Optimization of Material Layup for Wind Turbine Blade Trailing Edge Panels. Agnieszka Roczek

Transcription

1 Optimization of Material Layup for Wind Turbine Blade Trailing Edge Panels Agnieszka Roczek Roskilde, 2009

2 Risø DTU National Laboratory for Sustainable Energy Wind Energy Department DK-4000 Roskilde, Denmark Tel , Fax Technical University of Denmark Department of Informatics and Mathematical Modelling Building 321, DK-2800 Kongens Lyngby, Denmark Phone , Fax

3 i Abstract This thesis studies different solutions for the layup of materials used in wind turbine blades. The main goal is to create an optimization tool and to demonstrate the potential improvement that could be brought to the material design without additional costs involved. The optimization objective is to minimize the out of plane deformation of the blade s trailing edge panels. Classical laminate theory and sandwich construction principles are utilized in the development of the material layup optimization tool. A pre-study is conducted in order to ensure a motivated choice of the blade region considered in the main part of the thesis. The relevance of the deformations is investigated from both the aerodynamic and structural point of view. A non-linear finite element analysis of the chosen blade region is conducted. A detailed FE-model of an entire blade used in the thesis has been provided by Risø DTU. The FE-results are used to approximate the loading and boundary conditions for the studied panel. The composite layup optimization algorithm is implemented based on the plate problem solution derived. Several glass fibre layup solutions are implemented in the blade model and a thorough analyses focusing on out of plane deformations of the panel are conducted. The efforts for improvement are then continued by introducing new materials, i.e. carbon and bamboo. The primary conclusion drawn from this study confirms significant improvement in the local behaviour of the trailing edge panels obtained by rearranging the original layup of the material. The findings for the utilization of new materials reveal large potential in weight saving, which could be employed in the future wind turbine blade design. Finally, the limitations and challenges of the utilized method for optimization of material layup are summarized.

4 ii Preface and Acknowledgment This thesis has been elaborated at Wind Energy Department, Risø DTU National Laboratory for Sustainable Energy in cooperation with Department of Informatics and Mathematical Modelling at the Technical University of Denmark. The project work has been carried out from April to September 2009 in fulfilment of the requirements for acquiring the Master of Science degree in Engineering. It is intended that the tools and knowledge documented in this report may be freely available for any interested party, whether for research or commercial purposes. Although every care has been taken in the preparation of this report, the author takes no responsibility for the accuracy of the presented results. Hereby, I would like to thank my supervisor, Kim Branner, Senior Scientist from Risø DTU for the support, patience and guidance. I would like to acknowledge my appreciation to the project s co-supervisor, Find Mølholt Jensen, PhD from Risø DTU, for the critical appraisal, support, providing me access to the model, experimental results, but also ensuring the office conditions. I would also like to evince my thankfulness to my co-supervisor, Niels Kjølstad Poulsen from DTU Informatics for his never-ending advice and support. I would like to thank Hans-Bruun Nielsen from DTU Informatics, for a helping hand and Robert Bitche, Postdoc from Risø DTU, for motivating me to push over my own limitations.

5 iii I would like to evince my deepest gratitude to my wonderful parents, who supported all my efforts and made it possible for me to have the lifechanging experience of studying at Technical University of Denmark. Finally, I would like to dedicate my work and give special thankfulness to Tomasz Sieradzan, a colleague, fellow Master student at Risø DTU and, most importantly, my fiancé, for his patient understanding, full devotion and support. I could not accomplish this without his inspirational influence. Roskilde, September 2009 Agnieszka Roczek

6 iv Contents Abstract... i Preface and Acknowledgment... ii Contents... iv 1 Introduction Introduction to wind turbine blade Motivation and scope Mechanics of composite materials and sandwich structures Isotropic, orthotropic and anisotropic materials Introduction to composite materials Classical and First-Order Theories of Laminated Plates New materials utilized in the project Methods for wind turbine blade testing Finite element model Full scale test Model validation Summary Pre-study of the trailing edge panel Motivation for the choice of the blade region considered Finite element analysis of the considered panel the reference model Study of the deformation s nature Summary... 40

7 v 5 Optimization algorithm for sandwich plate material Loading distribution and boundary conditions Derivations of the numerical model of the plate The algorithm Summary Optimization of material layup in the trailing edge panel Results of the algorithm for the plate optimization Behaviour of the region with rearranged material layup Improvements based on a free layup Summary Study of the flapwise and combined loading Motivation Flapwise load case Combined loading Summary Utilization of new materials Composite laminate Carbon fibre Bamboo Summary Conclusions Future work Bibliography Appendices Definitions, symbols, abbreviations Profile normalization to XFOIL needs coordinate system Information on the blade and experimental equipment Additional study of the experimental data Material layups Initial Finite Element Analysis Distribution of the loading and boundary conditions Derivation of the plate deformation formula Additional results for the optimization Flapwise and combined loading Plate optimization algorithm...113

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9 1 CHAPTER 1 1 Introduction Over the past years the alternative energy sources have been taking over higher and higher share in energy production. In 2008, wind provided more than 1.5% of the electric power worldwide reaching 29% growth in the annually installed capacity. This situation is not only the result of more turbines being installed but also of the increasing diameter of the turbine rotor. High competitiveness of this market forces the industry to produce more efficient and cost effective wind turbines. Further up-scaling of the design may be very challenging from the structural and economical point of view. With ever-longer blades, there is a strong need for developing smart design solutions. The recent approach results in material layup with high component thicknesses and weight of the blades and often not satisfactory structural response. There is a large potential for reducing the amount of material in the blade, and thus its weight. A lighter rotor exerts lower loads on the remaining components of the wind turbine. Thus, the reduction of the blades weight is beneficial for the entire turbine. Since a number of completely new structural designs are considered today, ref. [10], it is a good moment to study also the material layup. The suggested refinements in this area could result in significant improvement of the blades structural behaviour. This thesis represents a small contribution to the massive research effort in developing a more economically efficient and structurally robust future wind turbine blade design.

10 Introduction to wind turbine blade Blade design Wind turbine blade design involves both aerodynamic and structural priorities. The structural considerations are dominating for the design of approximately one third of the blade length from the root, while aerodynamics has higher priority in the design of its remaining part. Close to the root, the carried bending moments are higher and the structure is designed to withstand the loads. Further from the root, bending moments are comparatively small and the blade design is mainly governed by aerodynamic considerations. The blade is a hollow structure formed by shells. Structural webs are fitted, joining the two shells together, in order to transfer shear loads. Most of the material is placed in the laminate caps between the webs. In some blade designs, a load carrying box girder is used. The box girder consists of flanges ( the caps ) and webs. It is wrapped with the skin designed to optimize the aerodynamic performance. Figure 1 presents the main blade features in a design with the girder. From a structural, as well as aerodynamic point of view, both designs show the same behaviour. The blade studied in this thesis is a 34m long blade supplied by SSP Technology A/S. It comprises a load carrying box girder and is made from glass fibre epoxy. Figure 1. Definition of the main blade features - scheme of blade cross-section from ref. [29]. Materials Composite materials have unique properties, which can be tailored for a specific solution depending on the fibre orientation in consecutive layers. Moreover, composite materials have outstanding strength as well as stiffness to weight ratios, what makes them an excellent choice for many applications that require light and robust structures. Therefore, they are becoming broadly used in virtually every area of our life, from aerospace to medicine applications, and also in wind turbine industry. Trailing edge panels, which will

11 3 be analysed in this thesis, are made of a sandwich construction, with a foam core and faces made of glass fibre laminates, see Figure 2. Figure 2. Composite construction overview of the blade. Area of interest marked with red ellipse. Figure from [29]. A detailed elaboration on composite materials and sandwich structure is given in Section Motivation and scope Failure in adhesive joints caused by out of plane deformations The study performed in this thesis is motivated by Risø DTU s extensive blade testing program that has lead to a number of conclusions regarding the structural design of wind turbine blades. Using full-scale tests and corresponding finite element models several new failure mechanisms have been identified. Some of these failure modes are directly related to trailing edge panels deformations, see ref. [10], [11] and [12]. Out of plane deformations of the panels cause peeling stresses in the trailing edge what often results in fatigue failure in the trailing edge adhesive joint. This phenomenon is presented in Figure 3. Also the load-carrying box girder is attached to the outer skin (aerofoil) with an adhesive joint sensitive to peeling stresses. This can lead to another failure mode, i.e. skin debonding. Therefore, minimizing the deformation of the aerofoil is needed e.g. to prevent fatigue problems in adhesive joints. The scope of the project does not concern the failure mechanisms themselves, for more detailed information about new phenomena observed see ref. [10], [25]. For the trailing edge fatigue problem, it is important how both panels, on the pressure and suction side, behave. However, only the panel on the pressure side is studied in this thesis.

12 4 Figure 3. Sketch of trailing edge panels with out of plane deformations. The close ups show fatigue failure in the trailing edge and debonding of outer skin from the box girder. The goal The goal is to develop solutions that minimize, or at least significantly decrease, the out of plane deformations of the panels. This can be motivated by both structural behaviour and power production efficiency. From the structural mechanics perspective minimizing the panel deformations can prevent the fatigue failure of the adhesive joint. From the aerodynamic perspective minimizing the panel deformations may prevent a decrease in efficiency. Organization of the thesis This thesis studies different solutions for layup of the materials used in wind turbine blades. The aim is to develop an optimization tool and to demonstrate the potential improvement that could be brought to the structural design without increasing the costs. The optimization objective is to minimize the out of plane deformation of the trailing edge panel. The thesis is composed of the following consecutive parts. First, an introduction to composite materials and sandwich structure is given and laminated plates theories are presented. The methods for experimental and numerical studies used in the project are described and validation of the finite element model with experimental data is performed. A pre-study of the relevance of the trailing edge panels deformations is conducted for the blade s root region and its aerodynamic part. This short study is to allow a motivated choice of the region investigated in the main part of the thesis. A non-linear finite element analysis of the chosen blade region is performed and the character of the deformations is investigated.

13 5 The results from the original FE-model are further used as reference for the improved solutions. Moreover, the results are used to approximate the loading and boundary conditions for the studied panel. The composite layup optimization algorithm, based on the plate problem solution derived, is implemented in Matlab. The tool is prepared on basis of an analytical-numerical solution applied in terms of a small finite element model. Numerous optimized layup solutions are implemented in the blade model and a thorough finite element analysis focusing on out of plane deformation of the panels is conducted. The efforts for improvement of the panel behaviour are then continued by introducing different materials like carbon and bamboo. Finally, conclusions and suggestions on future wind turbine blade trailing edge panel design are drawn. Moreover, the limitations of the method applied for material optimization are described. The challenges ahead and possible extension of the work are briefly summarized.

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15 7 CHAPTER 2 2 Mechanics of composite materials and sandwich structures In the following section an introduction to composite materials, sandwich structure and laminated plate theories is given. A comprehensive summary of the listed topics necessary for the needs of this thesis is presented. This chapter creates a theoretical basis for derivations performed during development of the optimization tool. Moreover, the materials utilized in the investigations are described. 2.1 Isotropic, orthotropic and anisotropic materials According to Jones (ref. [13]), an isotropic body has the same material properties in every direction at any point in the body, i.e. the properties are independent of orientation at a point in the body. This is equivalent to having an infinite number of symmetry planes. Such materials have only two independent variables in their stiffness and compliance matrices, i.e. elastic constants. The two elastic constants are the Young's modulus (E) and the Poisson's ratio (ν). However, an alternative elastic constant - shear modulus (G) can also be used since for isotropic materials we have the following: (2.1) An orthotropic material has at least two orthogonal planes of symmetry (transversely isotropic material), where the material properties are independent of direction within each

16 8 plane. The orthotropic materials require nine independent variables in their constitutive matrices. By convention, those 9 elastic constants are: 3 Young's moduli E x, E y, E z, 3 Poisson's ratios ν yz, ν zx, ν xy, and the 3 shear moduli G yz, G zx, G xy. For specially ortotropic materials, at least five of the elastic constants are necessary. Due to the symmetry planes the following relations are satisfied.,, (2.2) Anisotropic materials have different mechanical properties in all directions at a given point in the body. The properties are a function of the orientation at a point. There are no planes of material symmetry and therefore 21 elastic constants are required. The difference in behaviour between iso-, ortho-, and anisotropic material behaviour is presented in Figure 4. For isotropic materials, normal stress causes extension in the direction of stress application and contraction in perpendicular directions. It does not cause shear deformation. Similarly, shear stress causes only shearing deformation, but no elongation or contraction. Figure 4. Mechanical behaviour of various material types. Figure from [13]. For orthotropic materials, normal stress in a principal material direction results in elongation in this direction and perpendicular contraction. In orthotropic materials, the magnitude of extension differs for the same normal stress applied for different principal directions (different Young s moduli in different directions). Moreover, the contraction can differ from respective contraction for isotropic materials with the same elastic modulus, because here it depends on different material properties in two principle directions. Therefore, for different pairs of principal directions there are different Poisson ratios. Shear deformation is independent of the Young s moduli and Poisson s ratios for orthotropic materials. For anisotropic materials, normal stress causes not only extension in stress application direction and perpendicular contraction, but also shearing deformation. Similarly, apart from distortion, shear stress causes elongation and contraction. This coupling is an important characteristic of anisotropic materials.

