Uncertainty Assessment of Large Finite Element Systems [electronic resource] / by Christian A. Schenk, Gerhart I. Schuëller.Material type: TextLanguage: English Series: Lecture Notes in Applied and Computational Mechanics: 24Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: IX, 165 p. 61 illus. Also available online. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540323983Subject(s): Engineering | Physics | Mechanics | Materials | Mechanical engineering | Vibration | Engineering | Vibration, Dynamical Systems, Control | Structural Mechanics | Mechanics | Complexity | Numerical and Computational Methods in Engineering | Continuum Mechanics and Mechanics of MaterialsAdditional physical formats: Printed edition:: No titleDDC classification: 620 LOC classification: TA355TA352-356Online resources: Click here to access online
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.
The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. In this monograph novel computational procedures for the uncertainty assessment of large finite element systems are presented. The procedures are applicable to well known problems in computational stochastic mechanics, such as the stability analysis of systems with random imperfections and the dynamic analysis of deterministic systems under stochastic loading. For the dynamic analysis of deterministic systems under stochastic loading, an efficient procedure based on the Karhunen-Loève representation of the response is presented. The capabilities of the developed procedures are demonstrated with several numerical examples.