Stability Analysis for Imperfect Systems with Random Loading

fi nite elements method, probability theory, M onte C arlo simulation ABSTRACT: This paper shows an extension of research activities to stochastic dynamic stability problems. Both, the structure and the loading conditions are supposed to be random. The structures investigated are subjected to fluctuating loads in the vicinity of the static buckling load. The fluc-tuating components of the loading are modeled by stationary random processes, described by their power spectral density. As the loading is time dependent, the top Lyapunov exponent of the system has to be derived to determine the stability of the system. The top Lyapunov exponent can either be determined by nonlinear time integration of the system with accompanying stability analysis or by linear Itô analysis. The determination of the Lyapunov exponent by time integration shows one major difficulty: In statistical sense, the statement with respect to the Lyapunov exponent gets less precise as the structural response gets more critical. The Itô calculus principally represents an efficient linear analysis method to determine the second moment stability behavior of the structural system, suit-able for Finite Element analysis. Within this paper both approaches are performed and compared for geometrically perfect and imperfect systems.