17 9 Such coupling between loading and deformation modes (shear-extension coupling) occurs also for orthotropic materials loaded with normal stress in a non-principal direction. More details about coupling between deformation modes and loading type are given in Sections 0, where fundamental matrix is introduced. In engineering applications, simplification of the material behaviour is used to reduce complexity of problem and to allow to estimate an overall stiffness and strength. However, in reality, all the materials are anisotropic on a certain scale. 2.2 Introduction to composite materials In general sense, the term composite material means any material made of combination of at least two different constituent materials with significantly different properties, just to list reinforced concrete and plywood. In this thesis, term composite material will be used when referring to fibre reinforced composites, i.e. fibrous materials imbedded in polymer based resins. Composite materials mechanical behaviour characteristic is different from conventional engineering materials. They have unique properties, which can be tailored for a specific application depending on the fibre orientation in consecutive layers. A typical fibre composite consists of a bonded stack of laminae (plies) constructing a laminate. The lamina is a flat (sometimes curved) layer of unidirectional or woven fibres (shown in Figure 5b) embedded in matrix (Figure 5a). There is also third kind, a randomly oriented ply, built-up of continuous fibres or, most commonly, randomly placed short fibre bundles. The random ply is however rarely used for high performance purposes. Fig. 5a Fig. 5b Figure 5. Laminae. a) Lamina creation principle. Figure from [13]. b) Various types of fibre reinforced composite laminae: unidirectional ply, discontinuous fibres and lamina with woven fibres. Figure from [24]. The fibres, typically strong and stiff, are the main load carrying element in lamina. The matrix supports and protects the fibres from damage. It distributes the load between the fibres. If a single fibre is broken, the load is transferred from one part of the broken fibre, through the matrix to adjacent fibres and the other part of the broken fibre. The matrix may be organic, metallic, ceramic or carbon. The mechanical behaviour of laminated composite plates is strongly dependent on the degree of orthotropy of individual layers and the ply stacking sequence.

18 10 The laminae have various orientations of principal material directions, see Figure 6. The layers are glued together, usually with the same matrix material as used within laminae. The ply is usually considered orthotropic. The three principal directions, i.e. length, width and transverse direction, are commonly defined as local 1,2,3-coordinate system (as in Figure 5a) or equivalently x,y,z system, as in Figure 6. Figure 6. A laminate made up of laminae of different orientations. Figure from [24]. The uniqueness of composite materials comes from possibility of obtaining tailored mechanical properties by orienting each layer according to the needs. The directional strength and stiffness dependence is then adjusted to the loading assumed. What is more, the laminae may be arranged asymmetrically with respect to middle surface of the laminate, resulting in coupling between bending end extension. More details about coupling between deformation modes and loading type are given in Section 2.3, where the fundamental matrix is introduced. Fibre reinforced composites have also disadvantages. The difference in material properties between the plies causes the shear stresses between them, which may result in delamination. Similarly, due to the difference in properties between matrix and fibres, fibre debonding may occur. Moreover, manufacturing issues may produce damaged fibres, voids, delamination or incorrect fibre orientation or layer thickness. It is impossible to entirely prevent manufacturing defects. However, in this thesis, the focus does not include material defects or micromechanics approach. More information on the topic may be found in ref. [10], [13] and [24]. Failure criteria There are a large number of failure criteria and even more is under development. They are applied to define allowable stresses or strains. Commonly used failure criteria are empirical and do not consider micromechanical failure modes. Four of the most common criteria are

19 11 Maximum Stress, Maximum Strain, Tsai-Hill and Tsai-Wu. These design criteria are not described in details here since they have been shown not to be reliable for composite materials, see ref. [3]. For an interested Reader, ref. [9], [24] and [33] describe the topic succinctly. Since the failure criteria are not reliable, they were not applied in this thesis. Moreover, it is experimentally proven that the panels studied may withstand strain several times higher than the values obtained in the blade model. Strains measured in panel tests with large defects embedded reached µS, see ref. [10] and [32]. The values obtained in the full-scale test are several times lower and thus, failure of fibres is not an issue. What is more, in the thesis, the structural behaviour of the panel is improved, and thus the initially low strain values are further decreased. This confirms no necessity in applying any strain criteria. Sandwich structure Laminated composite materials are often combined with low density materials (core) to create so called sandwich structure. This topic is extensively described in ref. [1] and [23]. A sandwich consists of three main parts: two thin, stiff and strong faces and a thick, light and weaker core that separates the faces. The components are bonded with adhesive. The sandwich works similarly to an I-beam, see Figure 7. It is an efficient structural shape since most of the material is placed in the flanges farthest from the neutral axis. In the connecting web, the necessary amount of material is left to make the flanges work together to resist shear and buckling. Figure 7. Composite sandwich structure functions similarly to the connecting web of an I-beam, with the core separating the skins at a constant distance, while the faces themselves function as the I-beam flanges. Source: The faces (skin) represent the flanges and the core takes place of the web. The faces carry normal and bending stresses. Therefore materials used in skin layers need to be characterized by high strength in terms of in-plane loading. They also contribute significantly to the sandwich weight and thus a proper choice of material is of importance. The core counteracts the shear stresses and separates and supports faces against buckling and wrinkling. The interface between the faces and the core transfers stresses between components, thus it is also of high importance. The load carrying and stress distributions in sandwich construction can be shortly described as: the faces carry bending moments as tensile and compressive stresses and the core carries transverse forces as shear stresses.

20 12 In Figure 8, the normal and shear stresses distribution over thickness of a sandwich are presented for different levels of approximations. In Figure 8a no approximation is applied. Figure 8b and c present the distribution for sandwich with weak core and weak core combined with thin faces respectively. In practice, the latter one is utilized most often. Fig. 8a Fig. 8b Fig. 8c Figure 8. Normal and shear stresses distribution over thickness of a sandwich for different levels of approximations. Fig. a. No approximation. Fig. b. Weak core. Fig. c. Weak core and thin faces. Figure after Zenkert [34]. In sandwich construction, the core should be characterized by best possible performance to weight ratio. In aeronautic applications, honeycomb materials are mostly applied. Their main advantage is low weight and outstanding performance. Their cost is their significant disadvantage. Foam materials show very good performance in terms of thermal and acoustic insulation. The mechanical properties are however not as good as for honeycomb cores. Comparable stiffness is obtained for higher density. Nonetheless, they are a cheaper solution and, until now most common in wind turbine blade production. There are many advantages of sandwich design, e.g. high stiffness and strength to weight ratios, thermal and acoustic isolation, etc. Probably its most important feature is enhancing the flexural rigidity without adding significant weight. There are, however, several drawbacks to this solution, just to list the production issues and joining difficulties. However, the concept has been under development for many years and the knowledge of its mechanical behaviour is significantly increasing. 2.3 Classical and First-Order Theories of Laminated Plates This section briefly presents the main theories used in modelling of laminated composite plates. By utilization of laminate theory it is possible to proceed from a ply (a building block) properties to the final result, a structural laminate. According to Reddy [24] analyses of composite plates have been based on one of the following approaches:

21 13 1. Equivalent single-layer theories (2-D) - Classical laminated plate theory - Shear deformation laminated plate theories 2. Three-dimensional elasticity theory (3D) - Traditional 3-D elasticity formulations - Layerwise theories 3. Multiple model methods (2D and 3D) This chapter gives an overview of classical laminated plate theory (CLPT) and first-order shear deformation laminated plate theory (FSDT). These theories allow to reduce a complicated 3D elasticity problem to a manageable 2D problem. CLPT is an extension of the Kirchhoff assumption. It is built on the following assumptions: 1. The normals remain straight. 2. The normals do not elongate. 3. The normals rotate so that they remain perpendicular to the midsurface after deformation. FSDT is more complex and includes transverse shear deformation in the kinematic assumptions. The Reissner-Mindlin hypothesis, a basis for FSDT, does not restrict the transverse normals to remain perpendicular to the midsurface after deformation, i.e. it removes the last assumption of the Kirchhoff s hypothesis. This means adding transverse shear strains into the theory. The assumptions of the above two theories are compared in Figure 9. Fig. 9a Fig. 9b Figure 9. Undeformed and deformed geometries of an edge of a plate under different assumptions. Fig. a: Kirchhoff s theory. Fig. b: the first-order plate theory. Figure from [24]. The first-order shear deformation theory requires more information than the classical laminate theory, because of the included transverse shear deformation. However, the transverse shear deformation is only necessary for relatively thick plates. Therefore, for thin plates, as those studied in this thesis, the transverse shear effect vanishes and the FSDT and CLPT give virtually identical result.

22 14 Constitutive relations Most laminates are thin and experience a plane stress state. Although transverse shear stress components ( or equivalent in different notation are small in comparison to the remaining components, they can induce failure because fibre reinforced composite laminates are weak in the transverse direction. This is because the fibres, which provide laminate strength lie in x 1 x 2 -plane. Figure 10. A lamina in a plane state of stress, from ref. [24]. The generalized Hooke s law for an anisotropic material is given in contracted notation: or where: are the stress components, are the strain components are the material coefficients(elastic constants), C is the stiffness matrix S is the compliance matrix. All the coefficients refer to orthogonal Cartesian coordinate system (x 1,x 2,x 3 ). As described earlier, the lamina layer is thin and prevails plane stress state, i.e. Thus the Hooke s law takes form: or, shortly denoted for local values, i.e. referring to a lamina local system: where Q l is the lamina stiffness matrix or reduced stiffness matrix denoted: or

23 15 Transformation of stresses and strains In manufacturing of composite laminates several lamina are assembled in stack with different orientation angles with respect to the global coordinate system. Therefore, to depict the behaviour of the laminate, the behaviour of each lamina described in global coordinate system is needed. To obtain these, a relation defining the above Q l in the global coordinate system is needed. Figure 11. Positive rotation of principal material axes from x-y axes. Figure from ref. [24]. If the rotation angle of the coordinate system is to be considered, see Figure 11, the relation between the transformed stiffness matrix ( and Q l is then: where T, the transformation matrix is: This final formula is obtained by several stress-strain transformations presented in ref. [33]. Laminate From Kirchhoff s hypothesis, it follows that unloaded plane perpendicular to the middle plane remains perpendicular to the mid-plane after load application. Thus for bending of laminate the strain at each point can be written as: where is the strain in the middle plane is the distance from neutral axis is the curvature vector. The influence of the acting forces and bending moments on the stresses and strains in laminate is considered. Figures below present schematically the stresses and strains distribution over the thickness of the laminate. Figure 12 shows strains and corresponding stresses due to in-plane deformation.

24 16 Figure 12. Strains and corresponding stresses due to in-plane deformation, from ref. [33] Strain is uniform and equal in all laminas. Stress varies incrementally, it is due to the fact that stiffness in global coordinate system varies between laminas. In Figure 13, the strains and corresponding stresses due to bending are shown. Figure 13. Strains and corresponding stresses due to bending, from ref. [33]. In this case strains vary linearly and stresses show incremental changes. Now, a plate of total thickness t composed of N orthotropic layers is considered. Each k th lamina oriented at an angle θ k with respect to the laminate coordinate x has its own principal material coordinates For convenience, the global system is taken as in literature. The z-axis is positive downward from the mid-plane. The k th layer is located between the points z=z k and z=z k+1 in the thickness direction, see Figure 14. Figure 14. Geometry of an N-layered laminate, figure from ref. [33].

25 17 Starting from generalized Hooke s law derived (see ref. [33]) through stiffness matrix relations, the relation between forces with bending moments and strains with curvatures can be written in a matrix notation are as follows: where: A is called extensional stiffness matrix B the extension bending coupling matrix D the bending stiffness matrix N normal forces M bending moments ε 0 strains κ curvature where: Q i corresponds to stiffness matrix of i th lamina in global coordinate system z i represents position of the top and bottom of each lamina with respect to the neutral axis In the expanded form, where the matrix is called fundamental matrix we have: Coupling relations The composite laminate structure may be adjusted to the needs. As it was mentioned in Section 2.1, coupling between type of loading and the resulting deformation is an important characteristic of composite materials. Below, some relations between the loading and fundamental matrix are presented. Figures are from ref. [13]. General laminates: - No symmetry - Not balanced - E.g. [ 0, 45, 90, 22, 0, 45]

26 18 Unsymmetric cross-ply laminates: Unsymmetric angle-ply laminates: - Laminate composed of 0 and 90 plies - Laminate composed of +θ and -θ plies - Antisymmetric about the mid-plane - Antisymmetric about the mid-plane - E.g. [90, 0, 90, 0] - Balanced, e.g. [45, -45, 45, -45] Some most striking conclusions to the coupling are: - Stacking sequence does not affect the A matrix - B=0 if the laminate is symmetrical - D matrix is affected the most by the stacking sequence 2.4 New materials utilized in the project 3 Researchers strive for lighter and stronger structures, what results in an increasing use of advanced materials, such as composite materials. In particular, fibre reinforced plastics (FRP) have become popular due to their high strength to weight ratio. Also the wind energy has been dominated by these composites. The majority of wind turbine blades used for large wind turbines are manufactured using polymeric composites with glass fibres [7]. Also the blade studied in this thesis is built with glass (and in sandwich panels, PVC foam as the core material). In order to penetrate future design possibilities and potential performance improvement, not only commonly used glass fibre composites but also other materials were considered in the investigations. The goal is to minimize the trailing edge panel s deformation. Until now, the second priority would be minimizing the cost of the panel (and thus the cost of the blade). However recently, a new trend in design criteria was born that appreciates the influence of the rotor loads on the entire wind turbine. This opens the design for more expensive but lighter solutions that decrease the loads that the blade exerts on the remaining turbine components. Thus, the weight reduction is of higher importance than the cost reduction. Therefore, not only the currently utilized material layup is optimized, but also new solutions are studied. Table 1 presents comparison of fibre composites considered. Obviously, depending on the fabric produced by manufacturers, the mechanical properties will slightly differ.

