Computational analysis of randomness in structural mechanics. (©2009)

• Record Type: Book
• Further Information: Note: Christian Bucher.
• Other Names: (Structural engineer), Bucher, Christian
• Contents: 1 Introduction 1.1 Outline 1.2 Introductory examples 1.2.1 Outline of analysis 1.2.2 Static analysis 1.2.3 Buckling analysis 1.2.4 Dynamic analysis 2 Preliminaries in Probability Theory and Statistics 2.1 Definitions 2.2 Probabilistic models 2.2.1 Random variables 2.2.2 Some types of distributions 2.2.3 Conditional distribution 2.2.4 Functions of random variables 2.2.5 Random vectors 2.2.6 Joint probability density function models 2.2.7 Marginal and conditional distribution 2.3 Estimation 2.3.1 Basic properties 2.3.2 Confidence intervals 2.3.3 Chi-square test 2.3.4 Correlation statistics 2.3.5 Bayesian updating 2.3.6 Entropy concepts 2.4 Simulation techniques 2.4.1 General remarks 2.4.2 Crude Monte Carlo simulation 2.4.3 Latin Hypercube sampling 2.4.4 Quasirandom sequences 2.4.5 Transformation of random samples 2.4.6 Simulation of correlated variables 3 Regression and Response Surfaces 3.1 Regression 3.2 Ranking of variables 3.3 Response surface models 3.3.1 Basic formulation 3.3.2 Linear models and regression 3.3.3 First- and second-order polynomials 3.3.4 Weighted interpolation 3.3.5 Moving Least Squares Regression 3.3.6 Radial basis functions 3.4 Design of experiments 3.4.1 Transformations 3.4.2 Saturated designs 3.4.3 Redundant designs 4 Mechanical vibrations due to random excitations 4.1 Basic definitions 4.2 Markov processes 4.2.1 Upcrossing rates 4.3 Single-degree-of-freedom system response 4.3.1 Mean and variance of response 4.3.2 White noise approximation 4.4 Multi-degree-of-freedom response 4.4.1 Equations of motion 4.4.2 Covariance analysis 4.4.3 First passage probability 4.5 Monte-Carlo simulation 4.5.1 General remarks 4.5.2 Central difference method 4.5.3 Euler method 4.5.4 Newmark method 4.5.5 Digital simulation of white noise 4.6 Fokker-Planck equation 4.7 Statistical linearization 4.7.1 General concept 4.8 Dynamic stability analysis 4.8.1 Basics 4.8.2 Nonlinear stability analysis 4.8.3 Linear stability analysis 5 Response analysis of spatially random structures 5.1 Representation of Random Fields 5.1.1 Basic Definitions 5.1.2 Properties of the auto-covariance function 5.1.3 Spectral Decomposition 5.1.4 Conditional Random Fields 5.1.5 Local Averages of Random Fields 5.2 Geometrical Imperfections 5.3 Stochastic Finite Element Formulation 5.3.1 Elasticity (Plane Stress) 5.3.2 Principle of Virtual Work 5.4 Finite Element Method 5.4.1 Element Formulation 5.4.2 Structural response 5.4.3 Stochastic Stiffness Matrix 5.4.4 Integration Point Method 5.4.5 Static Response - Perturbation Method 5.4.6 Monte Carlo Simulation 5.4.7 Natural Frequencies of a Structure with Randomly Distributed Elastic Modulus 6 Computation of failure probabilities 6.1 Structural Reliability 6.1.1 Definitions 6.1.2 First Order - Second Moment Concept 6.1.3 FORM - First Order Reliability Method 6.2 Monte-Carlo-Simulation 6.2.1 Definitions and Basics 6.2.2 Importance Sampling (Weighted Simulation) 6.2.3 Directional Sampling 6.2.4 Asymptotic Sampling 6.3 Application of RSM 6.3.1 Basic concept 6.3.2 Structural examples 6.4 First Passage Failure 6.4.1 Problem formulation 6.4.2 Extension to Non-Linear Problems
• Publisher Details: Boca Raton [Fla.] London : CRC Press
• Publication Date: 2009
• Copyright Date: 2009
• Extent: 1 online resource (xii, 230 pages), illustrations
• Subjects: 624.1/71; Structural analysis (Engineering) -- Data processing; Stochastic analysis; TECHNOLOGY & ENGINEERING -- Structural; Stochastic analysis; Structural analysis (Engineering) -- Data processing; Electronic books
• Languages: English
• ISBNs: 9780203876534; 0203876539; 9780415403542; 0415403545; 9781134140954; 1134140959
• Notes: Note: Includes bibliographical references (pages 223-227) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.