Uncertainty assessment of large finite element systems.
Finite element models generally contain a large number of parameters like elasticity constants, geometry specifications, loading parameters, boundary conditions, etc., of which most values are not perfectly known. The values used in deterministic finite element analysis are so-called nominal values which deviate to a certain extent from the unknown true value. The uncertainties within the input parameters naturally result in uncertainties of the output, i.e. the response. The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. The developments in stochastic and deterministic computational mechanics began to be synchronized. To foster these developments, novel computational procedures for the uncertainty assessment of large finite element systems are presented in this monograph. The stochastic input is modeled by the so-called Karhunen-Loeve expansion, which is formulated in this context both for scalar and vector stochastic processes as well as for random fields. The Karhunen-Loeve expansion has been used in stochastic mechanics because of its attractive features; (i) the mean-square error resulting from a finite representation of a stochastic process is minimized; (ii) the expansion represents Gaussian stationary as well as non-stationary processes; (iii) for Gaussian stochastic processes the random coefficients are uncorrelated and thus are independent random variables. Particularly for strongly nonlinear structures and systems the direct Monte Carlo simulation technique has proven to be most advantageous as method of solution. The capabilities of the developed procedures are demonstrated by showing some practical applications. In order to place the procedures described in this monograph into perspectives, historical and current developments are illuminated. In this context, some areas of particular practical interest are treated in detail: the stability analysis of systems with random imperfections, the dynamics of deterministic systems subjected to stochastic loading, and finally random vibrations of large finite element systems.
scientific article; zbMATH DE number 5015568