27 19 Nonetheless, this is an approximated study demonstrating the potential improvements and such assumptions are satisfactory. Fibre E-glass Carbon (HM) Bamboo Thickness n E1 [GPa] E2 [GPa] G12 [GPa] ν Table 1. Typical stiffness data for unidirectional fibre reinforced composites: glass fibre, high modulus carbon fibre and bamboo. Data from ref. [33], for bamboo: ref. [7]. Due to the characteristics of bamboo-poplar laminate, its thickness is described with initial 3mm for the first layer and additional 2.5mm for each layer added. This section gives basic information on the introduced materials. For more details on design and manufacturing of composite materials, see ref. [2],[4],[5],[6],[7],[13]and[24]. Carbon fibre Mainly glass fibre composites are currently used in blade design. Recently, carbon fibre is being considered as well. It is suitable for this application due to its extremely high stiffness to weight ratio. It is also characterised by outstanding resistance to fatigue. Thus, in the modern designs carbon is utilized despite its high cost. There are, obviously, drawbacks of carbon fibre utilization in wind turbine blades. One of the most important is its high electric conductivity. A potential lightning stroke would cause more severe damage in a carbon blade than in one only composed of glass fibre. It is not within the scope of this project to divagate on solutions for additional problems caused by the material choice. For information on this subject, please visit ref. [2] and [5]. It is also important to consider the price of material used. Carbon for wind turbine blade applications is approx. 5 times more expensive than glass, see ref. [5], and its utilization would increase the overall blade cost significantly. However, as the key feature in blade design becomes its weight, even more expensive solution is justified as long as it considerably decreases the weight. Research is currently underway at Risø DTU to develop new design criteria for wind turbine blades that will include relation between the blade s weight and remaining turbine component and thus support these assumptions. Therefore, despite carbon fibres disadvantages, the layup composed of this material is also studied. Bamboo As mentioned before, the majority of wind turbine blades are manufactured using glass fibres. However, renewable materials, such as birch, have also proven to be very successful as a primary material in large horizontal-axis wind turbine blades. The limited supply and high cost of birch has led to a search for other renewable materials that can be used for wind turbine blades, see ref. [7]. Moreover, some researchers claim, that bamboo should substitute glass fibre in the secondary structure of the blade (i.e. aerofoil). Bamboo has many engineering and environmental attributes that make it an attractive material. It grows amazingly fast, many of over 1000 species reach full height in less than 6 months.

28 20 Most important features of bamboo for engineering applications: - Low density - Higher strength, modulus, toughness and fatigue limit than wood - Low raw material cost - Compatible with conventional manufacturing methods Bamboo-based composites offer the potential for recycling of wind turbine components. In the project, a bamboo-poplar laminate is considered. Figure 15. Macro-structure of bamboo-poplar laminate formed by alternating layers of 2 mm thick bamboo curtain mats and 0.5 mm thick poplar veneer. Research is currently underway at Risø DTU and ICBR to further develop and characterize bamboo-based composites, laminates with multi-directional bamboo reinforcement and also hybrid bamboo laminates reinforced with carbon-fibres. The specific cost data for this material is not available. However, assuming the same resin price and manufacturing technique the cost of final product can be estimated. According to ref. [7] fibre content in bamboo laminate is 1.5 times higher than glass. Assuming resin cost (according to 6 and 12 times higher than glass fibres and bamboo respectively, the bamboo price is estimated not to exceed 50% of the glass price. More detailed data were not available to the Author s knowledge. For the purpose of this thesis, this rough assumption is sufficient. However it should not be used as a reference. Fibre Cost of the final product Weight [kg/m 3 ] E-glass 6 $/kg 1940 Carbon $/kg 1540 Bamboo <3 $/kg 800 Table 2. Typical cost and weight data for unidirectional fibre reinforced composites: glass fibre, high modulus carbon fibre and bamboo. Data from ref. [18] and [7]. Considering laminate instead of a sandwich A new tendency has arisen in blade design that tries to avoid using sandwich structure. Not only is sandwich more expensive and complex to manufacture than laminate, but also it causes additional failure possibilities, e.g. wrinkling, delamination etc. Therefore, it would be beneficial to substitute the material used in the studied region with laminate plate, i.e. to eliminate the core.

29 21 CHAPTER 3 3 Methods for wind turbine blade testing In this section, the methods for experimental and numerical studies used in the thesis are described. The finite element approach and FE-model investigated is elaborated on. The measurement equipment used in the studied full-scale tests is presented and the solutions for testing are briefly introduced. Finally, the finite element model used is validated with respect to the experimental results. 3.1 Finite element model The work is based on a finite element model of a wind turbine blade developed by Risø DTU. The model consists of more than shell and solid elements composed of approximately 200 materials of various material properties. The full-scale tests conducted at Risø DTU analyze an experimental SSP 34m blade cut at 25m, presented in Section 3.2. The FE-model, presented in Figure 16, corresponds to the truncated blade. The part of the blade beyond 25m has been modelled with an isotropic bar element with characteristics assigned so that it corresponds to a rectangular hollow section (RHS) profile. This beam element is used because of its rigidity and computational properties. There was no need for more detailed representation of this region.

30 22 Fig. 16a Fig. 16b Figure 16. Fig. a. The blade geometry of the first 25m described by a number of cross- sections and splines linking the sections to preserve the best similarity to a real blade. Fig. b. Full FEmodel m region is defined by an isotropic beam. The section of the blade changes with distance from the root in the following manner: Fig. 17a Fig. 17b Fig. 17c Fig.17d Figure 17. Scaled sections, not exactly measured dimensions: Fig. a: root section, 0m cross-section; Fig. b: 8m section; Fig. c: 22m section: Fig. d: beam tip part 34m The forces have been applied, as it is done in the full-scale test, in three positions from the root: 13.2m, 18.6m and 24.9m. In the full-test, anchor plates are used to allow realistic structural behaviour of the blade, see Section 3.2. Each plate was simulated as force applied at the corners of the box-girder. Figure 18. The blade cross-section with force application points marked. Only four application points are presented, the remaining four markers are translated along blade. The nonlinear finite element analyses were performed by Marc solver on a powerful multi- CPU cluster. The analyses were established for several load cases applied to the same model with several modifications concerning material layup and mechanical properties.

31 23 The coordinate system Z Y X Figure 19. Co-ordinate system used in the finite element model. The x-axis is pointed in edgewise direction towards leading edge. The y-axis is in flapwise direction, positive in direction from pressure to suction side. The z-axis is along the blade, starting at the root of the blade, as indicated in the figure above. Load case PTS - pressure side towards suction side Load component STP - suction side towards pressure side -y TTL - trailing edge towards leading edge LTT - leading edge towards trailing edge -x Combined loading: TTL +PTS y x x & y Table 3. Loading directions on FE-blade model with respect to the global coordinates. The coordinate system presented in this section is valid for the finite element model and the full-scale test results. However, when dealing with analysis of the sandwich plate, the coordinate system used is different. It corresponds to the convention used in literature regarding the plate problem. It is important not to mismatch those two systems. Loading In this thesis, mainly the certification loading directions have been investigated. Primarily the Leading Towards Trailing edge load case (see Table 3), has been considered. This is because the fatigue failure addressed in the thesis is dominating in the edgewise loading. However, in order to strive for meaningful solutions, also PTS and combined loading has been studied. The Risø DTU researchers believe that the certification process is based on simplified assumptions. The method for load application in these tests prevents possibility of some failure modes which in real life do occur. Therefore, combined load case was prepared on basis of estimated influence of aerodynamic forces and gravity (considered to be acting in LTT direction) in operation conditions. For more detailed information on new failure mechanisms observed in wind turbine blades see [10].

32 24 The forces applied in the model in the combined load case are given in the table below. The percentage is with regards to 100% of the direction of loading in considered direction s load case at certain application point: Application position Force direction 13.2m 18.6m 24.9m TTL 11.1% 25% 44.8% PTS 51.8% 49.1% 50.8% Table 4. Force distribution in combined loading load case model. The directions of loads applied to the blade described above are schematically presented in Figure 20. Fig. 20a Fig. 20b Fig. 20c Figure 20. Scheme presenting directions and method of load application on the model. Fig. a: LTT loading. Fig. b: PTS loading. Fig. c: combined loading. Methods used in connection to the model - Local displacement Since this thesis deals with minimization of local deformation amplitude, it is necessary to define a reliable measure of this deformation. Local deflection of the panel was derived using global displacement of three points defining the panel, see Figure 21. Figure 21. Scheme presenting the points (nodes) used in the local deformation definition presented on an auxiliary section (10m).

33 25 As a reference, one point was chosen at shear web towards trailing edge (points 1 and 6 for pressure and suction side respectively) and one close to trailing edge (points 3 and 4). The local deformation refers to the mid-point deflection (point 2 for pressure side and 5 for suction side). The value of the local displacement ( in Figure 22) of the latter is found by means of its distance from a line formed by the former two points. All three dimensions (x, y and z) are considered in this method. Figure 22 presents a scheme of the method for obtaining the local deformations from finite element analysis results. Figure 22. Scheme defining the local deformation obtained from finite element analysis. and The above method corresponds to the local deformation measurements performed in fullscale tests, see Figure 23. Metal frames were attached to the blade on both sides in order to ensure measurement of the local deformation of the trailing edge panels. For more detailed description of the measurement method, see Appendix Frame holding NT sensor Fig. 23a Fig. 23b Figure 23. Fig. a: Picture showing position of local displacement sensors of the trailing edge panel mounted on the blade in Risø DTU s new test center for blade structure. Fig. b: Schematic description of the measuring devices placed at m from the root section.

34 26 Layered structure of the model At this point it is useful to acknowledge consistency in layer notation for FE-results. The definition of layers layup will be needed in strain analyses. The plots from FEA are described with outer and inner layer, what corresponds to the experimental results. Figure 24. Scheme presenting system of layers numbering used in blade model. The number of layers of element depends on number of plies in panel and thus on its physical thickness. 3.2 Full scale test The blade tested at Risø DTU is a 34m blade sponsored by SPP Technology A/S. The preparation of the full-scale test was not a part of this thesis work. However, the Author has participated in the preparations before the thesis duration. Although in real life, the blade is subjected to loading from the tip until the root, the full-scale tested blade, it was cut off at the distance of 25m from the root. This could be done since no loads are applied nor measurements were to be done in the remaining part of the blade. The studied full-scale tests do not consider aerodynamic response but focus on structural behaviour of the blade. That is why no measurements are performed in this part of the blade. Load application The design strength of the blade was known from the manufacturer and the test was planned to achieve a distribution of the bending moment in the blade that would make it possible to predict the damage in the desired region. For confidentiality reasons, the ultimate load referred to throughout the report is a confidential Risø-defined load. All the values and percentages given in the thesis are scaled to the so-called Risø scale. The loads have been applied at 3 positions along the blade: 13.21m, 18.61m and 24.91m, see Figure 25.

35 27 Figure 25. Locations for load application - scheme of the blade placed on the rig. Most common solution for load application used in blade tests until now has been clamps, which prevent the blade from transverse shear distortion, see Figure 26a. It also prevents the trailing edge panels to deform outwards, see Figure 26d. This behaviour is crucial for the thesis core problem presented in Section 1.2. Risø DTU has developed new technique for loading, which allows the profile to deform in a more realistic manner. The anchor plates, presented in Figure 26b, allow transverse shear distortion of the profile as well as the deformations of trailing edge panels. Fig.26a Undeformed panel Deformed panel Fig. 26c Fig. 26d Fig.26b Figure 26. Different ways to apply load to the blade structure. Fig. a: Clamps preventing transverse shear distortion; Fig. b: scheme of anchor plates. Fig. c: anchor plate glued to the blade; Fig. d: sketch of trailing edge shells with out of plane deformation, possibly leading to fatigue failure in the trailing edge. Measurement equipment During the tests performed at Risø DTU, the structural behaviour of the blade was monitored with many sensors inside the blade and on its surface. The global deflection of the blade and local deformation of the trailing edge panels were measured with two different kinds of displacement transducers. Strain measurements were done at many positions along the blade and in the sections. More than 300 strain gauges have been

36 displacement [mm] 28 mounted on the blade, including uni- and bi-directional strain gauges as well as rosettes. Many of them were mounted in so called back-to-back manner to enable defining character of the out of plane deformations. Moreover, Digital Image Correlation system called ARAMIS has been used at Risø DTU to study the deformation distribution. The measurement equipment used in the full-scale test is presented in details in Appendix 12.3 and full description of the equipment positioning is given in [10] and forthcoming data reports for the tests currently conducted. 3.3 Model validation Before studying results of finite element analysis, the FE-model must be validated against full-scale test. For this thesis purpose, results from wind turbine blade full-scale test, described in Section 3.2, were used. The validation includes global as well as local behaviour study. The investigation of the addressed deformation considers checking the position of the wave to ensure corresponding position of the maximum deformation amplitude. The local displacement and strains are also compared. Global displacement Global trailing edge displacement in edgewise direction has been compared. Te results are compared until the maximal load applied in the conducted full-scale tests, which was 51%. As it is clearly visible in Figure 27, the data for numerical and experimental tests are well aligned. 300 Comparison of experimental and numerical results for global displacement in the edgewise direction % 10% 20% 30% 40% 50% load [% of ultimate load] FEM - 22m Test - 22m FEM - 16m Test - 16m FEM - 10m Test - 10m Figure 27. Comparison of experimental and numerical results for global deformation in edgewise direction measured at trailing edge.

37 29 The deviation in numerical and experimental data is the highest at 22m and it is 6% for the maximal measured load. Such a difference almost at the blade tip is very satisfactory and confirms that the blade model was calibrated properly. The local deformation Risø researchers performed measurements by means of Digital Image Correlation system presented in Appendix This data allow to present the deformation distribution and to depict the position of its highest amplitude. The results, presented in Figure 28, confirm that the FE-model corresponds well with the full-scale test. In both cases, there appears a double wave and there is no phase shift of the deformation position. Some insignificant differences come from the fact that the frames of reference (black frames visible in Figure 28a) were mounted in not precise positions. Nonetheless, the distribution is virtually identical both in shape and values attained. Frame of reference (5m) Fig. 28a Fig. 28b Figure 28. Comparison of experimental and numerical results for the out of plane deformation. Fig. a: Deformation distribution obtained with Aramis. Fig. b: FEM results from a corresponding load step in the same region. The scale has been adjusted for a better visualization of the comparison. The local displacement In the following, the local deformations from both numerical and experimental results for several subsequent sections are compared.

