Reliability Assessment Using Stochastic Finite Element AnalysisThe first complete guide to using the Stochastic Finite Element Method for reliability assessment Unlike other analytical reliability estimation techniques, the Stochastic Finite Element Method (SFEM) can be used for both implicit and explicit performance functions, making it a particularly powerful and robust tool for today's engineer. This book, written by two pioneers in SFEM-based methodologies, shows how to use SFEM for the reliability analysis of a wide range of structures. It begins by reviewing essential risk concepts, currently available risk evaluation procedures, and the use of analytical and sampling methods in estimating risk. Next, it introduces SFEM evaluation procedures, with detailed coverage of displacement-based and stress-based deterministic finite element approaches. Linear, nonlinear, static, and dynamic problems are considered separately to demonstrate the robustness of the methods. The risk or reliability estimation procedure for each case is presented in different chapters, with theory complemented by a useful series of examples. Integrating advanced concepts in risk-based design, finite elements, and mechanics, Reliability Assessment Using Stochastic Finite Element Analysis is vital reading for engineering professionals and students in all areas of the field. |
Contents
Commonly Used Probability Distributions | 9 |
Fundamentals of Reliability Analysis | 55 |
Simulation Techniques | 105 |
Introduction to SFEM | 127 |
SFEM for Linear Static Problems | 146 |
SFEM for Spatial Variability Problems | 168 |
105 | 185 |
SFEMBased Reliability Evaluation of Nonlinear Two | 197 |
Structures under Dynamic Loading | 263 |
Table of Cumulative Standard Normal Distribution | 297 |
Evaluation of Gamma Function | 301 |
GramSchmidt Orthogonalization | 303 |
Conversion Factors | 305 |
| 307 | |
| 321 | |
Common terms and phrases
0.05 Lognormal algorithm approximation assumed basic random variables beam behavior calculated chain rule Chapter closed-form closed-form expression cm² cm³ coefficients computed considered convergence coordinates correlation corresponding deflection deformation degrees of freedom design point deterministic discretization discussed displacement estimate evaluated extreme value distribution finite element analysis finite element method formulation limit state equation limit state function linear mean values midpoint method midspan Monte Carlo simulation nodal node obtained partial derivatives performance function plastic portal frame PR connections probability of failure problem random field element random numbers random process reliability analysis reliability index respect rotation safety index scale of fluctuation second-order Sensitivity Index SFEM SFEM-based reliability analysis shown in Figure SORM spatial averaging method standard deviation standard normal statistically independent statistics Step stiffness matrix stochastic finite element strength limit support conditions tion Type uncertainty variance vector Young's modulus ах диз