Reliability Evaluation of Dynamic Systems Excited in Time Domain: Alternative to Random Vibration and Simulation

Description

RELIABILITY EVALUATION OF DYNAMIC SYSTEMS EXCITED IN TIME DOMAIN – REDSET Multi-disciplinary approach to structural reliability analysis for dynamic loadings offering a practical alternative to the random vibration theory and simulation Reliability Evaluation of Dynamic Systems Excited in Time Domain – REDSET is a multidisciplinary concept that enables readers to estimate the underlying risk that could not be solved in the past. The major hurdle was that the required limit state functions (LSFs) are implicit in nature and the lack of progress in the reliability evaluation methods for this class of problems. The most sophisticated deterministic analysis requires that the dynamic loadings must be applied in the time domain. To satisfy these requirements, REDSET is developed. Different types and forms of dynamic loadings including seismic, wind-induced wave, and thermomechanical loading in the form of heating and cooling of solder balls used in computer chips are considered to validate REDSET. Time domain representations and the uncertainty quantification procedures including the use of multiple time histories are proposed and demonstrated for all these dynamic loadings. Both onshore and offshore structures are used for validation. The potential of REDSET is demonstrated for implementing the Performance Based Seismic Design (PBSD) concept now under development in the United States. For wider multidisciplinary applications, structures are represented by finite elements to capture different types of nonlinearity more appropriately. Any computer program capable of conducting nonlinear time domain dynamic analysis can be used, and the underlying risk can be estimated with the help of several dozens or hundreds of deterministic finite element analyses, providing an alternative to the simulation approach. To aid comprehension of REDSET, numerous illustrative examples and solution strategies are presented in each chapter. Written by award-winning thought leaders from academia and professional practice, the following sample topics are included: Fundamentals of reliability assessment including set theory, modeling of uncertainty, the risk-based engineering design concept, and the evolution of reliability assessment methods Implicit performance or limit state functions are expressed explicitly by the extensively modified response surface method with several new experimental designs Uncertainty quantification procedures with multiple time histories for different dynamic loadings, illustrated with examples The underlying risk can be estimated using any computer program representing structures by finite elements with only few deterministic analysesREDSET is demonstrated to be an alternative to the classical random vibration concept and the basic simulation procedure for risk estimation purposesREDSET changes the current engineering design paradigm. Instead of conducting one deterministic analysis, a design can be made more dynamic load tolerant, resilient, and sustainable with the help of a few additional deterministic analyses This book describing REDSET is expected to complement two other books published by Wiley and authored by Haldar and Mahadevan: Probability, Reliability and Statistical Methods in Engineering Design and Reliability Assessment Using Stochastic Finite Element Analysis. The book is perfect to use as a supplementary resource for upper-level undergraduate and graduate level courses on reliability and risk-based design. Cover Title Page Copyright Page Contents Chapter 1 REDSET and Its Necessity 1.1 Introductory Comments 1.2 Reliability Evaluation