Jensen / Papadimitriou Sub-structure Coupling for Dynamic Analysis

Application to Complex Simulation-Based Problems Involving Uncertainty
1. Auflage 2019
ISBN: 978-3-030-12819-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 89, 231 Seiten

Reihe: Lecture Notes in Applied and Computational Mechanics

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.

Autoren/Hrsg.

Jensen, Hector

Papadimitriou, Costas

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgements;7
3;Contents;8
4;Reduced-Order Models;13
5;1 Model Reduction Techniques for Structural Dynamic Analyses;14
5.1;1.1 Structural Model;14
5.2;1.2 Substructure Modes;15
5.2.1;1.2.1 Fixed-Interface Normal Modes;16
5.2.2;1.2.2 Interface Constraint Modes;16
5.3;1.3 Reduced-Order Model: Standard Formulation;18
5.3.1;1.3.1 Transformation Matrix;18
5.3.2;1.3.2 Reduced-Order Matrices;21
5.4;1.4 Reduced-Order Model: Improved Formulation;22
5.4.1;1.4.1 Static Correction;22
5.4.2;1.4.2 Improved Transformation Matrix;24
5.4.3;1.4.3 Enhanced Reduced-Order Matrices;26
5.4.4;1.4.4 Remarks on the Use of Residual Modes;26
5.5;1.5 Numerical Implementation: Pseudo-Code No. 1;27
5.6;1.6 Global Interface Reduction;29
5.6.1;1.6.1 Interface Modes;29
5.6.2;1.6.2 Reduced-Order Matrices Based on Dominant Fixed-Interface Modes;30
5.6.3;1.6.3 Reduced-Order Matrices Based on Residual Fixed-Interface Modes;32
5.7;1.7 Numerical Implementation: Pseudo-Code No. 2;33
5.8;1.8 Local Interface Reduction;35
5.9;1.9 Numerical Implementation: Pseudo-Code No. 3;37
5.10;1.10 Reduced-Order Model Response;39
5.11;References;41
6;2 Parametrization of Reduced-Order Models Based on Normal Modes;43
6.1;2.1 Motivation;43
6.2;2.2 Parametrization Scheme;44
6.2.1;2.2.1 Substructure Matrices;44
6.2.2;2.2.2 Normal Modes and Interface Constraint Modes;45
6.3;2.3 Parametrization of Reduced-Order Matrices;46
6.3.1;2.3.1 Unreduced Matrices;47
6.3.2;2.3.2 Transformation Matrix TD;47
6.3.3;2.3.3 Reduced-Order Matrices D and D;48
6.3.4;2.3.4 Transformation Matrix TR;49
6.3.5;2.3.5 Reduced-Order Matrices R and R;51
6.3.6;2.3.6 Expansion of R and R Under Partial Invariant Conditions of TR;51
6.4;2.4 Numerical Implementation: Pseudo-Code No. 4;53
6.5;References;55
7;3 Parametrization of Reduced-Order Models Based on Global Interface Reduction;58
7.1;3.1 Meta-Model for Global Interface Modes;58
7.1.1;3.1.1 Baseline Information;59
7.1.2;3.1.2 Approximation of Interface Modes;59
7.1.3;3.1.3 Determination of Interpolation Coefficients;61
7.1.4;3.1.4 Higher-Order Approximations;62
7.1.5;3.1.5 Support Points;63
7.2;3.2 Numerical Implementation: Pseudo-Code No. 5;63
7.3;3.3 Reduced-Order Matrices Based on Global Interface Reduction;66
7.3.1;3.3.1 Transformation Matrix TDI;66
7.3.2;3.3.2 Reduced-Order Matrices DI and DI;67
7.3.3;3.3.3 Transformation Matrix TRI;68
7.3.4;3.3.4 Reduced-Order Matrices RI and RI;68
7.3.5;3.3.5 Expansion of RI and RI Under Global Invariant Conditions of TRI;69
7.4;3.4 Numerical Implementation: Pseudo-Code No. 6;70
7.5;3.5 Treatment of Local Interface Modes;72
7.6;3.6 Final Remarks;73
7.7;References;74
8;Application to Reliability Problems;75
9;4 Reliability Analysis of Dynamical Systems;76
9.1;4.1 Motivation;76
9.2;4.2 Reliability Problem Formulation;77
9.3;4.3 Reliability Estimation;78
9.3.1;4.3.1 General Remarks;78
9.3.2;4.3.2 Basic Ideas;79
9.3.3;4.3.3 Failure Probability Estimator;80
9.4;4.4 Numerical Implementation;81
9.4.1;4.4.1 Basic Implementation;81
9.4.2;4.4.2 Implementation Issues;82
9.5;4.5 Stochastic Model for Excitation;82
9.5.1;4.5.1 General Description;82
9.5.2;4.5.2 High-Frequency Components;83
9.5.3;4.5.3 Pulse Components;83
9.5.4;4.5.4 Synthesis of Near-Field Ground Motions;84
9.5.5;4.5.5 Seismicity Model;85
