Reliability-based Structural Design

✍ Scribed by Seung-Kyum Choi, Ramana V. Grandhi, Robert A. Canfield

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 309
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

This book provides readers with an understanding of the fundamentals and applications of structural reliability, stochastic finite element method, reliability analysis via stochastic expansion, and optimization under uncertainty. It examines the use of stochastic expansions, including polynomial chaos expansion and Karhunen-Loeve expansion for the reliability analysis of practical engineering problems.

✦ Table of Contents

Contents......Page 7
1.1 Motivations......Page 11
1.2 Uncertainty and Its Analysis......Page 12
1.3 Reliability and Its Importance......Page 14
1.4 Outline of Chapters......Page 16
1.5 References......Page 17
2.1.1 Characteristics of Probability Distribution......Page 18
2.1.2 Common Probability Distributions......Page 29
2.2.1 Random Field and Its Discretization......Page 45
2.2.2 Covariance Function......Page 50
2.3 Fitting Regression Models......Page 52
2.3.1 Linear Regression Procedure......Page 53
2.3.2 Linear Regression with Polynomial Fit......Page 54
2.3.3 ANOVA and Other Statistical Tests......Page 55
2.4 References......Page 59
3.1.1 Structural Reliability Assessment......Page 60
3.1.2 Historical Developments of Probabilistic Analysis......Page 65
3.2.1 Monte Carlo Simulation (MCS)......Page 69
3.2.2 Importance Sampling......Page 77
3.2.3 Latin Hypercube Sampling (LHS)......Page 79
3.3 Stochastic Finite Element Method (SFEM)......Page 81
3.3.2 Perturbation Method......Page 82
3.3.3 Neumann Expansion Method......Page 84
3.3.4 Weighted Integral Method......Page 86
3.4 References......Page 88
4.1.1 First-order Second Moment (FOSM) Method......Page 90
4.1.2 Hasofer and Lind (HL) Safety-index......Page 95
4.1.3 Hasofer and Lind Iteration Method......Page 97
4.1.4 Sensitivity Factors......Page 106
4.1.5 Hasofer Lind - Rackwitz Fiessler (HL-RF) Method......Page 108
4.1.6 FORM with Adaptive Approximations......Page 119
4.2 Second-order Reliability Method (SORM)......Page 133
4.2.1 First- and Second-order Approximation of Limit-state Function......Page 134
4.2.2 Breitung's Formulation......Page 139
4.2.3 Tvedt's Formulation......Page 142
4.2.4 SORM with Adaptive Approximations......Page 145
4.3.1 Ten-bar Truss......Page 147
4.3.2 Fatigue Crack Growth......Page 151
4.3.3 Disk Burst Margin......Page 153
4.3.4 Two-member Frame......Page 155
4.4 References......Page 159
5.1 Multidisciplinary Optimization......Page 161
5.2 Mathematical Problem Statement and Algorithms......Page 163
5.3.1 Feasible Directions Algorithm......Page 165
5.3.2 Penalty Function Methods......Page 168
5.4 Sensitivity Analysis......Page 186
5.4.1 Sensitivity with Respect to Means......Page 189
5.4.2 Sensitivity with Respect to Standard Deviations......Page 190
5.4.3 Failure Probability Sensitivity in Terms of β......Page 191
5.5.1 Design Variable Linking......Page 205
5.5.4 Move Limits......Page 206
5.7 Reliability-based Design Optimization......Page 208
5.8 References......Page 209
6.1.1 Fundamentals of PCE......Page 211
6.1.2 Stochastic Approximation......Page 217
6.1.3 Non-Gaussian Random Variate Generation......Page 219
6.1.4 Hermite Polynomials and Gram-Charlier Series......Page 221
6.2 Karhunen-Loeve (KL) Transform......Page 226
6.2.1 Historical Developments of KL Transform......Page 227
6.2.2 KL Transform for Random Fields......Page 228
6.2.3 KL Expansion to Solve Eigenvalue Problems......Page 234
6.3 Spectral Stochastic Finite Element Method (SSFEM)......Page 237
6.3.1 Role of KL Expansion in SSFEM......Page 238
6.3.2 Role of PCE in SSFEM......Page 239
6.4 References......Page 241
7.1.1 Stochastic Analysis Procedure......Page 244
7.1.2 Gaussian Distribution Examples......Page 246
7.1.3 Non-Gaussian Distribution Examples......Page 255
7.2 Random Field......Page 259
7.2.2 Cantilever Plate Example......Page 260
7.2.3 Supercavitating Torpedo Example......Page 263
7.3 Stochastic Optimization......Page 267
7.3.2 Implementation of Stochastic Optimization......Page 268
7.3.3 Three-bar Truss Structure......Page 271
7.3.4 Joined-wing SensorCraft Structure......Page 274
7.4 References......Page 277
8. Summary......Page 279
A. Function Approximation Tools......Page 281
A.1 Use of Approximations and Advantages......Page 282
A.2 One-point Approximations......Page 283
A.3 Two-point Adaptive Nonlinear Approximations......Page 286
A.4 References......Page 295
B. Asymptotic of Multinormal Integrals......Page 296
B.1 References......Page 298
C. Cumulative Standard Normal Distribution Table......Page 299
D. F Distribution Table......Page 300
D......Page 304
H......Page 305
M......Page 306
R......Page 307
U......Page 308
W......Page 309