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Table of Contents
Intro; Preface; Acknowledgements; Contents; Reduced-Order Models; 1 Model Reduction Techniques for Structural Dynamic Analyses; 1.1 Structural Model; 1.2 Substructure Modes; 1.2.1 Fixed-Interface Normal Modes; 1.2.2 Interface Constraint Modes; 1.3 Reduced-Order Model: Standard Formulation; 1.3.1 Transformation Matrix; 1.3.2 Reduced-Order Matrices; 1.4 Reduced-Order Model: Improved Formulation; 1.4.1 Static Correction; 1.4.2 Improved Transformation Matrix; 1.4.3 Enhanced Reduced-Order Matrices; 1.4.4 Remarks on the Use of Residual Modes; 1.5 Numerical Implementation: Pseudo-Code No. 1
1.6 Global Interface Reduction1.6.1 Interface Modes; 1.6.2 Reduced-Order Matrices Based on Dominant Fixed-Interface Modes; 1.6.3 Reduced-Order Matrices Based on Residual Fixed-Interface Modes; 1.7 Numerical Implementation: Pseudo-Code No. 2; 1.8 Local Interface Reduction; 1.9 Numerical Implementation: Pseudo-Code No. 3; 1.10 Reduced-Order Model Response; References; 2 Parametrization of Reduced-Order Models Based on Normal Modes; 2.1 Motivation; 2.2 Parametrization Scheme; 2.2.1 Substructure Matrices; 2.2.2 Normal Modes and Interface Constraint Modes
2.3 Parametrization of Reduced-Order Matrices2.3.1 Unreduced Matrices; 2.3.2 Transformation Matrix TD; 2.3.3 Reduced-Order Matrices D and D; 2.3.4 Transformation Matrix TR; 2.3.5 Reduced-Order Matrices R and R; 2.3.6 Expansion of R and R Under Partial Invariant Conditions of TR; 2.4 Numerical Implementation: Pseudo-Code No. 4; References; 3 Parametrization of Reduced-Order Models Based on Global Interface Reduction; 3.1 Meta-Model for Global Interface Modes; 3.1.1 Baseline Information; 3.1.2 Approximation of Interface Modes; 3.1.3 Determination of Interpolation Coefficients
3.1.4 Higher-Order Approximations3.1.5 Support Points; 3.2 Numerical Implementation: Pseudo-Code No. 5; 3.3 Reduced-Order Matrices Based on Global Interface Reduction; 3.3.1 Transformation Matrix TDI; 3.3.2 Reduced-Order Matrices DI and DI; 3.3.3 Transformation Matrix TRI; 3.3.4 Reduced-Order Matrices RI and RI; 3.3.5 Expansion of RI and RI Under Global Invariant Conditions of TRI; 3.4 Numerical Implementation: Pseudo-Code No. 6; 3.5 Treatment of Local Interface Modes; 3.6 Final Remarks; References; Application to Reliability Problems; 4 Reliability Analysis of Dynamical Systems
4.1 Motivation4.2 Reliability Problem Formulation; 4.3 Reliability Estimation; 4.3.1 General Remarks; 4.3.2 Basic Ideas; 4.3.3 Failure Probability Estimator; 4.4 Numerical Implementation; 4.4.1 Basic Implementation; 4.4.2 Implementation Issues; 4.5 Stochastic Model for Excitation; 4.5.1 General Description; 4.5.2 High-Frequency Components; 4.5.3 Pulse Components; 4.5.4 Synthesis of Near-Field Ground Motions; 4.5.5 Seismicity Model; 4.6 Application Problem No. 1; 4.6.1 Model Description and Substructures Characterization; 4.6.2 Reduced-Order Model Based on Dominant Fixed-Interface Normal Modes
1.6 Global Interface Reduction1.6.1 Interface Modes; 1.6.2 Reduced-Order Matrices Based on Dominant Fixed-Interface Modes; 1.6.3 Reduced-Order Matrices Based on Residual Fixed-Interface Modes; 1.7 Numerical Implementation: Pseudo-Code No. 2; 1.8 Local Interface Reduction; 1.9 Numerical Implementation: Pseudo-Code No. 3; 1.10 Reduced-Order Model Response; References; 2 Parametrization of Reduced-Order Models Based on Normal Modes; 2.1 Motivation; 2.2 Parametrization Scheme; 2.2.1 Substructure Matrices; 2.2.2 Normal Modes and Interface Constraint Modes
2.3 Parametrization of Reduced-Order Matrices2.3.1 Unreduced Matrices; 2.3.2 Transformation Matrix TD; 2.3.3 Reduced-Order Matrices D and D; 2.3.4 Transformation Matrix TR; 2.3.5 Reduced-Order Matrices R and R; 2.3.6 Expansion of R and R Under Partial Invariant Conditions of TR; 2.4 Numerical Implementation: Pseudo-Code No. 4; References; 3 Parametrization of Reduced-Order Models Based on Global Interface Reduction; 3.1 Meta-Model for Global Interface Modes; 3.1.1 Baseline Information; 3.1.2 Approximation of Interface Modes; 3.1.3 Determination of Interpolation Coefficients
3.1.4 Higher-Order Approximations3.1.5 Support Points; 3.2 Numerical Implementation: Pseudo-Code No. 5; 3.3 Reduced-Order Matrices Based on Global Interface Reduction; 3.3.1 Transformation Matrix TDI; 3.3.2 Reduced-Order Matrices DI and DI; 3.3.3 Transformation Matrix TRI; 3.3.4 Reduced-Order Matrices RI and RI; 3.3.5 Expansion of RI and RI Under Global Invariant Conditions of TRI; 3.4 Numerical Implementation: Pseudo-Code No. 6; 3.5 Treatment of Local Interface Modes; 3.6 Final Remarks; References; Application to Reliability Problems; 4 Reliability Analysis of Dynamical Systems
4.1 Motivation4.2 Reliability Problem Formulation; 4.3 Reliability Estimation; 4.3.1 General Remarks; 4.3.2 Basic Ideas; 4.3.3 Failure Probability Estimator; 4.4 Numerical Implementation; 4.4.1 Basic Implementation; 4.4.2 Implementation Issues; 4.5 Stochastic Model for Excitation; 4.5.1 General Description; 4.5.2 High-Frequency Components; 4.5.3 Pulse Components; 4.5.4 Synthesis of Near-Field Ground Motions; 4.5.5 Seismicity Model; 4.6 Application Problem No. 1; 4.6.1 Model Description and Substructures Characterization; 4.6.2 Reduced-Order Model Based on Dominant Fixed-Interface Normal Modes