Reliability-based structural design / Seung-Kyum Choi, Ramana V. Grandhi and Robert A. Canfield.

Includes bibliographical references and index.

"Reliability-based Structural Design will be a valuable reference for graduate and post graduate students studying structural reliability, probabilistic analysis and optimization under uncertainty; as well as engineers, researchers, and technical managers who are concerned with theoretical fundamentals, computational implementations and applications for probabilistic analysis and design."--Jacket.

1.1 Motivations 1 -- 1.2 Uncertainty and Its Analysis 2 -- 1.3 Reliability and Its Importance 4 -- 2.1 Basic Probabilistic Description 9 -- 2.1.1 Characteristics of Probability Distribution 9 -- Random Variable 9 -- Probability Density and Cumulative Distribution Function 10 -- Joint Density and Distribution Functions 12 -- Central Measures 13 -- Dispersion Measures 14 -- Measures of Correlation 15 -- Other Measures 17 -- 2.1.2 Common Probability Distributions 20 -- Gaussian Distribution 20 -- Lognormal Distribution 25 -- Gamma Distribution 28 -- Extreme Value Distribution 29 -- Weibull Distribution 31 -- Exponential Distribution 34 -- 2.2 Random Field 36 -- 2.2.1 Random Field and Its Discretization 36 -- 2.2.2 Covariance Function 41 -- Exponential Model 42 -- Gaussian Model 42 -- Nugget-effect Model 42 -- 2.3 Fitting Regression Models 43 -- 2.3.1 Linear Regression Procedure 44 -- 2.3.2 Linear Regression with Polynomial Fit 45 -- 2.3.3 ANOVA and Other Statistical Tests 46 -- 3 Probabilistic Analysis 51 -- 3.1 Solution Techniques for Structural Reliability 51 -- 3.1.1 Structural Reliability Assessment 51 -- 3.1.2 Historical Developments of Probabilistic Analysis 56 -- First- and Second-order Reliability Method 56 -- Stochastic Expansions 58 -- 3.2 Sampling Methods 60 -- 3.2.1 Monte Carlo Simulation (MCS) 60 -- Generation of Random Variables 62 -- Calculation of the Probability of Failure 65 -- 3.2.2 Importance Sampling 68 -- 3.2.3 Latin Hypercube Sampling (LHS) 70 -- 3.3 Stochastic Finite Element Method (SFEM) 72 -- 3.3.2 Perturbation Method 73 -- Basic Formulations 74 -- 3.3.3 Neumann Expansion Method 75 -- Basic Procedure 75 -- 3.3.4 Weighted Integral Method 77 -- Formulation of Weighted Integral Method 77 -- 3.3.5 Spectral Stochastic Finite Element Method 79 -- 4 Methods of Structural Reliability 81 -- 4.1 First-order Reliability Method (FORM) 81 -- 4.1.1 First-order Second Moment (FOSM) Method 81 -- 4.1.2 Hasofer and Lind (HL) Safety-index 86 -- 4.1.3 Hasofer and Lind Iteration Method 88 -- 4.1.4 Sensitivity Factors 97 -- 4.1.5 Hasofer Lind -- Rackwitz Fiessler (HL-RF) Method 99 -- 4.1.6 FORM with Adaptive Approximations 110 -- TANA 111 -- TANA2 111 -- 4.2 Second-order Reliability Method (SORM) 124 -- 4.2.1 First- and Second-order Approximation of Limit-state Function 125 -- Orthogonal Transformations 125 -- First-order Approximation 126 -- Second-order Approximation 128 -- 4.2.2 Breitung's Formulation 130 -- 4.2.3 Tvedt's Formulation 133 -- 4.2.4 SORM with Adaptive Approximations 