38 deformation [mm] deformation [mm] deformation [mm] Local deformation of the trailing edge panels at 4m section 0% 10% 20% 30% 40% 50% load [% of ultimate load] Figure 29. Comparison of local deformation for experimental and numerical data for pressure side trailing edge panel mid-point at section 4m from the root. FEM full-scale test As visible in Figure 29 and Figure 30b, a sudden change in trend occurs in experimental data at approximately 25% load. It causes further deformation increase to be steeper and deviate slightly from the FE-results. Nonetheless the nonlinearity shows a very similar behaviour in experimental and numerical results throughout the range of the studied deformation. Moreover, the local deformation at 3.5m, where the discussed change in trend does not occur, shows almost ideal alignment of the data, see Figure 30a. The overall behaviour of the deformation obtained in the FE-model is well correlated with the one observed in full-scale test Comparison of local deformations of trailing edge panel at 3.5m section FEM full-scale test 0% 10% 20% 30% 40% 50% load [% of ultimate load] Fig. 30a Fig. 30b Figure 30. Comparison of local deformations for experimental and numerical data for trailing edge panel s mid-point at 3.5 and 4.5m from the root, pressure side Comparison of local deformations of trailing edge panel at 4.5m 0% 10% 20% 30% 40% 50% load [% of ultimate load] FEM In Figure 31, the relative deformation is presented considering measurements of local deformation of both, pressure and suction side, panels. The suction side will not be studied in this thesis. However, for demonstration of the problem it is presented here, since for the trailing edge fatigue failure, it is important how both panels behave. The relative local behaviour is again well mirrored in the FE-model.

39 strain [µs] strain [µs] displacement [mm] 31 8 Local displacement of trailing edge panels' at 4m section % 10% 20% 30% 40% 50% load [percentage of ultimate load] Figure 31. Local displacement of trailing edge panels' at section 4m from the root. FEM, pressure side FEM, suction side test - pressure side test -suction side Strain analysis Figure 32 presents the comparison of experimental and numerical data for the strain confirming a satisfactory similarity. FE-results extracted in local coordinate system for the trailing panel reveal significantly better alignment than for the global system Strain in edgewise direction at 4m 0% 10% 20% 30% 40% 50% load [% of ultimate load] Strain in longitudinal direction at 4m 0% 10% 20% 30% 40% 50% load [% of ultimate load] FEM -inner layer FEM -outer layer experiment - inside experiment - outside FEM - inner layer FEM - outer layer experiment - inside experiment - outside Figure 32. Strain in the edgewise (top) and longitudinal (bottom) direction in the midpoint of pressure side trailing edge panel. Numerical and experimental results are compared.

40 Summary In this section, the methods of experimental and numerical studies used in the thesis were presented. The finite element approach and full-scale testing method were introduced briefly. Finally, the FE-model studied was validated with respect to the full-scale test results. It has been shown that both global and local behaviour of the model satisfactorily mirror the response of the blade tested experimentally. The investigation of the trailing edge panel confirmed the same position of the double wave deformation and its maximum amplitude in both result sources. The local displacement and strains were also proved valid.

41 33 CHAPTER 4 4 Pre-study of the trailing edge panel In this section, the study performed prior to the main part of the thesis is presented. First, a pre-study is performed to motivate the choice of the blade region considered. Next, a non-linear finite element analysis of the selected region is conducted. These initial FE-results will be used in the following sections as reference data for the improved solutions. Finally, the nature of the deformation is investigated. 4.1 Motivation for the choice of the blade region considered In this thesis out of plane deformation of the trailing edge panels is to be minimized. For demonstration of the potential improvement, a bounded region of the panel will be studied. The following presents a pre-study giving background for the choice of region studied further. The relevance of the deformation is investigated both from structural and aerodynamic point of view.

42 34 Aerodynamic region In the deflection optimization algorithm, the load distribution will be applied on the plate cut out of the trailing edge panel. In case of aerodynamic part, the loads in trailing edge panel region may be approximated by some nonlinear lateral load distribution, see Figure 33. Therefore, the algorithm developed for this region analysis could consider a relatively simple case of only lateral load application. If it appears that changes of the blade profile may reduce the aerodynamic efficiency, it would be beneficial to minimize this behaviour and to keep the profile in the aerodynamic region as close to design profile as possible. Figure 33. Aerodynamic loads on wind turbine blade section (pressure and drag) including gravity loads. The loads exerted on trailing edge panels are circled. Aerodynamic efficiency change caused by the trailing edge panels deformations was studied. The measure was chosen to be the change of dependence of the lift on the angle of attack, i.e. lift curve. The angle of attack is the angle formed by the chord of the airfoil and the direction of the relative wind. The lift and drag of the airfoil depend not only on the angle of attack, but also upon the shape and area of the airfoil, the airspeed etc. Although it is desirable to obtain as much lift as possible from a blade, this cannot be done without increasing the drag. It is therefore necessary to find the best compromise. The drag and lift definitions, as well as issues in application are introduced and derived in ref. [16]. Fig. 34a Fig. 34b Figure 34. Fig. a: wind velocity as seen by the blade (steady model), from ref. [16]. Fig. b: Aerodynamic coefficients with respect to angle of attack theoretical plots. Cx - the drag coefficient, Cy - the lift coefficient. After

43 Cl Cl 35 Both undeformed and deformed blade profiles exported from FEM have been normalized, as presented in Appendix By means of a study performed with internal Risø piece of software, XFOIL, the lift curves have been obtained. In Figure 35 the results for two representative sections are shown. The changes in lift caused by the panels deformations were almost negligible. At the section with the highest amplitude of local panel deformation, i.e. at 22m, the difference is below 1.5%. Lift curve comparison for 16m section 2 Lift curve comparison for 22m section alpha deformed profile undeformed profile Figure 35. Lift coefficient versus angle of attack plots for sections 16 and 22m from the root alpha deformed profile undeformed profile During the period of this thesis, Risø Aeroelastic Design of Wind Energy Division has published a report confirming insignificant influence of panels deformations on the aerodynamic efficiency, see ref. [14]. This publication confirmed the results presented above. Therefore, further aerodynamic study was omitted and the root section deformations were investigated. Root region As visible in Figure 36 presenting a blade section, a local deformation occurs on the pressure side between 4 and 5 meters. This localized out of plane deformation is directed outwards the trailing edge panel reaching the highest amplitude at approximately 4.25m from the root. The deformation shape is regular, implying it could be buckling on a square element. However, it is impossible to state this explicitly at this point. Moreover, the character of the deformation is not the motivation for the need of improvement addressed in this thesis. As described in Section 1.2, trailing edge panels deformations cause fatigue in the adhesive joints which can lead to failure. From SSP-Technology experience this behaviour is considered a critical problem in the root region. What is important, the phenomenon is likely to become even more severe once the failure mechanisms currently causing the blade s failure are solved. Several solutions for the currently critical failure modes have already been patented, see ref. [10]. As it was discussed, for the fatigue failure the deformations occurring on both, pressure and suction side, panel are crucial. However, for demonstration of potential improvement, the more pronounced deformation, i.e. the pressure side alone is studied.

44 36 Figure 36. View of the root section between distances 3m and 5m from the root. The fringe shows displacement in flapwise (Y) direction. The red circle indicates clearly visible local deformation at the pressure side trailing edge panel. Although defining the nature of the addressed deformation is not within the scope of the thesis and it has been studied, see ref. [25], more thorough analysis bringing insight into the character of the deformation is presented in Section Finite element analysis of the considered panel the reference model The following presents investigation of the localized out of plane deformation on the pressure side trailing edge panel observed in Section 4.1. The initial state results of a nonlinear finite element analysis presented here will be further used as reference data for the improved solutions. Moreover, the results will be used to approximate the loading and boundary conditions for the studied panel. Figure 37 presents the out of plane displacement in the studied part cut out of the trailing edge panel in the FE-model. This plate will be investigated in the optimization algorithm. The shape of deformation is close to regular, deformation continues slightly towards 5m distance from the root.

45 37 5m 3m Figure 37. The out of plane displacement of the original layup plate presented in local coordinate system. The results are presented on the plate cut out of the model. In order to get more information about the deformation, the subsequent steps in the process of its development were observed, see Figure 38. It can be noticed that a double wave is forming from the very first load increment. With the load increase, the wave transforms through a kind of mode shift from double wave into a single deformation with highamplitude. This behaviour will be important in assessment of the improved solutions. Figure 38. Development of the studied local deformation. Steps 2.5%, 25%, 50% and final 100% are presented. In Figure 39, a profile of the deformation at the pressure side trailing edge panel is presented for several load increments. The displacement plotted is measured at the panel midpoints, which correspond to the point where the deformation reaches its highest amplitude. This figure demonstrates highly localised character of the deformation. It also visualizes the duplex shape of the deformation even in very early stage of its development. At 5% of load the amplitude is very small and the double wave is not easily visible. Thus, these results were scaled 4 times.

46 Strain [ S] Strain [ S] deformation [mm] Development of the out of plane deformation at the pressure side trailing panel % load 5% load scaled 4 times 25% load 50% load -25 distance from the root [m] 100% load Figure 39. Development of the out of plane deformation profile at the pressure side trailing edge panel in the blades' root section. 4.3 Study of the deformation s nature An investigation of the nature of deformation has been conducted. The aim is to test if the nonlinear behaviour of the deformation is dominated by buckling. First, the strain results are studied. Then to further test the hypothesis of buckling influence, the response of the panel subjected to tension is investigated. Strain analysis Strains in longitudinal and edgewise directions are investigated. This is because the studied panel is thin and prevails plane stress state. In order to check if the deformation is influenced by buckling, strains in outer and inner layers and their relation have been studied to present character of bending. The strain results at the point of the highest amplitude are presented in Figure 40. The values obtained lie within safety range. However, the strain nonlinear behaviour, more pronounced in the longitudinal direction plot in compression, is of concern Strain in the edgewise at the point of the highest deformation amplitude inner layer layer 1 outer layer layer 6 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Figure 40. Strain in edgewise (left) and longitudinal (right) direction in the midpoint of the pressure side trailing panel at 4.25m section, where the deformation reaches the highest amplitude Strain in the longitudinal direction at the point of the highest deformation amplitude 0% 20% 40% 60% 80% 100% layer inner 1layer layer outer 6layer load [% of the ultimate load]

47 displacement [mm] 39 In order to show the bending contribution to the strain, the membrane average strain was taken away. This revealed nonlinear behaviour of the bending, which could indicate influence of buckling. In order to test this hypothesis, the plates behaviour in tension has been investigated. Buckling occurs only in compression and shear that causes local compression. Therefore, if the studied panel in tension does not deform, it will indicate that the phenomenon may be caused by buckling. Behaviour of the panel under tension In order to put the panel under tension, load was applied to the blade in Trailing Towards Leading edge direction (TTL). The trailing edge panel under this load is presented in Figure 41. Not only an oppositely directed (inwards) deformation occurs in tension but also it has a similar shape to the one observed in compression. Figure 41. The pressure side trailing edge panel in tension (TTL loading of the blade). The fringe presents displacement transverse to the loading direction. The local displacement in the point of the deformation s highest amplitude is presented in Figure 42. It is clearly visible that the deformation develops in the same non-linear manner achieving virtually the same value as in compression (the difference is 1.5%) Comparison of local deformation development for different loading directions 0% 20% 40% 60% 80% 100% LTT TTL mirored at max load [% of the ultimate load] Figure 42. Local out of plane displacement comparison for tension and compression of the panel (corresponding to LTT and TTL load cases).

48 40 These results show that behaviour corresponding to the one observed in compression occurs for the panel in tension. Therefore it can be concluded that the investigated local deformation nonlinearity is not buckling driven. However, if the loading continues above the ultimate value it is expected that the deformation will result in buckling occurrence. It needs to be stressed that the deformation needs to be addressed independently of its nature. This is because the high deformation amplitude causes the failure in the adhesive joint. Basing on the above results, which reject the hypothesis of buckling nature of the addressed deformation, the buckling analysis is not included in the optimization algorithm. 4.4 Summary In this section the pre-study considerations are covered. First, an investigation of the deformation s relevance was performed to motivate a choice of the region that will be considered in the main part of the thesis. The considerations revealed insignificant influence of the trailing panels deformations on the aerodynamic efficiency of the blade. The study of the root region behaviour confirmed a structurally significant local deformation of the pressure side trailing edge panel. Further investigations showed that the localized out of plane deformation discussed is strongly localized and has large amplitude. It needs to be addressed since it causes critical failure in adhesive joints. Moreover, it has been shown that the deformation is not dominated by buckling.

49 41 CHAPTER 5 5 Optimization algorithm for sandwich plate material At this point, the finite element model is validated and it is decided what region shall be considered in the optimization of the material layup. The following section presents the process of the optimization tool preparation. The wind turbine blade pressure side trailing edge panel chosen as the object of material layup optimization is considered as a separate plate modelled in the optimization study. The method for obtaining the loading distribution applied on the plate is described and an overview of the derivation of the explicit formulae for the considered plate problem is given. The results of FE-study performed in Section 4 are used to approximate the loading and boundary conditions for the studied panel. Moreover, choice of searching engine for the algorithm is motivated. 5.1 Loading distribution and boundary conditions The local behaviour addressed in this thesis is pronounced the most for the Leading Towards Trailing edge loading applied on the blade. On basis of the FE-results for the blade s response, the loading and boundary conditions for the considered panel are found. In Figure 43, the translation of the blade problem into the plate problem is schematically presented. The pressure side trailing edge panel is treated as a separately investigated plate. Some approximations are introduced, but the behaviour of the optimized loaded plate corresponds to the original deformation of the analysed trailing edge panel.

