Structural Analysis of Composite Wind Turbine Blades

Structural Analysis of Composite Wind Turbine Blades
اسم المؤلف
Dimitrios I. Chortis
التاريخ
25 ديسمبر 2020
المشاهدات
التقييم
(لا توجد تقييمات)
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Structural Analysis of Composite Wind Turbine Blades
Nonlinear Mechanics and Finite Element Models with Material Damping
Dimitrios I. Chortis
Research Topics in Wind Energy 1
Contents
Abstract . VII
1 Introduction 1
1.1 The Significance of the General Problem . 1
1.2 Scope and Objectives 3
1.3 Chapters Outline 4
1.4 DAMPBEAM Finite Element Code 6
2 Historical Review on the Linear and Nonlinear Damped Structural
Behavior of Composite Structures 9
2.1 Development of Models for the Undamped Structural Analysis of
Thin-Walled Composite Beams and Blades 9
2.1.1 Nonlinear Beam Theory Models . 9
2.1.1.1 Analytical Solution Methods 10
2.1.1.2 Finite Element Approaches 11
2.1.2 Incorporation of Material Coupling in the Static and
Dynamic Analysis of Composite Beams . 13
2.1.3 Effect of Rotational and Buckling Loads on
Composite Structures 15
2.1.4 Brief Description of Multi-body Dynamic System
Approaches 17
2.2 Damping Models for Composite Structures 18
2.2.1 Macro- and Micro-mechanical Models of Damping . 18
2.2.2 Discrete Layer Damping Model Theories . 21
2.2.3 Optimization of Composite Damping . 22
2.3 Theoretical Framework for the Prediction of Nonlinear
Damping in Composite Structures 23
3 Linear Material Coupling Effect on Structural Damping of Composite
Beams and Blades . 25
3.1 Tubular Laminated Beam 26
3.2 Composite Ply Level . 26
3.2.1 Constitutive Equations 27
3.2.2 Strain-Displacement Relations 28X Contents
3.2.3 Equations of Motion 29
3.2.3.1 Differential Form of Stress Equilibrium
Equation . 29
3.2.3.2 Weak Formulation 29
3.3 Composite Cross-Section Mechanics 30
3.3.1 Section Kinematics 30
3.3.2 Variational Form of Beam Equations of Motion . 32
3.3.3 Section Stiffness Terms . 33
3.3.4 Section Damping Terms 34
3.3.5 Section Mass Terms 36
3.4 Structural Level . 37
3.4.1 Damped Beam Finite Element Formulation 37
3.4.1.1 Shape Functions of the Tubular Beam Finite
Element 38
3.4.1.2 Total Structural Matrices of the Beam Finite
Element 39
3.4.1.3 Calculation of Structural Matrices at the Local
Coordinate System of the Element . 40
3.4.2 Discrete System of Equations of Motion . 41
3.4.3 Calculation of the Modal Loss Factor of the Composite
Beam . 41
3.5 Validation of Coupling Terms . 42
3.5.1 Box-Section Carbon/Epoxy Beams . 42
3.5.1.1 Static Response of Carbon/Epoxy Beam 43
3.5.1.2 Modal Characteristics of Carbon/Epoxy Beam 47
3.5.2 Small Model Blade 51
3.5.2.1 Blade Testing and Numerical Simulation 51
3.5.2.2 Effect of Coupling Terms . 53
3.5.3 19m Wind-Turbine Blade 56
3.6 Application of the Developed Finite Element on a 61.5m
Wind-Turbine Blade Model 58
3.6.1 Advanced Cross-Section Structural Properties 59
3.6.2 Modal Analysis of the Wind-Turbine Blade . 65
3.7 Conclusions . 65
4 Nonlinear Damping Mechanics and Finite Element Model for the Static
and Damped Free-Vibration Analysis of Composite Strips 69
4.1 Composite Ply Level . 71
4.1.1 Constitutive Equations 71
4.1.2 Composite Ply Damping . 72
4.1.3 Equations of Motion 72
4.1.3.1 Differential Form of Stress Equilibrium Equation 72
4.1.3.2 Weak Formulation 72Contents XI
4.2 Laminate Level 73
4.2.1 Section Kinematics 73
4.2.2 Strains-Displacements Compatibility Equations . 75
4.3 Composite Laminate Section Matrices 75
4.3.1 Section Stiffness Terms . 76
4.3.2 Section Damping Terms 78
4.3.3 Section Mass Terms 81
4.4 Structural Level . 81
4.4.1 Damped Nonlinear Beam Finite Element 82
