Sub-structure Coupling for Dynamic Analysis (eBook)

Application to Complex Simulation-Based Problems Involving Uncertainty

Hector Jensen, Costas Papadimitriou (Autoren)

eBook Download: PDF

2019 | 1st ed. 2019
XIII, 227 Seiten
Springer International Publishing (Verlag)
978-3-030-12819-7 (ISBN)

Infos

This book combines a model reduction technique with an efficient parametrization scheme for the purpose of solving a class of complex and computationally expensive simulation-based problems involving finite element models. These problems, which have a wide range of important applications in several engineering fields, include reliability analysis, structural dynamic simulation, sensitivity analysis, reliability-based design optimization, Bayesian model validation, uncertainty quantification and propagation, etc.  The solution of this type of problems requires a large number of dynamic re-analyses. To cope with this difficulty, a model reduction technique known as substructure coupling for dynamic analysis is considered. While the use of reduced order models alleviates part of the computational effort, their repetitive generation during the simulation processes can be computational expensive due to the substantial computational overhead that arises at the substructure level. In this regard, an efficient finite element model parametrization scheme is considered.  When the division of the structural model is guided by such a parametrization scheme, the generation of a small number of reduced order models is sufficient to run the large number of dynamic re-analyses. Thus, a drastic reduction in computational effort is achieved without compromising the accuracy of the results. The capabilities of the developed procedures are demonstrated in a number of simulation-based problems involving uncertainty.