50 42 5m 3m Figure 43. The blade trailing edge panel presented schematically as a separate plate with loading applied in a realistic manner. The local coordinate system for the plate is also shown. Boundary conditions The simple support at all edges was chosen preventing the plate from deflecting at the boundaries and allowing its rotation at the edges. This type of boundaries was chosen on basis of the panel s structure connections. The plate considered is a cut out part of a long trailing edge panel prone to deformations. Therefore, the two edges corresponding to 3m and 5m panel s sections are considered to be allowed to deform and rotate, distributing the bending moment to the entire panel structure. In the remaining direction, the panel is jointed with box girder and trailing edge. The sudden change in material thickness facilitates rotation of the panel plate at these joints and causes it to be more prone to deformations. The connections are presented and discussed in Appendix It is however important to say that in real life the supports are always a combination of several types of boundary conditions and the choice is only an estimate of the one that fits the reality the most. Moreover, for the needs of the plate material optimization, the results would not differ qualitatively for a different support applied. The boundary conditions may change the amplitude of deformation obtained, but the choice of the stacking sequence for the sandwich faces would not be affected. Loading distribution The plate was subjected to a lateral load combined with forces in two in-plane directions. The load distribution was to represent the real situation occurring in the blade panel. Thus, the results of initial FE-analysis were used in the process of derivation of approximated loading distribution for the plate. In order to avoid influence of the connection-related behaviour, the plate considered was bounded not exactly at the joints, see Appendix It was assumed that all layers of the panel are perfectly bonded together and thus the displacements and strains are continuous throughout the thickness. The strain results were chosen as basis for force distribution due to its linear variation throughout the thickness. Interlaminar effects, such as delamination were not predicted.

51 43 The strain results at the edges of the studied panel were transformed using mechanical properties and the panel s dimensions. On basis of these results, an approximated load distribution applied to the plate in the optimization algorithm was found. The lengthy derivation is omitted here, but the milestone transformations are presented in Appendix Figure 44 presents a scheme of the loading distribution applied to the plate studied in the optimization process. Figure 44. Scheme of the loaded plate. The forces are presented in general, as a function of distance from the plate origin. Right: top view. Left: cross-section in both vertical planes. 5.2 Derivations of the numerical model of the plate In the following, the theoretical derivation of the formulae used in the algorithm is presented. Since the trailing edge panel studied is considered to be a separate plate, its geometry is decided upon. The considered panel in the blade root section is a flat plate. The coefficient of determination (R 2 ) for linear approximation for the plate geometry can be found in Appendix For all the edges it is highly above 99% and therefore a flat plate is chosen to be studied. The analysis is developed for orthotropic plate with x- and y-axes, i.e. the principal axes of orthotropy, for which the properties are constant throughout the plate. The following constants serve to fully describe the properties of the plate and its deformation associated with the loading applied: - flexural rigidities D x and D y - twisting stiffness D xy - the Poisson s ratios xy and yx denoted also xy and yx - and the shear stiffnesses S x and S y denoted also D Qx and D Qy The additional symbols have been introduced during the derivation in order to keep consistency with the notation used by Robbinson [26].

52 44 Equations of equilibrium are derived on basis of notation presented in Figure 45a. The coordinate system and loads are defined as in Figure 45b. Fig. 45a Fig. 45b Figure 45. Forces and bending moments acting on a differential element. Sign convention used in the plate analysis. After Zenkert [33]. Uniformly Distributed Load If the aerodynamic region was considered, the load distribution could be approximated by a distributed lateral load. In that case, the solution is nearly available for use. Namely, the literature (e.g. ref. [17] and [34]) gives derivation and solution for a Uniformly Distributed lateral Load (UDL). This solution would require only limited transformations in order to obtain some realistic distribution of the lateral load. However, for the considered problem, derivation of a solution not available in the literature is needed. Combined in-plane forces and distributed load The loading and boundary conditions for the studied plate have been found in Section 5.1. Bending and buckling of orthotropic sandwich plates under various boundary conditions have been investigated in several reports from the U.S. Forest Laboratory, e.g. ref. [21] by March et al. The solutions derived are not exact and thus, for the needs of this thesis, an exact solution for the considered problem is developed. The derivations performed here are based on Timoshenko and Woinowsky-Krieger [30],[31] as well as work by Libove and Batdorf [17], Robbinson [26] and others [22],[27]. In order to stay consistent with the notation used by the latter, additional symbols, denoted earlier, have been introduced. Since it is impossible to obtain the analytical solution to the problem, see ref. [26], it was attempted to find an analytical-numerical solution approach by applying the method of power series expansion of continuous displacement components. The plate theory consists of six differential equations, three of which express the equilibrium of an infinitesimal plate element and three relate the curvatures and twist of the element to the forces and moments acting on it.

53 45 Starting with these equations, after minor rearrangement presented in literature, e.g. ref. [17] and [34] it holds: - from equation of vertical equilibrium (see Figure 45a): - from equilibrium of bending moments:,, By assuming that normal forces are constant throughout the plate and that they do not change when it bends, the following holds: Thus the small deformation theory is applied. and After some rearrangement (presented in details in [17] and [34]) including the equations defining curvature the following representation of the fundamental equations is obtained ( denotes Poisson s ratio): (**) Considering the forces distribution on the studied blade trailing edge panel, the shear forces are not included in further derivations. The forces distribution is presented in Section 5.1. To the Author s knowledge, the solution to plate problem with the considered loading and boundary conditions is not available in the literature. Therefore additional force directions are included in the above formula. In the following, a solution to the above system of equations (denoted (**)) satisfying the appropriate boundary conditions is to be found. General function for deflection can be written: For simple support boundary conditions, all edges are free to rotate and their out of plane movement is restricted, i.e.: and. The solution for this system under given loading can be written in the form: (***) Now, the constants A mn, B mn and C mn can be obtained by substituting eqns. (***) into the system (**). The system of external loads considered is in-plane loads N x and N y as well as lateral loading q in form:

54 46 Finding the partial derivatives:,, etc. for all combination up to 3 rd order for deflection and 2 nd order for shear forces, it gives: (****-1) (****-2) (****-3) Main transformations of the performed solution of this system are presented in Appendix Solving the above system (****) for A mn, B mn and C mn gives: and it can be stated that the deflection of the plate is governed by: After the transformations presented briefly in the Appendix, the coefficients in the above formula are finally expressed as: where and

55 47 Since the core in the considered case is isotropic: The difference between the derived formulae for combined in-plane and lateral loads and the one available in the literature for forces applied only in one direction seems to appear in the last component only (Z mn ). The altered terms are circled in the formula above. This implies, for future applications, that a superposition could be used to consider also the shear forces in the solution. Load distribution term The lateral load on the plate can be described by the following:, where: For uniformly distributed load the expression is available from literature: In the specific load distribution considered it takes the form: Solving and rearranging the q mn term, see Appendix 12.8, the representation of the lateral load term is derived to be: This is the final form of lateral load that is then substituted into the formula for deformation derived above. The formulae for sandwich plate problem derived in Section 5.1 together with the obtained load distribution create a basis for the optimization algorithm. Although in the approximated loading distribution the forces vary linearly throughout the edges lengths, the prepared algorithm is adjusted for more complex distribution. 5.3 The algorithm The following gives an overview of the development of the optimization algorithm. The features of the algorithm are briefly presented. The goal of the algorithm application is to efficiently solve the problem of material optimization for a sandwich plate. The objective is to minimize the out of plane deformation of the plate. The geometry and thickness of the structure are assumed to be fixed.

56 48 The problem statement The optimum design is chosen to minimize the deformation w at its maximum amplitude throughout the plate. That could be defined generally: The loading and boundary conditions and relations needed to define the objective functions are presented in Section 5.1 and 5.2. In principle, the main task for the algorithm is to return the stacking sequence for composite layers in a layup that minimizes the deflection of the plate under loading given as an input. Additionally, the program generates a model of the analysed plate and presents the deformation, both initially and after rearranging the material layup. The scheme of the algorithm is presented in Figure 46. The optimization algorithm primarily rearranges the composite layup, i.e. the stacking sequence of the plies. The design variables are the orientation angles for the face layers. The study is expanded by using new materials in the sandwich faces. Figure 46. Flow-chart presenting the principle of work of the prepared optimization algorithm. The additional feature is computing the plate s behaviour for decreased as well as increased amount of material. The thickness change allowed in the calculations is predefined by the programmer. It shall be based on common sense and engineering feeling. The idea is not to increase the weight more than necessary to bring significant improvement. No failure criteria have been considered, as described in Section 2.2. What is more, neither material nor manufacturing cost was included in the considerations. When using the created algorithm, the engineer is to decide with some realistic approach how much material it is worth to add. There is a need for a trade-off between the performance and cost efficiency. The searching engines applied in the optimization In the past, many researchers have investigated sandwich plate behaviour and numerous techniques have been proposed for sandwich plate analysis, see ref. [8], [15] including

57 49 several earlier references, [19] and [28]. Until now, however, most of the methods have met obstacles, either in difficulty in finding optimum (Olsen and Vanderplaats, 1989) or the computational power required. Kam and associates have studied the global optimal design of laminated composite plates treating fibre orientation angles as continuous design variables. Similar, although simplified approach is utilized in this thesis. Optimization software developers strive to find balance between numerical techniques that deliver rapid execution time and those that deliver robust and reliable solution. Also in this application a balance between priorities needed to be found. Below, several searching engines utilized in the layup optimization are presented. In all the implemented algorithms parameters have been adjusted so as to ensure crude accuracy. This is motivated not only by avoiding local minima but also by realistic approach from manufacturing point of view. Since it is infeasible to obtain great accuracy of orienting layers to the blade structure, an approximation of a jump of 15 degrees has been chosen as sufficient. Such approach also decreases the computation time considerably. The Simplex method This method, known as the Nelder-Mead method is a multidimensional unconstrained nonlinear minimization. In principle, this method considers an equilateral triangle ( the simplex, in a three variable search space is tetrahedron, etc). It takes the vertex with the largest objective function value and creates a new simplex (triangle, tetrahedron etc.) by reflecting this point in the hyperplane spanned by the other vertices. The schematic behaviour of the algorithm is presented in Figure 47. The side length of a simplex can be reduced or increased, contracting or expanding the step if along the direction, further improvement is expected. The main disadvantage of this technique is that it requires a large number of function evaluations and thus a long computation time. The Simplex method was implemented by means of function built in Matlab called fminsearch. It is probably the best of the Matlab s toolbox optimizing functions, however very expensive in computational power terms. Fig. 47a Fig. 47b Figure 47. Simplex algorithm. Fig. a: Basic simplex method. Fig. b: Simplex method with expansions and contractions. Figure from ref. [20]

58 50 Levenberg Marquardt method This is a combination of Gauss-Newton and gradient descent directions. It is a popular alternative to the Gauss-Newton method of finding the minimum of the sum of squares of nonlinear functions. The damping parameter, adjusted at each iteration, influences both the direction and the size of the step. The algorithm is described in details in ref. [20]. According to Madsen and Nielsen, this is, together with the Dog Leg method, currently considered the best method for solving systems of nonlinear equations. Levenberg-Marquardt method was utilized in the project by means of a Matlab function. It is, see Appendix 12.11, available from optimization toolbox of Department of Informatics and Mathematical Modelling, called immoptibox. Discreet Material Optimization -based algorithm An additional algorithm has been prepared on basis of Discreet Material Optimization approach. It is a method for performing material optimization on general laminated composite structures. Essentially it is related to structural topology optimization. This problem has been addressed numerous times and several methods have been proposed, also dealing with local optimum issue, see ref. [15], [19] and [28]. The problem considered does not deal with a structure with complicated geometry and therefore a simple algorithm built for this purpose is satisfactory. Since this method was used only for comparison, the time of its convergence is not of high priority. The structure tailored for this approach is presented in Appendix Summary This section presented the process of preparation of the tool for optimizing material layup in the studied sandwich panel. The loading distribution and boundary conditions have been established for the plate subjected to optimization, the explicit formulae for the plate behaviour have been derived and the searching engine choice for the algorithm has been studied. This leaves the way for the optimization process itself. It is now possible to run the analysis and then apply the obtained material layup to the FE-model of the entire blade and to study the response of the panel.

59 51 CHAPTER 6 6 Optimization of material layup in the trailing edge panel The deliberations presented in Section 4 showed that the localized out of plane deformation occurring in the trailing edge panel on the pressure side is structurally significant. Therefore, in Section 5, a tool has been prepared to minimize this phenomenon in a new design of the blade panel. In the following, the results of the plate optimization are implemented in the FE-model of the entire blade and analysed by a non-linear FE-solver. The results for several suggested layups are studied. Moreover, a parameter study is performed for the core thickness. 6.1 Results of the algorithm for the plate optimization The optimization algorithm has been created as described in Section 5. The Matlab code for the algorithm is given in Appendix The function performs search of the optimal material layup for the input given (material data, loading distribution and the initial stacking sequence). It also searches through solutions for different layers number and stacking sequence in the faces. Moreover, it creates a small finite element model of the plate used in the calculation process and presents initial and optimal deformation of the plate for the applied load distribution and boundary conditions.

