A Geometrically Non Linear Structural Response

Published Date: 02 Nov 2017

Acknowledgments

This Master of Science Thesis arose from my stay as visiting master student at the Technical

University of Denmark, DTU Wind Energy at Risø Campus. During my work in the

department of Wind Turbine Structures, I could benefit from well developed software tools

and the knowledge gained by the full-scale test facility at Risø Campus. As well, I had the

opportunity to visit the Blade Test Centre A/S in Aalborg.

First, I would like to thank my supervisor from the University of Applied Sciences Bre-merhaven, Professor Henry Seifert for his trust and the helpful references. Second, thanks

to my co-supervisor, Senior Scientist Kim Branner to make contact with me and to take

over the role as supervisor from DTU Wind Energy.

Thanks to my advisor, Scientist Peter Berring for his great assistance in numerical and

analytical studies, and his donated time. Thanks to my advisor, Development Engineer

Magda Nielsen, who gave me the opportunity work in the test facility, and useful com-ments while writing this work. Thanks to Development Engineer Angelo Tesauro for his

discussions and the experiences with measurement facility. Thanks to Anne Margrethe

Larsen for her help with the Risø Linux Cluster ’Gorm’.

Further thanks to the PROMOS scholarship committee at the University of Applied

Sciences Bremerhaven for the financial support during my time in Denmark.

Roskilde, February 12, 2013

Abstract

A geometrically non-linear structural response of a 34 m wind turbine blade under flap-wise loading was compared with a linear analysis to show the need of non-linear analysis

in wind turbine blade design. Non-linear effects revealed from a numerical finite element

model were compared with an analytical plate model of the capunder compression load.

The plate model was subjected to a transversal load due to thenon-linear Brazier effect,

and to in-plane loading to reveal the local cap displacementand the buckling resistance

respectively. Focus was on the verification of the characteristic and design resistance in the

ultimate strength and stability limit state. For the designresistance, an analysis due to the

lowest GL requirements was used and compared with the results of a non-linear approach

proposed by GL that required the application of an imperfection to the model. The way

to apply an imperfection due to Eurocodeseemed more realistic compared with GL’s

approach. Numerous simulations revealed the requirement of non-linear analysis methods

in design of wind turbine blades. A linear analysis due to the lowest GL requirements

yielded less conservative results than a non-linear approach proposed by GL. That led to

the fact, that the investigated blade designed after the lowest requirements would pass the

certification, whereas the same blade design verified with the non-linear approach would

not. The non-linear structural response was significantly dependent on the scaling of an

applied imperfection.

Contents i

Contents

Figures v

Tables vii

Notation ix

1 Introduction 1

2 State-of-the-Art 5

2.1 Standards and Guidelines in Wind Energy . . . . . . . . . . . . . . . . . . . 5

2.2 Design Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Process Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.2 Partial Safety Factors due to GL . . . . . . . . . . . . . . . . . . . . 8

2.3.3 Analysis due to GL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Analysis Methods due to Eurocode . . . . . . . . . . . . . . . . . . . . . . . 11

3 Theoretical Background 15

3.1 Rotor Blade Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Composite Laminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Macromechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.2 Classical Laminate Theory . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2.3 Unsymmetrically Cross-Ply Laminated Plates . . . . . . . . . . . . . 20

3.3 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Non-linear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Analytical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Methods 31

4.1 Finite Element Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.1 Software Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.3 Materials and Layup . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1.4 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1.5 Load Application and Constraints . . . . . . . . . . . . . . . . . . . . 36

4.1.6 Solver Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.7 Output Request . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

ii Contents

4.1.8 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.1.9 Model Singularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Numerical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.1 Global Blade Deflection . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.2 Strain Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.3 Local Displacement of the Cap . . . . . . . . . . . . . . . . . . . . . 41

4.2.4 Buckling Resistance of the Cap . . . . . . . . . . . . . . . . . . . . . 41

4.2.5 Strength Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.5.1 Characteristic Resistance . . . . . . . . . . . . . . . . . . . 42

4.2.5.2 Design Resistance . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.6 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.6.1 Characteristic Resistance . . . . . . . . . . . . . . . . . . . 46

4.2.6.2 Design Resistance . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.7 Stimulation of Imperfections . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.7.1 Global Scaling . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.7.2 Local Modification . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Analytical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3.1 Global Deflection of the Blade . . . . . . . . . . . . . . . . . . . . . . 53

4.3.2 Strain Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.3 Local Displacement of the Cap . . . . . . . . . . . . . . . . . . . . . 55

4.3.4 Buckling Resistance of the Cap . . . . . . . . . . . . . . . . . . . . . 56

5 Results 59

5.1 Plausibility of the FEA Results . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Strength Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2.1 Characteristic Resistance . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.2 Design Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.3 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3.1 Characteristic Resistance . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3.2 Design Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.4 Stimulation of Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6 Discussion 75

6.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1.1 Finite Element Model Setup . . . . . . . . . . . . . . . . . . . . . . . 75

6.1.2 Numerical Computations . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1.3 Analytical Computations . . . . . . . . . . . . . . . . . . . . . . . . . 76

Contents iii

6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2.1 Plausibility Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2.2 Non-linear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2.3 Load Carrying Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2.4 Verification of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2.5 Stimulation of Imperfections . . . . . . . . . . . . . . . . . . . . . . . 80

7 Conclusions 83