Uncertainty Assessment of Large Finite Element Systems (Lecture Notes in Applied and Computational Mechanics)

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. 1 Objectives....Pages 1-7 2 Outline....Pages 9-9 3 Spectral Analysis of Finite Dimensional Operators....Pages 13-17 4 Finite Element Method....Pages 19-21 5 Non-Linear Static Analysis....Pages 23-27 6 Dynamic Analysis....Pages 29-35 7 Rational Treatment of Uncertainties....Pages 39-46 8 Karhunen-Loève Expansion....Pages 47-58 9 Direct Monte Carlo Simulation....Pages 59-61 10 Equivalent Statistical Linearization....Pages 63-65 11 Random Vibrations of Large Finite Element Systems....Pages 67-77 12 Stability Analysis of Cylindrical Shells with Random Imperfections....Pages 81-109 13 Random Vibrations of Multi-Story Structures....Pages 111-139 A Imperfection Data Bank....Pages 143-148 B Lyapunov Matrix Differential Equation....Pages 149-151 "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-Loeve representation of the response is presented. The capabilities of the developed procedures are demonstrated with several numerical examples."--Résumé de l'éditeur "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-Loeve representation of the response is presented. The capabilities of the developed procedures are demonstrated with several numerical examples."--Jacket Complex deterministic systems under deterministic loading are generally analyzed by the finite element method.