9.6;4.6 Application Problem No. 1;86
9.6.1;4.6.1 Model Description and Substructures Characterization;86
9.6.2;4.6.2 Reduced-Order Model Based on Dominant Fixed-Interface Normal Modes;87
9.6.3;4.6.3 Reduced-Order Model Based on Dominant and Residual Fixed-Interface Normal Modes;91
9.6.4;4.6.4 Reduced-Order Model Based on Interface Reduction;93
9.6.5;4.6.5 Reliability Problem;96
9.6.6;4.6.6 Remarks on the Use of Reduced-Order Models;98
9.6.7;4.6.7 Support Points;99
9.6.8;4.6.8 Reliability Results;100
9.6.9;4.6.9 Computational Cost;102
9.7;4.7 Application Problem No. 2;103
9.7.1;4.7.1 Structural Model;103
9.7.2;4.7.2 Definition of Substructures;105
9.7.3;4.7.3 System Reliability;110
9.7.4;4.7.4 Results;112
9.7.5;4.7.5 Computational Effort;114
9.8;References;115
10;5 Reliability Sensitivity Analysis of Dynamical Systems;119
10.1;5.1 Motivation;119
10.2;5.2 Reliability Sensitivity Analysis Formulation;120
10.3;5.3 Sensitivity Measure;120
10.4;5.4 Failure Probability Function Representation;121
10.5;5.5 Sensitivity Estimation;122
10.6;5.6 Sensitivity Versus Threshold;123
10.7;5.7 Particular Cases;124
10.8;5.8 Application Problem;126
10.8.1;5.8.1 Model Description;126
10.8.2;5.8.2 Rubber Bearings;127
10.8.3;5.8.3 Reliability Sensitivity Analysis Formulation;130
10.8.4;5.8.4 Reduced-Order Model;131
10.8.5;5.8.5 Results: Failure Event F1;134
10.8.6;5.8.6 Results: Failure Event F2;135
10.8.7;5.8.7 Results: Failure Event F3;138
10.8.8;5.8.8 Computational Cost;144
10.9;References;145
11;6 Reliability-Based Design Optimization;148
11.1;6.1 Motivation;148
11.2;6.2 Optimization Problem Formulation;149
11.3;6.3 Method of Solution;150
11.4;6.4 Interior Point Algorithm;151
11.4.1;6.4.1 Search Direction;151
11.4.2;6.4.2 Descent Feasible Direction Concept;153
11.4.3;6.4.3 Line Search;153
11.5;6.5 Gradient Estimation;154
11.5.1;6.5.1 Approximate Gradient of Failure Probability Function;155
11.5.2;6.5.2 Coefficient Estimation;156
11.6;6.6 Final Remarks;157
11.7;6.7 Numerical Examples;158
11.7.1;6.7.1 Example 1: Model Description;158
11.7.2;6.7.2 Example 1: Design Problem;161
11.7.3;6.7.3 Example 1: Results - Linked Design Variables Case;162
11.7.4;6.7.4 Example 1: Results - Independent Design Variables Case;163
11.7.5;6.7.5 Example 1: Numerical Effort;165
11.7.6;6.7.6 Example 2: Structural Model;165
11.7.7;6.7.7 Example 2: Design Problem Formulation;167
11.7.8;6.7.8 Example 2: Results;169
11.7.9;6.7.9 Example 2: Numerical Considerations;171
11.7.10;6.7.10 Example 3: Reliability-Based Design Formulation;172
11.7.11;6.7.11 Example 3: Substructures Characterization;173
11.7.12;6.7.12 Example 3: Design Scenario No. 1;175
11.7.13;6.7.13 Example 3: Design Scenario No. 2;176
11.7.14;6.7.14 Example 3: Computational Cost;178
11.8;References;179
12;Application to Identification Problems;182
13;7 Bayesian Finite Element Model Updating;183
13.1;7.1 Motivation;183
13.2;7.2 Bayesian Inference Framework;185
13.2.1;7.2.1 Finite Element Model and Uncertainty;185
13.2.2;7.2.2 Bayesian Model Parameter Estimation;185
13.2.3;7.2.3 Bayesian Model Selection;187
13.2.4;7.2.4 Data-Driven Robust Posterior Predictions;187
13.3;7.3 Bayesian Computational Tools;189
13.3.1;7.3.1 Asymptotic Approximations;189
13.3.2;7.3.2 Gradient-Based Optimization Algorithms;190
13.3.3;7.3.3 Stochastic Optimization Algorithms;191
13.3.4;7.3.4 Sampling Algorithms;192
13.4;7.4 Implementation in Structural Dynamics;193
13.4.1;7.4.1 Likelihood Formulation for Linear Models Based on Modal Properties;193
13.4.2;7.4.2 Likelihood Formulation Based on Response Time Histories;202
13.5;7.5 Numerical Examples;204
13.5.1;7.5.1 Example 1: Updating of Linear Model;204
13.5.2;7.5.2 Example 2: Updating of Nonlinear Model;220
13.6;References;229