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

 
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1994 (EN)
A qualitative analysis for the local and global dynamic buckling and stability of autonomous discrete systems (EN)

Kounadis, AN (EN)

N/A (EN)

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)

journalArticle

Nonlinear dynamics (EN)
Convergence of numerical methods (EN)
System stability (EN)
Nonlinear dynamical gradient system (EN)
Estimation (EN)
Dynamic loads (EN)
Topology (EN)
Global dynamic buckling (EN)
Geometry (EN)
Discrete dissipative systems (EN)
Jacobian eigenvalues (EN)
Numerical analysis (EN)
Degrees of freedom (mechanics) (EN)
Chaos theory (EN)
Differential equations (EN)
Eigenvalues and eigenfunctions (EN)
Qualitative analysis (EN)
Buckling (EN)
Structural analysis (EN)

Εθνικό Μετσόβιο Πολυτεχνείο (EL)
National Technical University of Athens (EN)

Quarterly Journal of Mechanics and Applied Mathematics (EN)

1994


OXFORD UNIV PRESS UNITED KINGDOM (EN)



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