60 y [nr of elements] 52 Figure 48 shows initial deformation of the plate model. The coordinate system used in Matlab is corresponding to the one used in the derivations and is aligned with the local coordinate system introduced for the panel in the FE-model as presented in Section 5.2. x [nr of elements] x [nr of elements] y [nr of elements] Figure 48. Initial deformation of the loaded plate presented by Matlab. The vertical axis corresponds to the blades longitudinal direction, whereas the horizontal one represents the edge at 3m and 5m respectively. Several subsequent runs of layup optimization are performed. First, only the triax layers originally used in the model are optimized. In the next stage, the triax layers are disintegrated into three sub layers treated as separate plies. Since the algorithm forces the all fibre layers to be placed in unidirectional manner, a third approach is used. Thick UD layers are introduced and investigated. The material change is applied in the pressure side trailing edge panel from 3 to 5m. Results from the optimization algorithm runs are presented in Table 5 in page 53 and Table 6 in page 57. The results for the study of the trailing edge panel are presented in the following sections. 6.2 Behaviour of the region with rearranged material layup. The material layup obtained from the optimization tool is implemented in the FE-model of the entire blade. Then loads are applied to the model and nonlinear analysis is performed. This procedure is repeated for each of the layups suggested by the algorithm. First, only the layers originally used in the model are considered. The stacking sequence of laminas is the only parameter changed. Since it is assumed that trailing edge panels transfer mainly the shear in edgewise loading, the sandwich face is originally composed of triax layers with additional uni-directional layer on the inner face. The triax fabric is composed of three thin layers oriented in ±45 /0. This is the starting point for the optimization process. Figure 49 presents schematically the change of ply orientation proposed by the algorithm. The fibres are rotated exactly by 90. This suggests significant change in the panel s response. The material layup in this panel for both the original and improved case is presented in Appendix 12.5.

61 53 Figure 49. Scheme presenting change in fibre orientation in the sandwich panel. Selected results from the first set of optimization runs and their implementation in the FEmodel are given in Table 5. Added layers Deflection (Matlab) Improvement Local displacement (FEM) INITIAL 12.1mm 17.5mm Improvement in local displ. (FEM) Optimized 8.45mm 30% 9.5mm 46% Added ~50% of the material in faces Nearly doubled material in the faces 6.23mm 49% 7mm 60% 4.83mm 60% 5mm 71% Table 5. Selected results from optimization runs and new layups implementation in FEM. In this version, the algorithm does not consider the unidirectional ply present in the inner face. This layer is however rotated in the improved layup in the FE-model (results given in columns to the right). This is the main cause for the difference between the ratio of improvement for Matlab simulation and FEM. More detailed results are presented in Appendix Improvement obtained only by rearranging the ply orientation In the following, results from the improved material only by means of rearranging the angles of orientation of the original triax layers are discussed. Figure 50 presents the out of plane displacement in the considered region. For comparison with the reference, original results see Figure 37. The studied local deformation is still visible, but its amplitude is significantly decreased. Additional deformation is noticeable to the left, i.e. farther than 5m from the root, where the material has not been improved. If the behaviour in this region was to be addressed, the loading and boundary conditions would need to be re-established. This is, however, not of concern in this thesis. Thus, only the region 3 to 5m is considered and the behaviour beyond its range is not of interest. However, it can be noticed that the deformation s shape corresponds to early stages of development of the original panel deformation presented in Figure 38, Section 4.2.

62 displacement [mm] 54 Figure 50. Out of plane displacement, in local coordinate system, for the studied panel with improved layup. The local deformation is still visible, but it has significantly decreased amplitude. Additional deformation is forming beyond 5m from the root, where the material was not improved. This is, however, not of concern in this thesis. The local deflection of the panel is studied as described in Section 3.1. Figure 51 presents the decrease in local deformation amplitude achieved by rearranging plies alone, without adding material m introduced material change Comparison of the local deformation at the point of highest amplitude 0% 20% 40% 60% 80% 100% load [% of the ultimate load] ORIGINAL rearranged triax glass layup triax Figure 51. Change in local deformation obtained by rearranging plies without adding any laminas. The local deflection is reduced by 46%, i.e. from 17.5mm to 9.5mm. The strains are not improved significantly for this layup and therefore, the efforts towards a better solution are continued. Nonetheless, the local deflection is improved by 46%, from originally 17.5mm to 9.5mm, only by changing the stacking sequence of the plies. Such result shows great potential of further improvement. Improvement obtained with laminas added in the faces In order to further improve the panel s performance, the behaviour of the sandwich panel with additional layers in the faces is studied. Selected data for the improved layups implementation in FEM are given in Table 5 in page 53. It can be noticed that adding material gives less improvement than the change of the ply orientation. The rearranging alone decreases the deformation more than almost doubling the amount of material in the faces. In the latter case, i.e. 2 layers added in each sandwich face, the thickness of the faces is increased by 71%. The out of plane displacement for this layup is presented below. The further improvement brought by adding material is not as

63 displacement [mm] 55 dramatic as in case of rearrangement of the ply orientation only. The deformation beyond 5m is now more pronounced due to significant improvement in the studied region. Figure 52. Out of plane displacement for optimized layup with 2 layers added in each face given in local coordinate system. The deformation beyond the improved region is more pronounced. Figure 53 presents comparison of the improved layups performance in terms of local out of plane deformation of the panel. The local deformation is decreased by 46% only by rearranging the plies. Adding a layer to each side, and therefore increasing the overall thickness of sandwich plates by 38%, decreased the local deformation by 27% with respect to the optimal layup and by 60% with respect to the original one. Adding yet another layer to each of the faces and thus increasing the original faces thickness by 77%, brought additional improvement of 26% and decreasing deformation by 71% with respect to the original one m introduced material change Comparison of the local deformation for several sandwich panel layups ORIGINAL glass triax added 1 layer to each face added 2layers to each face 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Figure 53. Comparison of local deflection of pressure side trailing edge panel at highest amplitude for optimized layups. The improvement is even 71% for 2 layers added at each faces, i.e. nearly doubling the thickness of faces. These data imply that adding material gives less improvement when more material is already present in the panel faces. Since adding material increases the blade s weight and thus loads on the rotor, the design needs to be a trade-off between improving performance and weight reduction. In the light of above results, a conclusion can be drawn that increasing the weight is not an efficient way of improving the panel s behaviour. In general, during the process of blade design, it should be decided when adding material gives less benefit than brings cost (in terms of material cost as well as load increase).

64 56 Strain analysis The strain behaviour is studied in order to investigate nature of the deformation for the improved material layup. It confirms that not only is the local deformation s amplitude decreased dramatically, but also the nonlinear characteristic of the bending is linearized. The results are presented in Appendix As it is demonstrated above, the local out of plane behaviour of trailing edge panel was improved significantly by rearranging the stacking sequence of plies in sandwich faces. These deliberations were performed for material currently used in manufacturing. It gives a great potential in performance improvement without additional costs. In the following section, improvement possibilities will be explored for different types of layers used in sandwich faces. 6.3 Improvements based on a free layup In the following, the triax layers used in the previous section are disintegrated into three sublayers treated as Uni-Directional fibre plies. First, the material layup is designed to imitate the original layup by means of these thin UD sublayers. Mechanical properties of these sublayers are not proven to be realistic. They are estimated so as to obtain behaviour similar to the original layup. The free layup means that no boundary is imposed in form of a ready triax fabric used in the original material. Utilization of triax layers imposes fixed relative orientation of the sublayers and therefore prevents numerous stacking sequence combinations. Flapwise deformation in root region for the free material layup designed to imitate the original layup is presented in Figure 54. This figure is comparable with the original model behaviour presented in Figure 36, Section 4.1. Figure 54. Fringe of flapwise displacement in the root region for trailing edge panel material layup designed to imitate the original layup by means of Uni-Directional sublayers. The maximal global flapwise displacement in the redesigned panel is 12.7mm and differs by less than 4% from the original one. The local deformation obtained is 17.1mm, which is by 2.3% lower than the original one.

65 57 Such redesigned layup is now subjected to the optimization. Selected results of this study are presented in Table 6. It can be noticed that the outcome is even better when a possibility of total rearrangement of the sandwich faces is allowed. Not only the algorithm results show more improvement, but also their implementation reveals higher local deformation decrease. Layup Matlab Improvement achieved FEM - LOCAL Initial mm FEM % improv. Initial redesigned mm Optimized % 6.6mm 68% Optimized layup with a thick UD layer added to the outer face Optimized layup with added thick UD and 1 layer to each face Optimized layup with added thick UD and 2 layers to each face % 5mm 71% % 4mm 76% % 3mm 82% Table 6. Comparison of FEM results of local out of plane deformation of the panel for total rearrangement of the layup. Selected results from optimization runs are also presented. Three sublayers are equivalent to one triax layer in the previous section considerations. In the table above, it can be noticed that the ratio of improvement in FEM is slightly higher than the one in Matlab simulation. This can be caused by the approximated loading boundary conditions for the plate optimization, described in Section 5.2. The data from Table 6 may be compared to those given in the previous section, where only the plies used in original layup were rearranged. In the previous case adding two layers to each face decreased the local deformation by 71%. Now, such improvement is obtained with adding one material layer only. This means achieving similar improvement while adding 4 times less material. The obtained difference in response is the result of allowing unidirectional orientation of all the fibres. The obtained UD layup could seem to be inadequate for complex loading conditions as the ones applied in a wind turbine blade trailing edge panel. This could be explained with the fact that most of the load, both bending and shear, is carried by the primary structure, as well as the suction side panel, which is twice thicker than the pressure side panel. Moreover, it is important to stress that the loading conditions used in the utilized optimization algorithm were approximated. The algorithm did not consider shear forces sensu stricto but involved a shear-like force representation, what could lead to some uncertainty. Nonetheless, the implementation of the plate optimization results in the FEmodel confirms the improvement obtained with such layup. Figure 55 presents the out of plane displacement for the optimized free material layup implemented in the pressure side trailing edge panel. The deformation shape and values attained are comparable to the results with triax layers optimized with one layer of glass fibre lamina added at each face. This means that even more improvement than for the triax layup is observed for the UD solution.

66 displacement [mm] 58 An additional deformation visible to the left is most probably caused by the sudden change in material thickness and stiffness occurring at 5m section. This will be addressed further. 5m introduced material change Figure 55. Out of plane displacement for optimized free material layup applied in the pressure side trailing edge panel. The deformation amplitude, measured in local coordinate system, is significantly decreased. The decrease of local deformation achieved is presented in Figure 56. The improvement obtained is 68%, decreasing the deformation from 17.5mm to 5.6mm. The results for layups with additional material implemented are given further Comparison of local deflection of pressure side trailing edge panels' highest amplitude, improvement achieved only by stacking sequence rearrangement 0% 20% 40% 60% 80% 100% load [% of the ultimate load] ORIGINAL glass UD Figure 56. Comparison of local deflection of the pressure side trailing edge panel at highest amplitude for the layup with rearranged stacking sequence and the original one. The improvement is 68%, decreasing the deformation from 17.5mm to 5.6mm. Figure 57 shows the out of plane displacement for improved free material layup with one additional layer of thick UD fibres at the inner face. As it was predicted, the displacement is further decreased. The deformation shape and values attained are comparable to the results with triax layers optimized with approximately 70% material added in the faces.

67 displacement [mm] 59 5m introduced material change Figure 57. Fringe of out of plane displacement in the considered plate region for optimized free material layup with one additional layer of thick UD fibres at the inner side. The displacement is measured in local coordinate system. The improvement process is continued as the algorithm allows increase of number of layers. At some point the increase of the panel thickness is not reasonable since, as one of the priorities, the weight of the panel should be minimized. Even though the objective function of the optimization algorithm does not include the thickness of the panel, it is the engineer s task to set a realistic boundary on amount of material added to the sandwich faces. In Figure 58, the performance comparison is given for several improved layups studied. The local out of plane displacement of the trailing edge panel at highest amplitude is plotted. The deformation amplitude is decreased 5 times by achieving 3mm of the local deformation for the layup with exactly doubled thickness of the sandwich faces. Nonetheless, 68% improvement without adding any weight to the panel is a great step towards solution of the fatigue problem addressed in the thesis Comparison of local deformation development for several sandwich panel layups ORIGINAL glass triax glass UD % 20% 40% 60% 80% 100% load [% of the ultimate load] glass with added thick UD and 3triaxes at each face glass with added thick UD and 6 triaxes at each face Figure 58. Comparison of local displacement of the pressure side trailing edge panel at the highest amplitude of deformation for several layups. The highest improvement achieved was 82% for sandwich panel with doubled thickness of the faces. The results discussed above confirm observation from the previous section, that adding material gives less improvement than the rearrangement of ply orientation sequence alone. Therefore, it can be stated that increasing the amount of material in sandwich faces should not be the first solution utilized for preventing deformations.