Inhalt

Preface 6
Acknowledgements 7
Contents 8
Reduced-Order Models 13
1 Model Reduction Techniques for Structural Dynamic Analyses 14
1.1 Structural Model 14
1.2 Substructure Modes 15
1.2.1 Fixed-Interface Normal Modes 16
1.2.2 Interface Constraint Modes 16
1.3 Reduced-Order Model: Standard Formulation 18
1.3.1 Transformation Matrix 18
1.3.2 Reduced-Order Matrices 21
1.4 Reduced-Order Model: Improved Formulation 22
1.4.1 Static Correction 22
1.4.2 Improved Transformation Matrix 24
1.4.3 Enhanced Reduced-Order Matrices 26
1.4.4 Remarks on the Use of Residual Modes 26
1.5 Numerical Implementation: Pseudo-Code No. 1 27
1.6 Global Interface Reduction 29
1.6.1 Interface Modes 29
1.6.2 Reduced-Order Matrices Based on Dominant Fixed-Interface Modes 30
1.6.3 Reduced-Order Matrices Based on Residual Fixed-Interface Modes 32
1.7 Numerical Implementation: Pseudo-Code No. 2 33
1.8 Local Interface Reduction 35
1.9 Numerical Implementation: Pseudo-Code No. 3 37
1.10 Reduced-Order Model Response 39
References 41
2 Parametrization of Reduced-Order Models Based on Normal Modes 43
2.1 Motivation 43
2.2 Parametrization Scheme 44
2.2.1 Substructure Matrices 44
2.2.2 Normal Modes and Interface Constraint Modes 45
2.3 Parametrization of Reduced-Order Matrices 46
2.3.1 Unreduced Matrices 47
2.3.2 Transformation Matrix TD 47
2.3.3 Reduced-Order Matrices D and D 48
2.3.4 Transformation Matrix TR 49
2.3.5 Reduced-Order Matrices R and R 51
2.3.6 Expansion of R and R Under Partial Invariant Conditions of TR 51
2.4 Numerical Implementation: Pseudo-Code No. 4 53
References 55
3 Parametrization of Reduced-Order Models Based on Global Interface Reduction 58
3.1 Meta-Model for Global Interface Modes 58
3.1.1 Baseline Information 59
3.1.2 Approximation of Interface Modes 59
3.1.3 Determination of Interpolation Coefficients 61
3.1.4 Higher-Order Approximations 62
3.1.5 Support Points 63
3.2 Numerical Implementation: Pseudo-Code No. 5 63
3.3 Reduced-Order Matrices Based on Global Interface Reduction 66
3.3.1 Transformation Matrix TDI 66
3.3.2 Reduced-Order Matrices DI and DI 67
3.3.3 Transformation Matrix TRI 68
3.3.4 Reduced-Order Matrices RI and RI 68
3.3.5 Expansion of RI and RI Under Global Invariant Conditions of TRI 69
3.4 Numerical Implementation: Pseudo-Code No. 6 70
3.5 Treatment of Local Interface Modes 72
3.6 Final Remarks 73
References 74
Application to Reliability Problems 75
4 Reliability Analysis of Dynamical Systems 76
4.1 Motivation 76
4.2 Reliability Problem Formulation 77
4.3 Reliability Estimation 78
4.3.1 General Remarks 78
4.3.2 Basic Ideas 79
4.3.3 Failure Probability Estimator 80
4.4 Numerical Implementation 81
4.4.1 Basic Implementation 81
4.4.2 Implementation Issues 82
4.5 Stochastic Model for Excitation 82
4.5.1 General Description 82
4.5.2 High-Frequency Components 83
4.5.3 Pulse Components 83
4.5.4 Synthesis of Near-Field Ground Motions 84
4.5.5 Seismicity Model 85
4.6 Application Problem No. 1 86
4.6.1 Model Description and Substructures Characterization 86
4.6.2 Reduced-Order Model Based on Dominant Fixed-Interface Normal Modes 87
4.6.3 Reduced-Order Model Based on Dominant and Residual Fixed-Interface Normal Modes 91
4.6.4 Reduced-Order Model Based on Interface Reduction 93
4.6.5 Reliability Problem 96
4.6.6 Remarks on the Use of Reduced-Order Models 98
4.6.7 Support Points 99
4.6.8 Reliability Results 100
4.6.9 Computational Cost 102
4.7 Application Problem No. 2 103
4.7.1 Structural Model 103
4.7.2 Definition of Substructures 105
4.7.3 System Reliability 110
4.7.4 Results 112
4.7.5 Computational Effort 114
References 115
5 Reliability Sensitivity Analysis of Dynamical Systems 119
5.1 Motivation 119
5.2 Reliability Sensitivity Analysis Formulation 120
5.3 Sensitivity Measure 120
5.4 Failure Probability Function Representation 121
5.5 Sensitivity Estimation 122
5.6 Sensitivity Versus Threshold 123
5.7 Particular Cases 124
5.8 Application Problem 126
5.8.1 Model Description 126
5.8.2 Rubber Bearings 127
5.8.3 Reliability Sensitivity Analysis Formulation 130
5.8.4 Reduced-Order Model 131
5.8.5 Results: Failure Event F1 134
5.8.6 Results: Failure Event F2 135
5.8.7 Results: Failure Event F3 138
5.8.8 Computational Cost 144
References 145
6 Reliability-Based Design Optimization 148
6.1 Motivation 148
6.2 Optimization Problem Formulation 149
6.3 Method of Solution 150
6.4 Interior Point Algorithm 151
6.4.1 Search Direction 151
6.4.2 Descent Feasible Direction Concept 153
6.4.3 Line Search 153
6.5 Gradient Estimation 154
6.5.1 Approximate Gradient of Failure Probability Function 155
6.5.2 Coefficient Estimation 156
6.6 Final Remarks 157
6.7 Numerical Examples 158
6.7.1 Example 1: Model Description 158
6.7.2 Example 1: Design Problem 161
6.7.3 Example 1: Results - Linked Design Variables Case 162
6.7.4 Example 1: Results - Independent Design Variables Case 163
6.7.5 Example 1: Numerical Effort 165
6.7.6 Example 2: Structural Model 165
6.7.7 Example 2: Design Problem Formulation 167
6.7.8 Example 2: Results 169
6.7.9 Example 2: Numerical Considerations 171
6.7.10 Example 3: Reliability-Based Design Formulation 172
6.7.11 Example 3: Substructures Characterization 173
6.7.12 Example 3: Design Scenario No. 1 175
6.7.13 Example 3: Design Scenario No. 2 176
6.7.14 Example 3: Computational Cost 178
References 179
Application to Identification Problems 182
7 Bayesian Finite Element Model Updating 183
7.1 Motivation 183
7.2 Bayesian Inference Framework 185
7.2.1 Finite Element Model and Uncertainty 185
7.2.2 Bayesian Model Parameter Estimation 185
7.2.3 Bayesian Model Selection 187
7.2.4 Data-Driven Robust Posterior Predictions 187
7.3 Bayesian Computational Tools 189
7.3.1 Asymptotic Approximations 189
7.3.2 Gradient-Based Optimization Algorithms 190
7.3.3 Stochastic Optimization Algorithms 191
7.3.4 Sampling Algorithms 192
7.4 Implementation in Structural Dynamics 193
7.4.1 Likelihood Formulation for Linear Models Based on Modal Properties 193
7.4.2 Likelihood Formulation Based on Response Time Histories 202
7.5 Numerical Examples 204
7.5.1 Example 1: Updating of Linear Model 204
7.5.2 Example 2: Updating of Nonlinear Model 220
References 229

Produkt-Details

• Erscheint lt. Verlag: 26.3.2019
• Reihe/Serie: Lecture Notes in Applied and Computational Mechanics
• Reihe/Serie: Lecture Notes in Applied and Computational Mechanics
• Zusatzinfo: XIII, 227 p. 106 illus., 47 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Computational Mechanics • Model reduction techniques • Reliability Analysis • Reliability Optimization • Reliability Sensitivity • Structural Dynamic Analysis • Structural Dynamic Simulation • uncertainty quantification
• ISBN-10: 3-030-12819-9 / 3030128199
• ISBN-13: 978-3-030-12819-7 / 9783030128197