STATIC AND DYNAMIC, LOCAL AND GLOBAL, BIFURCATIONS IN NONLINEAR AUTONOMOUS STRUCTURAL SYSTEMS

Discrete damped or undamped gradient systems described by nonlinear au tonomous ordinary differential equations (ODE) of motion are examined in detail. Emphasis is given to the relationship between static with p ossibly existing dynamic bifurcations. Criteria for dynamic bifurcatio ns and stability of precritical, critical, and postcritical states ass ociated with the nature of Jacobian eigenvalues are also presented. Ca ses of discrepancies between local and global dynamic analysis regardi ng the stability of equilibriums are reported for the first time. Fina lly, using a simple energy criterion, exact dynamic buckling loads for vanishing but nonzero damping are readily obtained.