlinear Dynamics	en
dc.subject	Ordinary Differential Equation	en
dc.subject	Potential Energy Surface	en
dc.subject	Qualitative Analysis	en
dc.subject	Saddle Point	en
dc.subject	Multi Degree of Freedom	en
dc.subject	Two Degree of Freedom	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Approximation theory	en
dc.subject.other	Buckling	en
dc.subject.other	Computer simulation	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Differential equations	en
dc.subject.other	Dynamic loads	en
dc.subject.other	Dynamic response	en
dc.subject.other	Discrete systems	en
dc.subject.other	Field equations	en
dc.subject.other	Potential energy surfaces	en
dc.subject.other	Structural analysis	en
dc.title	Approximate dynamic buckling loads of discrete systems via geometric considerations of their energy surface	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s004660050317	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s004660050317	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	The nonlinear dynamic buckling characteristics of multi-degree-of-freedom (MDOF), autonomous, nondissipative structural systems are investigated both qualitatively and quantitatively. Attention is focused on systems which under the same loading applied statically exhibit snapping. The field equations are highly nonlinear ordinary differential equations (O.D.E.) which can be integrated only numerically. Instead, a qualitative analysis based on energy and geometric criteria is performed which allows to readily obtain approximate dynamic buckling loads, the accuracy of which can be established a priori. It is found that the accuracy depends on the geometry of the motion channel, defined by the total potential energy surface V in the V - displacement space between the starting point of motion and the saddle point with V = 0. It is established that the slenderness of this channel and the location within it of the starting point of motion in connection with the positions of the saddle point and the stable equilibrium point corresponding to the same load are related to the accuracy of the approximate dynamic buckling load. A symbolic manipulation software is used to study the geometric characteristics of the V-surface and of the motion channel, which lead to the evaluation of the degree of accuracy of the results obtained by the proposed qualitative analysis. The efficiency and reliability of the method is comprehensively demonstrated through numerous examples of a two-degree-of-freedom model.	en
heal.publisher	Springer-Verlag GmbH & Company KG, Berlin, Germany	en
heal.journalName	Computational Mechanics	en
dc.identifier.doi	10.1007/s004660050317	en
dc.identifier.isi	ISI:000074177700017	en
dc.identifier.volume	21	en
dc.identifier.issue	4-5	en
dc.identifier.spage	398	en
dc.identifier.epage	402	en