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Model order reduction techniques : with applications in finite element analysis

Author: Zu-Qing Qu
Publisher: London ; New York : Springer, ©2004.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This monograph explains the principles and applications of model reduction techniques, and the dynamic condensation technique in particular. It covers all the potentially useful condensation methods including static, exact, and iterative dynamic condensation and SEREP.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Zu-Qing Qu
ISBN: 1852338075 9781852338077 9781447138273 1447138279 9781849969246 1849969248
OCLC Number: 54079752
Description: xvi, 369 pages : illustrations ; 25 cm
Contents: Introduction to dynamic model reduction techniques --
Finite element modeling --
Theory of modal analysis --
Static condensation --
Dynamic condensation --
Iterative methods for dynamic condensation --
Selection of master degrees of freedom --
Dynamic condensation of nonclassically damped models --
Application I: model reduction on system level --
Application II: model reduction on component level: superelement modeling technique --
Application III: Modal testing --
Summary of other model order reduction techniques.
Responsibility: Zu-Qing Qu.
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Abstract:

This monograph explains the principles and applications of model reduction techniques, and the dynamic condensation technique in particular. It covers all the potentially useful condensation methods including static, exact, and iterative dynamic condensation and SEREP.

Table of Contents:

by quzuqing (WorldCat user on 2006-02-19)

