| Introduction | p. 1 |
| Motivations | p. 1 |
| Uncertainty and Its Analysis | p. 2 |
| Reliability and Its Importance | p. 4 |
| Outline of Chapters | p. 6 |
| References | p. 7 |
| Preliminaries | p. 9 |
| Basic Probabilistic Description | p. 9 |
| Characteristics of Probability Distribution | p. 9 |
| Random Variable | p. 9 |
| Probability Density and Cumulative Distribution Function | p. 10 |
| Joint Density and Distribution Functions | p. 12 |
| Central Measures | p. 13 |
| Dispersion Measures | p. 14 |
| Measures of Correlation | p. 15 |
| Other Measures | p. 17 |
| Common Probability Distributions | p. 20 |
| Gaussian Distribution | p. 20 |
| Lognormal Distribution | p. 25 |
| Gamma Distribution | p. 28 |
| Extreme Value Distribution | p. 29 |
| Weibull Distribution | p. 31 |
| Exponential Distribution | p. 34 |
| Random Field | p. 36 |
| Random Field and Its Discretization | p. 36 |
| Covariance Function | p. 41 |
| Exponential Model | p. 42 |
| Gaussian Model | p. 42 |
| Nugget-effect Model | p. 42 |
| Fitting Regression Models | p. 43 |
| Linear Regression Procedure | p. 44 |
| Linear Regression with Polynomial Fit | p. 45 |
| ANOVA and Other Statistical Tests | p. 46 |
| References | p. 50 |
| Probabilistic Analysis | p. 51 |
| Solution Techniques for Structural Reliability | p. 51 |
| Structural Reliability Assessment | p. 51 |
| Historical Developments of Probabilistic Analysis | p. 56 |
| First- and Second-order Reliability Method | p. 56 |
| Stochastic Expansions | p. 58 |
| Sampling Methods | p. 60 |
| Monte Carlo Simulation (MCS) | p. 60 |
| Generation of Random Variables | p. 62 |
| Calculation of the Probability of Failure | p. 65 |
| Importance Sampling | p. 68 |
| Latin Hypercube Sampling (LHS) | p. 70 |
| Stochastic Finite Element Method (SFEM) | p. 72 |
| Background | p. 73 |
| Perturbation Method | p. 73 |
| Basic Formulations | p. 74 |
| Neumann Expansion Method | p. 75 |
| Basic Procedure | p. 75 |
| Weighted Integral Method | p. 77 |
| Formulation of Weighted Integral Method | p. 77 |
| Spectral Stochastic Finite Element Method | p. 79 |
| References | p. 79 |
| Methods of Structural Reliability | p. 81 |
| First-order Reliability Method (FORM) | p. 81 |
| First-order Second Moment (FOSM) Method | p. 81 |
| Hasofer and Lind (HL) Safety-index | p. 86 |
| Hasofer and Lind Iteration Method | p. 88 |
| Sensitivity Factors | p. 97 |
| Hasofer Lind - Rackwitz Fiessler (HL-RF) Method | p. 99 |
| FORM with Adaptive Approximations | p. 110 |
| TANA | p. 111 |
| TANA2 | p. 111 |
| Second-order Reliability Method (SORM) | p. 124 |
| First- and Second-order Approximation of Limit-state Function | p. 125 |
| Orthogonal Transformations | p. 125 |
| First-order Approximation | p. 126 |
| Second-order Approximation | p. 128 |
| Breitung's Formulation | p. 130 |
| Tvedt's Formulation | p. 133 |
| SORM with Adaptive Approximations | p. 136 |
| Engineering Applications | p. 138 |
| Ten-bar Truss | p. 138 |
| Fatigue Crack Growth | p. 142 |
| Disk Burst Margin | p. 144 |
| Two-member Frame | p. 146 |
| References | p. 150 |
| Reliability-based Structural Optimization | p. 153 |
| Multidisciplinary Optimization | p. 153 |
| Mathematical Problem Statement and Algorithms | p. 155 |
| Mathematical Optimization Process | p. 157 |
| Feasible Directions Algorithm | p. 157 |
| Penalty Function Methods | p. 160 |
| Interior Penalty Function Method | p. 160 |
| Exterior and Quadratic Extended Interior Penalty Functions | p. 162 |
| Quadratic Extended Interior Penalty Functions Method | p. 163 |
| Sensitivity Analysis | p. 178 |
| Sensitivity with Respect to Means | p. 181 |
| Sensitivity with Respect to Standard Deviations | p. 182 |
| Failure Probability Sensitivity in Terms of [beta] | p. 183 |
| Practical Aspects of Structural Optimization | p. 197 |
| Design Variable Linking | p. 197 |
| Reduction of Number of Constraints | p. 198 |
| Approximation Concepts | p. 198 |
| Move Limits | p. 198 |
| Convergence to Local Optimum | p. 200 |
| Reliability-based Design Optimization | p. 200 |
| References | p. 201 |
| Stochastic Expansion for Probabilistic Analysis | p. 203 |
| Polynomial Chaos Expansion (PCE) | p. 203 |
| Fundamentals of PCE | p. 203 |
| Stochastic Approximation | p. 209 |
| Non-Gaussian Random Variate Generation | p. 211 |
| Generalized Polynomial Chaos Expansion | p. 212 |
| Transformation Technique | p. 212 |
| Hermite Polynomials and Gram-Charlier Series | p. 213 |
| Karhunen-Loeve (KL) Transform | p. 218 |
| Historical Developments of KL Transform | p. 219 |
| KL Transform for Random Fields | p. 220 |
| KL Expansion to Solve Eigenvalue Problems | p. 226 |
| Spectral Stochastic Finite Element Method (SSFEM) | p. 229 |
| Role of KL Expansion in SSFEM | p. 230 |
| Role of PCE in SSFEM | p. 231 |
| References | p. 233 |
| Probabilistic Analysis Examples via Stochastic Expansion | p. 237 |
| Gaussian and Non-Gaussian Distributions | p. 237 |
| Stochastic Analysis Procedure | p. 237 |
| Gaussian Distribution Examples | p. 239 |
| Demonstration Examples | p. 239 |
| Joined-wing Example | p. 244 |
| Non-Gaussian Distribution Examples | p. 248 |
| Pin-connected Three-bar Truss Structure | p. 248 |
| Joined-wing Example | p. 251 |
| Random Field | p. 252 |
| Simulation Procedure of Random Field | p. 253 |
| Cantilever Plate Example | p. 253 |
| Supercavitating Torpedo Example | p. 256 |
| Stochastic Optimization | p. 260 |
| Overview of Stochastic Optimization | p. 261 |
| Implementation of Stochastic Optimization | p. 261 |
| Three-bar Truss Structure | p. 264 |
| Joined-wing SensorCraft Structure | p. 267 |
| References | p. 270 |
| Summary | p. 273 |
| Appendices | p. 275 |
| Function Approximation Tools | p. 275 |
| Use of Approximations and Advantages | p. 276 |
| One-point Approximations | p. 277 |
| Linear Approximation | p. 278 |
| Reciprocal Approximation | p. 278 |
| Conservative Approximation | p. 279 |
| Two-point Adaptive Nonlinear Approximations | p. 280 |
| Two-point Adaptive Nonlinear Approximation | p. 280 |
| TANA1 | p. 281 |
| TANA2 | p. 283 |
| References | p. 289 |
| Asymptotic of Multinormal Integrals | p. 291 |
| References | p. 293 |
| Cumulative Standard Normal Distribution Table | p. 295 |
| F Distribution Table | p. 297 |
| Index | p. 301 |
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