68 Strain [ S] Strain [ S] deflection [mm] 60 As it was mentioned in the Section 1.2, behaviour of pressure and suction panels is significant in the fatigue problem in the trailing edge adhesive joint. In Figure 59, a comparison of the deformations on both panels is given for the initial and optimal pressure side panel layup. Even though the suction side panel is not improved, its local deformation decreased as well. It is probably a result of change in pressure side properties and transferring more loads on this improved panel. The initial relative panels deformation in this section is 22mm and for the optimized layup of the pressure side panel, it drops to 8mm, and thus is decreased by 63%. If the optimization algorithm is applied to the suction side as well, the overall deformation of this section could be diminished even more dramatically. This is however, not within the scope of this thesis Local displacement of suction and pressure side trailing edge panels at the highest deformation amplitude original - pressure side original - suction side optimized - pressure side optimized - suction side 0% 20% 40% 60% 80% 100% load [% of ultimate load] Figure 59. Comparison of the out of plane deformation of suction and pressure side panel for original model and the model with improved pressure side. Analogically to the previous section, the analysis of strains was performed to investigate the nature of the deformation for the optimized material layup. Figure 60 and Figure 61 present the strain in edgewise and longitudinal direction respectively at the point of maximal deformation amplitude. It compares the original layup material results with those obtained for the improved layup. The strains are decreased, especially for the originally high values in the longitudinal direction. The nonlinearity degree is also considerably lowered, more significantly for the longitudinal direction, for which it is pronounced the most in the original panel Strains in edgewise direction - initial layup layer inner 1layer layer outer layer 6 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Figure 60. Strain in the edgewise direction attained at the point of the deformation s maximal amplitude for the original and the improved layup without adding material Strains in edgewise direction - improved layup layer inner 1layer outer layer 6layer 0% 20% 40% 60% 80% 100% load [% of the ultimate load]

69 Strain [ S] Strain [ S] Strains in longitudinal direction - initial 0% 20% 40% 60% 80% 100% inner layer layer 1 outer layer 6layer load [% of the ultimate load] Figure 61. Strain in the longitudinal direction attained at the point of the deformation s maximal amplitude for the original and the improved layup without adding material. Displacement in the in-plane directions Strains in longitudinal direction direction - improved 0% 20% 40% 60% 80% 100% The former discussion demonstrated improvement of the local behaviour of the considered trailing edge panel brought by change in the sandwich layup. This gives optimistic prospects for the blade design. Nonetheless, it is relevant to remember that the improvement of panel deformation in one direction cannot worsen its behaviour in the remaining ones. Figure 62 presents the displacement in in-plane directions for the initial layup in the trailing panel inner layer 1layer outer layer 6layer load [% of the ultimate load] Fig. 62a Fig. 62b Figure 62. Displacement in local longitudinal (Fig. a) and transverse direction (Fig. b) in the plate considered in optimization - original layup. In Figure 63, the same results are shown for the optimized plate with no material added. It can be noticed that the displacement progresses in nearly identical manner. Also the values attained differ in a very narrow margin. For both directions, the displacement increase in the improved layup is within 5% with respect to the original one. Fig. 63a Fig. 63b Figure 63. Displacement in local longitudinal (Fig. a) and transverse direction (Fig. b) in the plate considered in optimization - improved layup. The above results confirm that the investigated improvement in material layup does not have any negative influence on the global behaviour of the panel.

70 62 Core thickness study The studied out of plane deformation occurring in 4-5m region on the pressure side panel may be caused by a sudden change in the core thickness occurring at 5m. In the region studied in the project, i.e. between 3 and 5m, the core thickness is 15mm, whereas beyond 5m section it is 25mm. In order to show the influence of that thickness drop and, possibly, to improve the trailing edge panel out of plane behaviour even further, the core thickness of the studied panel is increased to 25mm. Figure 64 presents the out of plane displacement for improved free material layup with 25mm thick core. As it was expected, the displacement amplitude dropped significantly. The local behaviour beyond 5m is probably caused by the remaining change in the material properties. Beyond the studied region, the material is not improved by orientation rearrangement and therefore, it does not handle the loading as well as the presented area. However, the change in behaviour occurring at 5m is now less pronounced than before. The local behaviour is significantly decreased and the displacement profile is smoother. 5m introduced material change Figure 64. Out of plane displacement in the trailing edge panel for optimized free material layup with one additional layer at the inner side and 25mm thick core. The local character of deformation is significantly decreased and the panel s profile is visibly smoother. 6.4 Summary This section gave an overview of results obtained in the sandwich panel material optimization process. The simulation results were implemented in FE-model of the entire blade. Results for several suggested layups were presented. Changing the orientation of the layers in the current design brought 46% decrease of the addressed deformation. A complete reorganization of the layup (without adding weight to the panel) brought an improvement of even 68%. Adding material to the optimized panel further decreased the local deformation. However, the additional layers gave relatively less improvement than the change of fibre orientation alone. Therefore, it can be concluded that increasing the amount of relatively expensive material in sandwich faces should not be considered as quick and dirty solution for preventing the panels deformations.

71 63 CHAPTER 7 7 Study of the flapwise and combined loading The discussion in the previous section demonstrated a promising improvement in the local behaviour of considered trailing panel in the edgewise loading. In the following, the improved panel is investigated in different load cases in order to check its reliability under realistic loading. The loading directions considered in this section are flapwise, Pressure Towards Suction side, and combined load case. 7.1 Motivation The goal of this thesis is to improve the local behaviour of trailing edge panel. In the root region, a significant deformation has been observed in edgewise, Leading Towards Trailing edge loading conditions. In the preceding section, this load case has been investigated demonstrating a promising improvement in the local behaviour of the trailing edge panel. Nonetheless, the operational loading conditions are not static but are alternating with the rotation of the blade. Thus, it is important to remember that the decrease of panel deformation in one load case cannot be accepted if it is to worsen the panels behaviour in realistic loading conditions. Therefore, the result is analysed under different load cases in order to check the panel s reliability. An overview of FE-results for optimized panels in the flapwise and combined loading are presented in Section 7.2 and 7.3 respectively. The results for the improved material by means of the ply orientation rearrangement alone are presented.

72 64 Flapwise load case Certification tests for wind turbine blades investigate edgewise, LTT, load application direction and flapwise direction, PTS. The project until now focused on the first one, for which the deformation developed and was minimized. If the change in the trailing edge panel s layup is to be accepted, it needs to meet expectations for the later one as well. The PTS loading is presented in Figure 65. More details regarding loading conditions and application are presented in Section 3.1. Figure 65. Loads in Pressure Towards Suction side loading direction (PTS) applied to the FE-model. The forces are presented at one of the sections of application. Combined load case In order to strive for realistically meaningful solutions, not only the certification loading directions are studied, but also combined loading is considered. Design criteria for wind turbine blades based on new design approach are currently under development at Risø DTU. Several ongoing projects are dealing with reliable design criteria considering the realistic failure modes that appear during wind turbine blade operation. The Risø DTU scientists believe that the certification process is based on simplified assumptions as is does not include fully realistic (operational) loading conditions. Only flapwise and edgewise loading directions are considered (ref. [10] giving further reference to DNV-OS-J102). In reality however, combined gravity and aerodynamic forces result in a load component different from the loads traditionally applied in the full-scale tests, see Figure 66. Moreover, the method for load application in these tests prevents important failure modes, which in real life do occur. For more detailed information on new failure mechanisms observed in wind turbine blades please visit [10]. Combined load case was prepared at Risø on basis of evaluated influence of aerodynamic forces and gravity in operation conditions. The forces applied in the model were described in details in Section 3.1. The gravity is considered to be acting in LTT direction although in operational conditions it is changing with the rotation of the blade.

73 65 Fig. 66a Fig. 66b Fig. 66c Figure 66. Fig. a and b: Combined gravity and aerodynamic forces result in a load component different from the traditional flap- and edgewise loads. After Jensen [10]. Fig. c: Loads in combined load case applied to the finite element model section. 7.2 Flapwise load case The following gives an overview of FE-results for the pressure side trailing edge panel in the root region under flapwise loading. It presents a comparison between the original model and a model with changes applied to the material in the panel. The results below show the magnitude of global displacement for original (Figure 67a) and improved (Figure 67b) layup in the considered panel. The results in the two cases are very similar. The values of displacement obtained differ by less than 1% and general trend is very similar. Although some minor differences in the displacement behaviour are visible, it can be considered corresponding. Fig. 67a Fig. 67b Figure 67. Comparison of results of total displacement for original (Fig. a) and improved (Fig. b) layup in pressure side trailing edge panel in the root region for PTS loading.

74 66 The following figures present the comparison of the displacement results in edgewise (Figure 68), flapwise (Figure 69) and longitudinal (Figure 70) directions. It can be shortly concluded that the influence of the material change in the flapwise loading can be neglected. No unwanted local behaviour resulting from the sandwich faces laminas rearrangement is observed. Fig. 68a Fig. 68b Figure 68. Comparison of edgewise direction displacement for original (Fig. a) and improved (Fig. b) layup in pressure side trailing edge panel in the root region for PTS load. Fig. 69a Fig. 69b Figure 69. Comparison of flapwise direction displacement for original (Fig. a) and improved (Fig. b) layup in the panel for PTS load. Fig. 70a Fig. 70b Figure 70. Comparison of longitudinal direction displacement for original (Fig. a) and improved (Fig. b) layup in pressure side trailing edge panel for PTS load. Local deformations or strain analysis is omitted due to great similarities in global behaviour of the original and improved panel. The analysis of flapwise loading is not within the scope of the thesis and thus more focus will not be put on this. The above deliberations present the influence of the sandwich faces rearrangement on the flapwise loading response. Also the changes in behaviour for the optimized layups with material added at sandwich faces were shortly studied. The results were satisfactory and are omitted here.

75 Combined loading In the following, the results of FEA of the blade model under combined loading are presented. Here, analogically to the previous section, the original model is compared to the model with rearranged plies in the sandwich faces without material added. In Figure 71, the total displacement for combined load is presented. For better visualization, the results can be observed on the region of the panel considered in the optimization. After implementing the material rearrangement suggested by the optimization algorithm, the results remain satisfactory. In fact, slight local behaviour is prevented in the improved layup. However, the values of displacement obtained differ by less than 1% so the change may not be considered significant. Fig. 71a Fig. 71b Figure 71. Comparison of results of total displacement for original (Fig. a) and improved (Fig. b) layup in pressure side trailing edge panel for the combined load. The following figures present the comparison of the displacement in edgewise (Figure 72), flapwise (Figure 73) and longitudinal (Figure 74) directions. Again, the results confirm that the material change slightly improved the panel s behaviour in the combined loading. Fig. 72a Fig. 72b Figure 72. Comparison of results of edgewise direction displacement for original (Fig. a) and improved (Fig. b) layup in the trailing edge panel for the combined load. Some improvement can be noticed in Figure 72 and Figure 73, presenting edgewise and flapwise displacement comparison. In these directions, the distribution of displacement is less localized for the model with introduced material change. Nonetheless, the differences in displacement values remain within a few percent for all the directions.

76 68 Fig. 73a Fig. 73b Figure 73. Comparison of results of flapwise displacement for original (Fig. a) and improved (Fig. b) layup in pressure side trailing edge panel in the root region for combined load. In the longitudinal direction, virtually no differences between the two panels are visible, see Figure 74. The values as well as displacement distribution remain virtually identical after applying the change in ply orientation. Fig. 74a Fig. 74b Figure 74. Comparison of results of longitudinal direction displacement for original (Fig. a) and improved (Fig. b) layup in the trailing panel in the root region for combined load. Local deformations and strain analysis are not studied due to great similarities in global behaviour between the panels with original and rearranged material. 7.4 Summary It is important that the improvement of the addressed panel behaviour, obtained in the former section, does not decrease the panels reliability in realistic loading conditions. This section presented considerations for the panel with changed material layup tested in flapwise and combined loading. It is concluded that the displacement behaviour in these loading conditions is not influenced by implementing change in material layup in the pressure side trailing edge panel. Therefore, it can be reasoned that the change in the plies orientation in sandwich panel suggested by the optimization algorithm indeed has improved the panel s local behaviour.

77 69 CHAPTER 8 8 Utilization of new materials The investigations presented in former sections demonstrated a significant decrease in the local deformation of the considered trailing edge panel. Therefore, in the following, the efforts for improvement are continued with introducing new materials. Recently, a trend in the blade design criteria was born that appreciates the influence of the rotor loads on the remaining components of the wind turbine. Such approach promotes light design solutions and decreases the importance of the costs. This study follows the tendency and thus, new materials are included in the considerations. The panel s response obtained with utilization of different materials, like bamboo and carbon, is presented in this section. Further improvement of the trailing edge panel s response is expected. Moreover, substitution of the sandwich panel with a laminate is studied. 8.1 Composite laminate Avoiding sandwich structure is beneficial from wind turbine blade manufacturers point of view. Not only is sandwich more expensive and complex to produce than the laminates, but also it causes additional failure possibilities due to the adhesive connection between faces and core, prone to e.g. wrinkling, delamination etc. Therefore, it could be advantageous to substitute the sandwich panel with laminate. In the following, an analysis of the laminate panel s behaviour instead of sandwich is performed. This study aims to investigate if eliminating the core changes the deformation significantly in the trailing edge panel. Keeping in mind the low weight strategy, it is also studied how

78 70 much more glass fibre is needed in laminated plate in order to prevent the local panel deformations. The study of the panel made of composite laminate revealed the limitations of the optimization algorithm utilized. The objective of this algorithm is to minimize the amplitude of the deformation. Therefore, the proposed layup strives to decrease the local deformation occurring, it does not however eliminate its buckling behaviour. It is observed that the trailing edge panels obviously buckle when constructed with laminate plate. Figure 75 presents results for the plate with the same amount of material as there is in the original sandwich faces. Figure 75. Displacement in flapwise direction in the plate with optimized layup without core. When a laminate plate is used, buckling is clearly visible. In order to find the amount of material needed to satisfy the performance expectations without core, a short parameter study is conducted. In Figure 76 the displacement in out of plane direction is presented for the plate with optimized layup with almost twice as much glass fibre laminas as in the original sandwich. It shows that adding significant amount of material does not compensate for the lack of core. This could have been expected, since due decreased panel thickness, the moment of inertia and thus flexural rigidity is also decreased. Figure 76. Displacement in out of plane direction (local coordinate system) in the plate with doubled laminate layers without core (now there are 10layers). Still, buckling occurs. Since the above result is not satisfactory, more layers of the laminate are added.