Procedures Existed Around 2000 1.3 Improvements or Alternative to Stochastic Finite Element Method (SFEM) 1.4 Other Alternatives Besides SFEM 1.4.1 Random Vibration 1.4.2 Alternative to Basic Monte Carlo Simulation 1.4.3 Alternatives to Random Vibration Approach for Large Problems 1.4.4 Physics-Based Deterministic FEM Formulation 1.4.5 Multidisciplinary Activities to Study the Presence of Uncertainty in Large Engineering Systems 1.4.6 Laboratory Testing 1.5 Justification of a Novel Risk Estimation Concept REDSET Replacing SFEM 1.6 Notes for Instructors 1.7 Notes to Students Acknowledgments Chapter 2 Fundamentals of Reliability Assessment 2.1 Introductory Comments 2.2 Set Theory 2.3 Modeling of Uncertainty 2.3.1 Continuous Random Variables 2.3.2 Discrete Random Variables 2.3.3 Probability Distribution of a Random Variable 2.3.4 Modeling of Uncertainty for Multiple Random Variables 2.4 Commonly Used Probability Distributions 2.4.1 Commonly Used Continuous and Discrete Random Variables 2.4.2 Combination of Discrete and Continuous Random Variables 2.5 Extreme Value Distributions 2.6 Other Useful Distributions 2.7 Risk-Based Engineering Design Concept 2.8 Evolution of Reliability Estimation Methods 2.8.1 First-Order Second-Moment Method 2.8.2 Advanced First-Order Reliability Method (AFOSM) 2.8.3 Hasofer-Lind Method 2.9 AFOSM for Non-Normal Variables 2.9.1 Two-Parameter Equivalent Normal Transformation 2.9.2 Three-Parameter Equivalent Normal Transformation 2.10 Reliability Analysis with Correlated Random Variables 2.11 First-Order Reliability Method (FORM) 2.11.1 FORM Method 1 2.11.2 Correlated Non-Normal Variables 2.12 Probabilistic Sensitivity Indices 2.13 FORM Method 2 2.14 System Reliability Evaluation 2.15 Fundamentals of Monte Carlo Simulation Technique 2.15.1 Steps in Numerical Experimentations Using Simulation 2.15.2 Extracting Probabilistic Information from N Data Points 2.15.3 Accuracy and Efficiency of Simulation 2.16 Concluding Remarks Chapter 3 Implicit Performance or Limit State Functions 3.1 Introductory Comments 3.2 Implicit Limit State Functions – Alternatives 3.3 Response Surface Method 3.4 Limitations of Using the Original RSM Concept for the Structural Reliability Estimation 3.5 Generation of Improved Response Surfaces 3.5.1 Polynomial Representation of an Improved Response Surface 3.6 Experimental Region, Coded Variables, and Center Point 3.6.1 Experimental Region and Coded Variables 3.6.2 Experimental Design 3.6.3 Saturated Design 3.6.4 Central Composite Design 3.7 Analysis of Variance 3.8 Experimental Design for Second-Order Polynomial 3.8.1 Experimental Design – Model 1: SD with Second-Order Polynomial without Cross Terms 3.8.2 Experimental Design – Model 2: SD with Second-Order Polynomial with Cross Terms 3.8.3 Experimental Design – Model 3: CCD with Second-Order Polynomial with Cross Terms 3.9 Comparisons of the Three Basic Factorial Designs 3.10 Experimental Designs for Nonlinear Dynamic Problems Excited in the Time Domain 3.11 Selection of the Most Appropriate Experimental Design 3.12 Selection of Center Point 3.13 Generation of Limit State Functions for Routine Design 3.13.1 Serviceability Limit State 3.13.2 Strength Limit State Functions 3.13.3 Interaction Equations for the Strength Limit State Functions 3.13.4 Dynamic Effect in Interaction Equations 3.14 Concluding Remarks Chapter 4 Uncertainty Quantification of Dynamic Loadings Applied in the Time Domain 4.1 Introductory Comments 4.2 Uncertainty Quantification in Seismic Loadings Applied in the Time Domain 4.2.1 Background Information 4.3 Selection of a Suite of Acceleration Time Histories Using PEER Database – Alternative 1 4.3.1 Earthquake Time History Selection Methodology 4.4 Demonstration of