Preface 1. Introduction to Dynamic Model Reduction Techniques 1.1 Model Order Reduction Techniques 1.1.1 Physical Coordinate Reduction 1.1.2 Generalized Coordinate Reduction 1.1.3 Hybrid Reduction 1.2 Dynamic Condensation Technique 1.2.1 Guyan Condensation 1.2.2 Single-Mode, Multi-Mode, and Response Dependent Dynamic Condensation 1.2.3 Physical-Type, Modal-Type, and Hybrid Dynamic Condensation 1.2.4 Single-Step, Two-Step, and Iterative Dynamic Condensation 1.2.5 Undamped and Damped Dynamic Condensation 1.3 Organization of this Monograph Reference 2. Finite Element Modeling 2.1 Finite Element Method in General Form 2.1.1 Fundamental Definitions 2.1.2 Stress and Strain 2.1.3 Strain- and Stress-Displacement Relationships 2.1.4 Virtual Work Principle 2.1.5 Dynamic Equations of Motion 2.2 General Steps of Finite Element Modeling 2.2.1 Discretization and Selection of Element Types 2.2.2 Selection of Displacement Function 2.2.3 Determination of Relationships Between Stresses, Strains, and Nodal Displacements 2.2.4 Derivation of the Element Matrices and Equations 2.2.5 Coordinate Transformation 2.2.6 Assemblage of Element Equations 2.2.7 Solution of Equations 2.3 Use of Symmetry 2.3.1 Modal Analysis 2.3.2 Dynamic Responses Analysis Reference 3. Theory of Modal Analysis 3.1 Modal Theory of Undamped Systems 3.1.1 Undamped Free Vibration and Eigenvalue Problem 3.1.2 Modal Orthogonality and Normal Coordinates 3.1.3 Mode Superposition 3.2 Power Series Expansion of Dynamic Flexible Matrix 3.3 Modal Theory of Proportionally Damped Systems 3.4 Modal Theory of Nonclassically Damped Systems 3.4.1 Dynamic Equations of Motion in the State Space 3.4.2 Free Vibration and Eigenvalue Problem 3.4.3 Complex Mode Orthogonality 3.4.4 Complex Mode Superposition 3.5 Summary Reference 4. Static Condensation 4.1 Guyan Condensation for Static Problems 4.1.1 Definitions of Reduced Static Model 4.1.2 Guass-Jordan Elimination 4.1.3 Numerical Demonstrations 4.2 Guyan Condensation for Dynamic Problems 4.2.1 Definitions of Reduced Dynamic Model 4.2.2 Condensation of Massless Coordinates 4.2.3 Numerical Demonstrations 4.3 Guyan Condensation for Eigenproblems 4.3.1 Definitions of Reduced Eigenproblems 4.3.2 Mode Expansion 4.3.3 Numerical Demonstrations 4.4 Generalized Guyan Condensation 4.5 Quasi-Static Condensation 4.6 Static Condensation Using Flexibility Matrix 4.7 Summary Reference 5. Dynamic Condensation 5.1 Exact Condensation 5.1.1 Direct Back-Substitution 5.1.2 Coordinate Transformation 5.1.3 Power Series Expansion of Dynamic Flexible Matrix 5.1.4 State Space Method for Higher Order Eigenproblems 5.2 Classical Dynamic Condensation 5.3 Further Discussions on Guyan Condensation 5.3.1 Valid Frequency Range of Guyan Condensation 5.3.2 Higher Order Guyan Condensation 5.3.3 Error Analysis of Guyan Condensation 5.4 Dynamic Substructuring Scheme 5.5 Solution Schemes for Nonlinear Eigenproblems 5.5.1 Iterative Scheme I 5.5.2 Iterative Scheme II 5.5.3 Iterative Scheme III 5.5.4 Numerical Demonstrations 5.5.5 Some Improvements 5.6 Modal Type Dynamic Condensation 5.6.1 Dynamic Condensation Matrix 5.6.2 Reduced System Matrices 5.6.3 Reduced Eigenvalue Problem 5.6.4 Hybrid Type Condensation 5.7 Comparisons and Summary Reference 6.Iterative Methods for Dynamic Condensation 6.1 Introduction 6.2 Two - Step Methods 6.2.1 Common Inverse 6.2.2 Generalized Inverse 6.2.3 Numerical Demonstrations 6.3 Governing Equations of Dynamic Condensation Matrix 6.3.1 Single-Mode Dependent Condensation 6.3.2 Multi-Mode Dependent Condensation 6.3.3 Response Dependent Condensation 6.3.4 Comments on These Definitions 6.4 Iterative Schemes for Dynamic Condensation Matrix 6.4.1 Iterative Scheme I 6.4.2 Iterative Scheme II 6.4.3 Numerical Demonstrations 6.4.4 Further Comments 6.5 Generalized Iterative Method 6.5.1 Governing Equations of Dynamic Condensation Matrix 6.5.2 Numerical Demonstrations 6.6 Iterative Method Using Subspace Iteration 6.6.1 Subspace Iteration Method 6.6.2 Governing Equation of Dynamic Condensation Matrix 6.6.3 Solution Schemes for Dynamic Condensation Matrix 6.6.4 Proof of Convergence 6.6.5 Numerical demonstrations 6.7 Frequency Shift Technique 6.7.1 Governing Equation of Dynamic Condensation Matrix 6.7.2 Selection of Frequency Shift Value 6.7.3 Numerical Demonstrations 6.8 Summary Reference 7.Selection of Master Degrees of Freedom 7.1 Physical Type Condensation 7.1.1 Qualitative Guidelines 7.1.2 Quantitative Algorithms 7.2 Modal Type Condensation 7.2.1 Selection of Masters 7.2.2 Assessment of Completeness 7.3 Other Considerations 7.3.1 Symmetry 7.3.2 Practicality 7.4 Number of Master Degrees of Freedom 7.5 Summary Reference 8.Dynamic Condensation of Nonclassically Damped Models 8.1 Introduction 8.2 Static Condensation 8.2.1 Static Condensation in Displacement Space (SCDS) 8.2.2 Static Condensation in State Space I - SCSS(I) 8.2.3 Static Condensation in State Space II - SCSS(II) 8.2.4 Comparison of These Methods 8.2.5 Numerical Demonstrations 8.3 Dynamic Condensation Methods in Displacement Space 8.3.1 Condensation With Damping 8.3.2 Condensation Without Damping 8.3.3 Numerical Demonstrations 8.4 Modal Type Condensation Method 8.4.1 Dynamic Condensation Matrix 8.4.2 Conversion of Complex Operation into Real Operation 8.5 Iterative Methods in State Space (I) 8.5.1 Governing Equations of Dynamic Condensation Matrix 8.5.2 Iterative Scheme 8.5.3 Model with Unsymmetrical Matrix 8.6 Iterative Methods in State Space (II) 8.7 Iterative Methods in State Space (III) 8.7.1 Governing Equations of Dynamic Condensation Matrix 8.7.2 Numerical Demonstrations 8.8 Iterative Method Using Subspace Iteration in State Space 8.8.1 Subspace Iteration Method for Complex Eigenproblems 8.8.2 Governing Equations of Dynamic Condensation Matrix 8.8.3 Iterative Schemes 8.8.4 Discussion on the Convergence 8.8.5 Numerical Demonstrations 8.9 Summary Reference 9.Application I: Model Reduction on System Level 9.1 Introduction 9.2 Active Vibration Control 9.2.1 Introduction 9.2.2 Full Order Control 9.2.3 Reduced Order Control 9.2.4 Numerical Simulations 9.3 Finite Element Modeling of Smart Structures 9.3.1 Introduction 9.3.2 Theory of Laminated Composite Plates 9.3.3 Theory of Sensors and Actuators 9.3.4 Finite Element Formulations and Reduction 9.3.5 Numerical Demonstrations 9.4 Structural Systems with Local Nonlinearities 9.4.1 Introduction 9.4.2 Model Reduction 9.4.3 Numerical Demonstrations 9.5 Summary 10.Application II: Model Reduction on Component Level – Superelement Modeling Technique 10.1 Introduction 10.2 Concepts of Superelement Modeling 10.3 Static Superelement 10.3.1 Construction of Superelement 10.3.2 Beam Superelement 10.3.3 High Order Element 10.3.4 Frame Superelement 10.4 Exact Superelement 10.5 Dynamic Superelement 10.5.1 Theory of Dynamic Superelement Modeling 10.5.2 Rigid Modes of Superelement 10.6 Modeling of Compound Systems With Local Nonlinearities 10.6.1 Linear Compound Systems 10.6.2 Compound Systems With Local Nonlinearities 10.7 Multi-level Superelement 10.8 Global-Local and Multiscale Analyses 10.9 Summary Reference 11.Application III: Modal Testing 11.1 Introduction 11.2 Selection of Measurement Locations 11.3 Test-Analysis Model Correlation 11.3.1 Accuracy and Robustness of TAM 11.3.2 TAM Mass Matrix 11.4 Mode Expansion and Data Recovery 11.5 Summary Reference 12.Summary of Other Model Order Reduction Techniques 12.1 Modal Coordinate Reduction 12.1.1 Low Frequency Reduction 12.1.2 Middle Frequency Reduction 12.2 Ritz Vector Methods 12.2.1 Introduction 12.2.2 Static Ritz Vector Methods 12.2.3 Quasi-Static Ritz Vector Methods 12.3 Compound Mode Synthesis 12.3.1 Fixed Interface Methods 12.3.2 Craig-Bampton TAM 12.3.3 Free Interface Methods 12.4 Proper Orthogonal Decomposition 12.5 Balanced Realization Reduction 12.6 Condensation Model Reduction Bibliography Index

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