A qualitative analysis for the local and global dynamic buckling and stability of autonomous discrete systems

Kounadis, AN

dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:09:40Z
dc.date.available	2014-03-01T01:09:40Z
dc.date.issued	1994	en
dc.identifier.issn	0033-5614	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11138
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	Buckling	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Degrees of freedom (mechanics)	en
dc.subject.other	Differential equations	en
dc.subject.other	Dynamic loads	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Estimation	en
dc.subject.other	Geometry	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Structural analysis	en
dc.subject.other	System stability	en
dc.subject.other	Topology	en
dc.subject.other	Discrete dissipative systems	en
dc.subject.other	Global dynamic buckling	en
dc.subject.other	Jacobian eigenvalues	en
dc.subject.other	Nonlinear dynamical gradient system	en
dc.subject.other	Nonlinear dynamics	en
dc.subject.other	Qualitative analysis	en
dc.subject.other	Chaos theory	en
dc.title	A qualitative analysis for the local and global dynamic buckling and stability of autonomous discrete systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1093/qjmam/47.2.269	en
heal.identifier.secondary	http://dx.doi.org/10.1093/qjmam/47.2.269	en
heal.language	English	en
heal.publicationDate	1994	en
heal.abstract	A general analytic approach is presented for the local and global dynamic buckling and stability of discrete dissipative systems described by the most general form of autonomous ordnary differential equations. Attention is focused on nonlinear dynamical gradient systems which under static loading exhibit all types of simple branching points emanating from a trivial fundamental equilibrium path. The relationship between the static stability (in the precritical, critical and postcritical stage) and the corresponding dynamic stability associated with the Jacobian eigenvalues is thoroughly discussed. Conditions are established for the boundedness of solutions based on the basins of attraction of stable equilibria as well as for dynamic buckling related to a certain saddle with specific potential topology. 'Exact' and lower-upper-bound estimates of dynamic-buckling loads based on a qualitative and geometrical analysis, as well as discrepancies between global and local dynamic analyses for systems exhibiting a postcritical limit-point instability, are also reported. © 1994 Oxford University Press.	en
heal.publisher	OXFORD UNIV PRESS UNITED KINGDOM	en
heal.journalName	Quarterly Journal of Mechanics and Applied Mathematics	en
dc.identifier.doi	10.1093/qjmam/47.2.269	en
dc.identifier.isi	ISI:A1994NQ89400006	en
dc.identifier.volume	47	en
dc.identifier.issue	2	en
dc.identifier.spage	269	en
dc.identifier.epage	295	en