the Selection of a Suite of Ground Motion Time Histories – Alternative 1 4.5 Simulated Ground Motions Using the Broadband Platform (BBP) – Alternative 2 4.5.1 Broadband Platform Developed by SCEC 4.6 Demonstration of Selection and Validation of a Suite of Ground Motion Time Histories Using BPP 4.7 Applications of BBP in Selecting Multiple Earthquake Acceleration Time Histories 4.8 Summary of Generating Multiple Earthquake Time Histories Using BPP 4.9 Uncertainty Quantification of Wind-Induced Wave Loadings Applied in the Time Domain 4.9.1 Introductory Comments 4.9.2 Fundamentals of Wave Loading 4.9.3 Morison Equation 4.10 Modeling of Wave Loading 4.10.1 Wave Modeling Using the New Wave Theory 4.10.2 Wheeler Stretching Effect 4.10.3 Three-Dimensional Directionality 4.10.4 Summary of Deterministic Modeling of Wave Loading 4.11 Uncertainty Quantifications in Wave Loading Applied in the Time Domain 4.11.1 Uncertainty Quantification in Wave Loading – Three-Dimensional Constrained New Wave (3D CNW) Concept 4.11.2 Three-Dimensional Constrained New Wave (3D CNW) Concept 4.11.3 Uncertainty in the Wave Height Estimation 4.11.4 Uncertainty Quantification of Wave Loading 4.11.5 Quantification of Uncertainty in Wave Loading 4.12 Wave and Seismic Loadings – Comparisons 4.13 Concluding Remarks Chapter 5 Reliability Assessment of Dynamic Systems Excited in Time Domain – REDSET 5.1 Introductory Comments 5.2 A Novel Reliability Estimation Concept – REDSET 5.2.1 Integration of Finite Element Method, Improved Response Surface Method, and FORM 5.2.2 Increase Efficiency in Generating an IRS 5.2.3 OptimumNumber of NDFEA Required for the Generation of an IRS 5.2.4 Reduction of Random Variables 5.3 Advanced Sampling Design Schemes 5.4 Advanced Factorial Design Schemes 5.5 Modified Advanced Factorial Design Schemes 5.5.1 Modified Advanced Factorial Design Scheme 2 (MS2) 5.5.2 Modified Advanced Factorial Design Scheme 3 5.6 Optimum Number of TNDFEA Required to Implement REDSET 5.7 Improve Accuracy of Scheme MS3 Further – Alternative to the Regression Analysis 5.7.1 Moving Least Squares Method 5.7.2 Concept of Moving Least Squares Method 5.7.3 Improve Efficiency Further to the Moving Least Squares Method 5.8 Generation of an IRS Using Kriging Method 5.8.1 Simple Kriging 5.8.2 Ordinary Kriging 5.8.3 Universal Kriging 5.8.4 Variogram Function 5.8.5 Scheme S3 with Universal Kriging Method 5.8.6 Scheme MS3 with Modified Universal Kriging Method 5.9 Comparisons of All Proposed Schemes 5.10 Development of Reliability Evaluation of Dynamical Engineering Systems Excited in Time Domain (REDSET) 5.10.1 Required Steps in the Implementation of REDSET 5.11 Concluding Remarks Chapter 6 Verification of REDET for Earthquake Loading Applied in the Time Domain 6.1 Introductory Comments 6.2 Verification – Example 1: 3-Story Steel Moment Frame with W24 Columns 6.2.1 Example 1: Accuracy Study of All 9 Schemes 6.2.2 Verification – Example 2: 3-Story Steel Moment Frame with W14 Columns 6.3 Case Study: 13-Story Steel Moment Frame 6.4 Example 4: Site-Specific Seismic Safety Assessment of CDNES 6.4.1 Location, Soil Condition, and Structures 6.4.2 Uncertainty Quantifications 6.4.3 Uncertainty Quantifications in Resistance-Related Design Variables 6.4.3.1 Uncertainty Quantifications in Gravity Load-related Design Variables 6.4.3.2 Selection of a Suite of Site-Specific Acceleration Time Histories 6.5 Risk Evaluation of Three Structures using REDSET 6.5.1 Selection of Limit State Functions 6.5.2 Estimations of the Underlying Risk for the Three Structures 6.6 Concluding Remarks Chapter 7 Reliability Assessment of Jacket-Type Offshore Platforms Using REDSET for Wave and Seismic Loadings 7.1 Introductory Comments 7.2 Reliability