Uncertainty Assessment of Large Finite Element Systems

The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. It is only in recent years that 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-Loève expansion, which is formulated in this context both for scalar and vector stochastic processes as well as for random fields. Particularly for strongly non-linear 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.

Presents novel computational procedures for the uncertainty assessment of large finite element systems Presents an efficient procedure based on the Karhunen-Loève representation of the response Includes several numerical examples

Inhalt
Part I Deterministic Methods and Procedures. Spectral Analysis of Finite Dimensional Operators. Finite Element Method. Non-Linear Static Analysis. Dynamic Analysis.- Part II Probabilistic Methods and Procedures. Rational Treatment of Uncertainties. Karhunen-Loève Expansion. Direct Monte Carlo Simulation. Equivalent Statistical Linearization. Random Vibrations of Large Finite Element Systems.- Part III Practical Applications. Stability Analysis of Cylindrical Shells with Random Imperfections. Random Vibrations of Multi-Story Office Buildings.