136 -- 4.3 Engineering Applications 138 -- 4.3.1 Ten-bar Truss 138 -- 4.3.2 Fatigue Crack Growth 142 -- 4.3.3 Disk Burst Margin 144 -- 4.3.4 Two-member Frame 146 -- 5 Reliability-based Structural Optimization 153 -- 5.1 Multidisciplinary Optimization 153 -- 5.2 Mathematical Problem Statement and Algorithms 155 -- 5.3 Mathematical Optimization Process 157 -- 5.3.1 Feasible Directions Algorithm 157 -- 5.3.2 Penalty Function Methods 160 -- Interior Penalty Function Method 160 -- Exterior and Quadratic Extended Interior Penalty Functions 162 -- Quadratic Extended Interior Penalty Functions Method 163 -- 5.4 Sensitivity Analysis 178 -- 5.4.1 Sensitivity with Respect to Means 181 -- 5.4.2 Sensitivity with Respect to Standard Deviations 182 -- 5.4.3 Failure Probability Sensitivity in Terms of [beta] 183 -- 5.5 Practical Aspects of Structural Optimization 197 -- 5.5.1 Design Variable Linking 197 -- 5.5.2 Reduction of Number of Constraints 198 -- 5.5.3 Approximation Concepts 198 -- 5.5.4 Move Limits 198 -- 5.6 Convergence to Local Optimum 200 -- 5.7 Reliability-based Design Optimization 200 -- 6 Stochastic Expansion for Probabilistic Analysis 203 -- 6.1 Polynomial Chaos Expansion (PCE) 203 -- 6.1.1 Fundamentals of PCE 203 -- 6.1.2 Stochastic Approximation 209 -- 6.1.3 Non-Gaussian Random Variate Generation 211 -- Generalized Polynomial Chaos Expansion 212 -- Transformation Technique 212 -- 6.1.4 Hermite Polynomials and Gram-Charlier Series 213 -- 6.2 Karhunen-Loeve (KL) Transform 218 -- 6.2.1 Historical Developments of KL Transform 219 -- 6.2.2 KL Transform for Random Fields 220 -- 6.2.3 KL Expansion to Solve Eigenvalue Problems 226 -- 6.3 Spectral Stochastic Finite Element Method (SSFEM) 229 -- 6.3.1 Role of KL Expansion in SSFEM 230 -- 6.3.2 Role of PCE in SSFEM 231 -- 7 Probabilistic Analysis Examples via Stochastic Expansion 237 -- 7.1 Gaussian and Non-Gaussian Distributions 237 -- 7.1.1 Stochastic Analysis Procedure 237 -- 7.1.2 Gaussian Distribution Examples 239 -- Demonstration Examples 239 -- Joined-wing Example 244 -- 7.1.3 Non-Gaussian Distribution Examples 248 -- Pin-connected Three-bar Truss Structure 248 -- Joined-wing Example 251 -- 7.2 Random Field 252 -- 7.2.1 Simulation Procedure of Random Field 253 -- 7.2.2 Cantilever Plate Example 253 -- 7.2.3 Supercavitating Torpedo Example 256 -- 7.3 Stochastic Optimization 260 -- 7.3.1 Overview of Stochastic Optimization 261 -- 7.3.2 Implementation of Stochastic Optimization 261 -- 7.3.3 Three-bar Truss Structure 264 -- 7.3.4 Joined-wing SensorCraft Structure 267 -- A Function Approximation Tools 275 -- A.1 Use of Approximations and Advantages 276 -- A.2 One-point Approximations 277 -- A.2.1 Linear Approximation 278 -- A.2.2 Reciprocal Approximation 278 -- A.2.3 Conservative Approximation 279 -- A.3 Two-point Adaptive Nonlinear Approximations 280 -- A.3.1 Two-point Adaptive Nonlinear Approximation 280 -- A.3.2 TANA1 281 -- A.3.3 TANA2 283 -- B Asymptotic of Multinormal Integrals 291 -- C Cumulative Standard Normal Distribution Table 295 -- D F Distribution Table 297.