Estimation of a Typical Jacket-Type Offshore Platform 7.3 Uncertainty Quantifications of a Jacket-Type Offshore Platform 7.3.1 Uncertainty in Structures 7.3.2 Uncertainty in Wave Loadings in the Time Domain 7.4 Performance Functions 7.4.1 LSF of Total Drift at the Top of the Platform 7.4.2 Strength Performance Functions 7.5 Reliability Evaluation of JTPs 7.6 Risk Estimations of JTPs Excited by the Wave and Seismic Loadings – Comparison 7.7 Comparison of Results for the Wave and Earthquake Loadings 7.8 Concluding Remarks Chapter 8 Reliability Assessment of Engineering Systems Using REDSET for Seismic Excitations and Implementation of PBSD 8.1 Introductory Comments 8.2 Assumed Stress-Based Finite Element Method for Nonlinear Dynamic Problems 8.2.1 Nonlinear Deterministic Seismic Analysis of Structures 8.2.2 Seismic Analysis of Steel Structures 8.2.3 Dynamic Governing Equation and Solution Strategy 8.2.4 Flexibility of Beam-to-Column Connection Models by Satisfying Underlying Physics – Partially Restrained Connections for Steel Structures 8.2.5 Incorporation of Connection Rigidities in the FE Formulation Using Richard Four-Parameter Model 8.3 Pre- and Post-Northridge Steel Connections 8.4 Performance-Based Seismic Design 8.4.1 Background Information and Motivation 8.4.2 Professional Perception of PBSD 8.4.3 Building Codes, Recommendations, and Guidelines 8.4.4 Performance Levels 8.4.5 Target Reliability Requirements to Satisfy Different Performance Levels 8.4.6 Elements of PBSD and Their Sequences 8.4.7 Explore Suitability of REDSET in Implementing PBSD 8.5 Showcasing the Implementation of PBSD 8.5.1 Verification of REDSET – Reliability Estimation of a 2-Story Steel Frame 8.6 Implementation Potential of PBSD – 3-, 9-, and 20-Story Steel Buildings 8.6.1 Description of the Three Buildings 8.6.2 Post-Northridge PR Connections 8.6.3 Quantification of Uncertainties in Resistance-Related Variables 8.6.4 Uncertainties in Gravity Loads 8.6.5 Uncertainties in PR Beam-to-Column Connections 8.6.6 Uncertainties in Seismic Loading 8.6.7 Serviceability Performance Functions – Overall and Inter-Story Drifts 8.7 Structural Reliability Evaluations of the Three Buildings for the Performance Levels of CP, LS, and IO Using REDSET 8.7.1 Observations for the Three Performance Levels 8.8 Implementation of PBSD for Different Soil Conditions 8.9 Illustrative Example of Reliability Estimation for Different Soil Conditions 8.9.1 Quantifications of Uncertainties for Resistance-Related Variables and Gravity Loads 8.9.2 Generation of Multiple Design Earthquake Time Histories for Different Soil Conditions 8.9.3 Implementation of PBSD for Different Soil Conditions 8.10 Concluding Remarks Chapter 9 Reliability Assessment of Lead-Free Solders in Electronic Packaging Using REDSET for Thermomechanical Loadings 9.1 Introductory Comments 9.2 Background Information 9.3 Deterministic Modelling of a Solder Ball 9.3.1 Solder Ball Represented by Finite Elements 9.3.2 Material Modeling of SAC Alloy 9.3.2.1 HISS Plasticity Model 9.3.2.2 Disturbed State Concept 9.3.2.3 Creep Modeling 9.3.2.4 Rate-Dependent Elasto-Viscoplastic Model 9.3.3 Temperature-Dependent Modeling 9.3.4 Constitutive Modeling Calibration 9.3.5 Thermomechanical Loading Experienced by Solder Balls 9.4 Uncertainty Quantification 9.4.1 Uncertainty in all the Parameters in a Solder Ball 9.4.2 Uncertainty Associated with Thermomechanical Loading 9.5 The Limit State Function for the Reliability Estimation 9.6 Reliability Assessment of Lead-Free Solders in Electronic Packaging 9.7 Numerical Verification Using Monte Carlo Simulation 9.8 Verification Using Laboratory Test Results 9.9 Concluding Remarks Concluding Remarks for the Book - REDSET References EULA Index