4.4.1.1 Shape Functions of the Two-Node Beam Strip
Finite Element 82
4.4.1.2 Discrete System Equations . 86
4.4.1.3 Transformation to the Local Coordinate System
of the Element . 88
4.4.1.4 Beam Element Matrices in the Local Coordinate
System 89
4.5 The Newton-Raphson Technique 90
4.6 Final System of Equation 92
4.6.1 Tangential Matrices at the Local Coordinate System of the
Finite Element . 93
4.6.2 Assembly of System Equations . 94
4.6.3 Boundary Conditions . 94
4.6.4 Expression of the Final Set of Equations 95
4.7 Small-Amplitude Free-Vibration of Composite Strip . 95
4.8 Displacement Control Method 96
4.9 Numerical Integration . 100
4.10 Conclusions . 100
5 Nonlinear Dynamic Response of Composite Plate-Beams 103
5.1 Calculation of System Eigenfrequencies and Modal Damping . 104
5.2 Experimental Determination of Elastic and Damping Material
Properties 104
5.2.1 Extraction of Material Elastic and Damping
Coefficients . 105
5.2.2 Relation of Damping with Natural Frequency 114
5.2.3 Damped Modal Testing of Composite Beam
Modal Characteristics 115
5.2.3.1 Tension Experimental Procedure . 115
5.2.3.2 Buckling Experimental Procedure 117
5.3 Numerical Results . 119
5.3.1 Effect of In-Plane Tensile Load 119
5.3.1.1 Cross-Ply Composite Strips . 119
5.3.1.2 Quasi-isotropic Composite Strips . 127
5.3.2 Aluminum Plate-Beam Model . 133XII Contents
5.3.2.1 Static Response of Aluminum Beam Specimen
Subject to Compressive In-Plane Load 134
5.3.2.2 Small-Amplitude Free-Vibration Response of
Aluminum Beam Specimen Subject to In-Plane
Tensile and Compressive Load. . 135
5.3.3 Nonlinear Buckling Analysis of Composite Strips 139
5.3.3.1 Composite Cross-Ply Beam Specimens . 139
5.3.3.2 Composite Beams with Quasi-isotropic and
Asymmetric Lamination . 145
5.4 Conclusions . 148
6 Prediction of Nonlinear Damped Response of Large-Scale Blade
Composite Structures . 151
6.1 Nonlinear Mechanics of Composite Blade Structures . 152
6.1.1 Nonlinear Section Mechanics 152
6.1.2 Nonlinear Stiffness Cross-Section Terms . 154
6.1.3 Linearized Stiffness Cross-Section Terms 160
6.1.4 Nonlinear Damping Cross-Section Terms . 163
6.2 Tubular Nonlinear Damped Beam Finite Element 168
6.3 Numerical Evaluation Cases on Box-Section Beams 169
6.3.1 Static Response under Large Loads 169
6.3.1.1 Hinged-Hinged Beam . 169
6.3.1.2 Pressure Loaded Clamped-Free Beam . 171
6.3.2 Effect of Rotational Stresses . 174
6.4 Modal Analysis of a Girder Box-Section Beam of a 5MW
Wind-Turbine Blade 178
6.5 Conclusions . 183
7 Conclusions and Suggestions for Future Research Topics . 185
7.1 General Concluding Remarks . 186
7.2 Future Research Topics . 188
References . 191
Appendix A 201
Appendix B 207
B.1 Damping Material Models 207
B.2 Viscous Damping 207
B.3 Hysteretic Damping 208
B.4 Kelvin-Voigt Model 210
B.5 Relationship of Kelvin Modal Parameters to Measure Damping 210
B.6 Other Damping Models . 212Contents XIII
Appendix C 215
C.1 Secondary Warping of the Cross-Section . 215
C.2 Ply and Laminate Damping Matrices 215
C.3 Skin Laminate Stiffness and Damping Matrices . 217
C.4 Reduction of Stiffness and Damping Laminate Matrices 217
C.5 Detailed Expressions of Section Stiffness, Damping and Mass
Linear Terms of the Tubular Beam Finite Element . 220
Appendix D 225
D.1 Tangential Section Stiffness Matrix of the Composite Strip
Finite Element . 225
D.2 Section Mass Matrices 225
D.3 Shape Function Matrices for the Two-Node Beam-Strip Finite
Element . 226
Appendix E 229
E.1 61.5m Wind-Turbine Blade Configuration . 229
E.2 54m Girder Box-Section Beam Cross-Sectional Geometric
Properties 233
About the Author .
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