79 71 Figure 77 presents results for a plate with three times more glass fibre laminae than originally. Here, the out of plane behaviour is similar to the one observed in early stage of the deformation development in the original layup. However, the deformation is more localised and has higher amplitude. Figure 77. Out of plane displacement in the plate with 15 layers laminate with optimized layup without core. Just now the obvious buckling behaviour has been prevented. The deformation however is not improved in comparison to the original. Even though the behaviour has been improved with respect to the thin laminate, it is still worse than in the original model. Moreover, this laminate plate is approximately 75% as thick as the original sandwich and its unit mass 2.5 times higher. Therefore, such design is not acceptable in the blade s secondary structure. Thus, other materials have been utilized in order to strive for decrease of the panel s weight. Apparently, there is still work to be done regarding utilization of laminates instead of sandwich plates in wind turbine blades. 8.2 Carbon fibre Recently, carbon fibre is being considered in wind turbine blade design. Despite the high cost it is used in the modern designs due to its outstanding properties as described in Section 2.4. The following section presents the study of the sandwich trailing edge panel with carbon fibre face layers instead of glass fibre ones. Due to its superior properties, carbon is expected to give better results even with thinner sandwich faces. First, a design with carbon fibre substituting the glass fibre without changing the thickness of the panel is studied. For such layup the decrease in out of plane deformation is 86%, which is impressive even considering high expectations with regards to carbon s performance. In this design the weight is decreased due to lower density of carbon with respect to glass. However, the cost, which is an important issue as well, increases significantly. There are no explicit data for the influence of mass of the blade on the entire wind turbine, but there are figures available on the cost relation of different materials. As presented in Section 2.4,

80 72 carbon fibre used in wind turbine blades is, on average, 5-10 times more expensive than glass fibre. Therefore, it is important to reduce the amount of material in carbon dominated design not only in order to reduce the loads on the hub but also to avoid increasing the cost of the blade. In order to meet these expectations, a panel with only 1mm carbon layer at each sandwich face is analysed. It decreases the local deformation by 83% with respect to the original layup. However, to further improve the panel s response while keeping its low weight, the core thickness has been increased. The result of this attempt, presented in plot in Figure 78, was superb. The local deformation s amplitude decreased by 89% with respect to the original and by 66% with respect to the optimized glass fibre-based layup. The localised behaviour of out of plane displacement in this region is nearly insignificant. 5m Figure 78. Displacement in out of plane direction in the plate with thin carbon faces and increased core thickness. This panel s unit weight is less than half of the original sandwich weight. The deformation has been improved by 89% with regards to the original. Results for sandwich with carbon faces, summed up in Figure 79, show a significant improvement despite very low amount of material in the faces. What is interesting, the deformation is smaller for a design with twice less carbon in the faces if the core is thicker by 1/3.

81 Strain [ S] Strain [ S] displacement [mm] Comparison of local deformation development for several sandwich panel layups with carbon and glass ORIGINAL 0% 20% 40% 60% 80% 100% load [% of the ultimate load] glass - triax glass - UD thin carbon faces thick carbon faces thin carbon faces with thicker core Figure 79. Comparison of local deflection of pressure side trailing edge panel at highest amplitude for several layups with carbon utilized. The improvement was even 89% by achieving 2mm local deformation for a light sandwich with thick core and thin carbon faces. The improvement with respect to the optimized glass fibre-based layup was 66%. In order to get more thorough information on the obtained improvement, strains have been analysed and compared with the original layup, see Figure 80. The results are presented only for the layup with thin carbon faces and thin core. Even though this is the weakest carbonbased layup, it still improves the strains with respect to the original one. They values of strain in edgewise direction decreased significantly, approximately 8 times. In longitudinal direction, the nonlinearity is nearly eliminated but the values reached are increased by 15%. Nonetheless, the fibres are oriented in this direction and therefore can withstand the obtained strain. Even though the strain limit for carbon fibre is lower than for glass fibre, it is well below the safety limit. 300 Strains in edgewise direction - optimized layup with with the use of carbon Strains in longitudinal direction - optimized layup with with the use of carbon 0% 20% 40% 60% 80% 100% layer inner 1layer layer outer 3layer layer inner 1layer layer 3 outer layer % 20% 40% 60% 80% 100% load [% of the ultimate load] Fig. 80a Fig. 80b Figure 80. Strain in edgewise (left) and longitudinal (right) direction at the point of maximal displacement amplitude for the layup utilizing carbon fibre laminate in sandwich faces. Figure 81 presents the strains without the membrane average compared to the same results obtained in the original. Not only are the strains several times lower for the carbon-based layup, but the nonlinear character of bending is significantly diminished load [% of the ultimate load]

82 Strain [ S] Strain [ S] Strains in edgewise direction without the membrane strain 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Fig. 81a Fig. 81b Figure 81. Comparison of the strains after the membrane strain was taken away. The figures compare results for original layup and the one with minimized amount of carbon as face laminate in the sandwich panel. Fig. a: strains in the edgewise direction. Fig. b: strains in the longitudinal direction Table 7 presents the summary of performance for several sandwich layups. Material layup Original inner layer- original layup outer layer - original layup inner layer- optimized layup with carbon faces outer layer - optimized layup with carbon faces Local deformation amplitude 17.5mm % of improvement Glass optimized (triax) 9.5mm 46% Glass UD 6mm 66% Thin carbon faces 3mm 83% Thin carbon faces with thicker core 2mm 89% Carbon in thick faces 2.5mm 86% Table 7. Comparison of local deflection of the panel for the chosen layups. The above results confirm a huge improvement brought by carbon utilization the panels faces. Such improvement together with the lower weight of the panel contributes to very promising solution. Nonetheless, the cost of the studied panel is considerably increased. Even the layup with the lowest amount of carbon would be approximately 2.5 times more expensive than the original sandwich. Thus, since the trailing edge panel is a part of secondary structure of the wind turbine blade, this design is not recommended. However, it could be beneficial to study its implementation in the load carrying part of the blade structure Strains in longitudinal direction without the membrane strain inner layer - original layup outer layer - original layup 0 inner layer optimized layup with carbon faces outer layer optimized layup wih carbon faces 0% 20% 40% 60% 80% 100% load [% of the ultimate load]

83 Bamboo Bamboo has many attributes that make it attractive for utilization in wind turbine blades. As it is described in Section 2.4, bamboo is advantageous mostly due to its low unit weight and relatively good mechanical properties. Therefore it is implemented in the panel considered in the optimization process. The first bamboo-based layup studied is a sandwich with the faces made of combined glass fibre and bamboo-poplar laminas. The local displacement is significantly increased and becomes strongly nonlinear, see Figure 83. Next, the analysed layup is composed entirely of bamboo-poplar laminas. The response of such panel is not satisfactory either. The out of plane deformation has similar amplitude as for the original design (decreased by 2%), see Figure 82. However, the deformation is strongly localized and therefore unwelcome. Figure 82. The out of plane displacement of a bamboo-made trailing edge panel. The out of plane deformation, measured in local coordinate system, is even more severe than originally. Another bamboo-based material considered is a sandwich with bamboo-faces. The panel is designed so that the unit weight does not exceed the original one. Moreover, the cost of such panel is lower than for the one with glass fibre faces, as described in Section 2.4. In this layup the deformation amplitude is decreased significantly with respect to the original one, see Figure 83. In fact, the result is even slightly better than for the optimized glass fibre layup. However, the nonlinear characteristic of the local displacement is much more pronounced in bamboo layup than in the one with glass fibre faces.

84 Strain [ S] Strain [ S] displacement [mm] Comparison of local deformation development for several sandwich panel layups with utilization of glass and bamboo 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Figure 83. Comparison of local out of plane displacement studied for several layups. The improvement achieved for a sandwich with bamboo-faces with the same weight as the original glass layup is 77% with amplitude of 4mm. The strains for sandwich with bamboo faces are studied. The global strain is significantly decreased for both directions (3 times in edgewise and by 30% in longitudinal direction). Moreover the strain nonlinearity is visibly diminished, see Figure Strains in the edgewise direction - optimized layup with with bamboo faces 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Fig. 84a inner layer layer 1 outer layer layer 5 Fig. 84b bamboo + glass ORIGINAL bamboo laminate glass - triax glass - UD bamboo faces Figure 84. Strain in edgewise (Fig. a) and longitudinal (Fig. b) direction for the sandwich with bamboo faces. The amplitudes decreased and the nonlinearity was visibly diminished Strains in longitudinal direction - optimized layup with with bamboo faces 0% 20% 40% 60% 80% 100% load [% of the ultimate load] inner layer layer 1 outer layer layer 5 The strains showing bending contribution, are presented in Figure 85. Again, the values decreased dramatically (4 times) with respect to the original panel. What is more important for these results, the nonlinearity is virtually eliminated.

85 Strain [ S] Strain [ S] Comparison of the strains in edgewise direction after taking away membrane strain inner layer- original layup outer layer - original layup inner layer- optimized layup with bamboo outer layer - optimized layup 0% 20% with bamboo 40% 60% 80% 100% load [% of the ultimate load] Fig. 85a Fig. 85b Figure 85. Comparison of the strains without the membrane average for the original layup and the layup with bamboo faces. Fig. a: edgewise direction. Fig. b: longitudinal direction Comparison of the strains in longitudinal direction after taking away membrane strain inner layer - original layup 500 outer layer - original layup 0 inner layer optimized layup with bamboo outer layer optimized layup wih bamboo 0% 20% 40% 60% 80% 100% load [% of the ultimate load] The strain results confirmed considerable improvement of the bamboo sandwich panel s performance with respect to the original one. Such response together with the preserved weight of the panel and decreased cost with respect to the original design contributes to a very promising solution. Nonetheless, it is still uncertain to recommend bamboo utilization since the data for its characteristics, both mechanical and economical, are not confirmed yet. Research is underway to further develop and characterize bamboo-based composites, laminates with multi-directional bamboo reinforcement and also hybrid bamboo laminates reinforced with carbon-fibres. The results of the above study confirm this material s potential to augment the performance of future wind turbine blade designs. 8.4 Summary In this section, advanced material solutions utilized in the considered trailing edge panel were studied. As expected, further improvement of the trailing edge panel s response was obtained. The results for the sandwich panel with carbon faces showed a superior improvement despite very low amount of material in the faces. Among the presented solutions, the deformation was decreased the most for a design with very thin carbon faces and a relatively thick core. Such design could be very promising especially considering the low weight of the panel. However, due to the high cost it is not recommended for the blade s secondary structure. Nonetheless, the findings reveal great potential in weight saving with stiffness preservation, which could be utilized in the primary structure of the blade. Also the analysis of the bamboo-based panel confirmed numerous benefits of application of this new material in wind turbine blades. The significant improvement obtained and the low weight of the panel contribute to a very attractive design. According to the results presented in this section, the new bamboo-based materials can be a groundbreaking solution for future wind turbine blades.

86 78

87 79 CHAPTER 9 9 Conclusions In the design and development of future wind turbine blades, there are several goals that the designers will try to meet. Among these goals, the weight is to be decreased, materials and manufacturing process are to be optimized, aerodynamic efficiency is to be increased etc. The aim of this thesis was to study different solutions for layup of the materials used in wind turbine blade trailing edge panels. In the current design, the out of plane deformations of these panels cause peeling stresses in the adhesive joints. The goal was to minimize the out of plane deformations of the trailing edge panels since that would directly reduce the peeling stresses. An optimization tool was created to demonstrate the potential improvement, which could be brought to the structural design without increasing the costs. The tool was prepared on basis of an analytical-numerical solution derived for the plate problem in the established loading and boundary conditions. The numerical study confirmed a significant improvement in the local behaviour of the trailing edge panel obtained by rearranging the original layup of this sandwich panel. A decrease of the addressed deformation by 46% was obtained only by changing the orientation of the layers in the current design. A complete reorganization of the layup (without adding weight to the panel) brought an improvement of even 68%. After investigating the behaviour of the optimized panel in different realistic load cases, it was reasoned that the change in the ply orientation obtained via the optimization algorithm indeed improved the local behaviour of the studied trailing edge panel.

88 80 Designing a wind turbine blade is a trade-off between improving the performance and reducing the weight. It has been demonstrated that increasing the amount of expensive material in sandwich faces brings relatively less improvement than the virtually cost-free solution of material rearrangement. It has been concluded that adding material should not be implemented as quick and dirty solution for preventing the deformations of the panels. Recently, a new trend in design criteria was born that appreciates the influence of the rotor weight on the remaining components of the wind turbine. Such approach promotes light design solutions and decreases the importance of the costs. Thus, the efforts for improvement were continued with introducing different materials. Results for sandwich panels with carbon faces showed a superior improvement despite the low amount of material used. Among the studied designs, the deformation was decreased the most for a layup with thin carbon faces and a relatively thick core. This solution could be very promising especially regarding its low weight. However, due to the high cost, such a design is not recommended for the trailing edge panels, which belong to the blade s secondary structure. Nonetheless, the findings revealed beneficial weight saving with performance preservation that could be beneficial if employed in the primary structure of the blade. The investigation considering bamboo-based panels revealed advantages brought by the application of this new material in wind turbine blades. The significant improvement obtained for the panel s local behaviour, accompanied by the low weight of the panel and considerable cost savings, contribute to a very attractive design. According to the study results, the new bamboo-based materials have the potential to be a groundbreaking design solution for future wind turbine blades.

89 81 CHAPTER Future work Due to the timeframe of a master thesis, the scope of the investigations was limited. The study brought promising findings and therefore it would be beneficial to continue the work in this area. In the following, the future work milestones are presented in chronological order of the process, starting with the genesis of the optimization tool. The load distribution throughout the blade should be studied in details. This would give more accurate input with regards to the boundary and loading conditions for the panel. The study was carried out for a flat plate alone. No investigation regarding single or double curved shells has been performed. A solution for a single curved shell panel could easily be found by introducing a term of initial curvature into the derivations of the flat plate solution. The following improvements could be introduced to the optimization algorithm. The possibility of choice between materials shall be incorporated within the algorithm. This would introduce additional discreet design variables. Moreover, with evolution of the algorithm, the searching engine could be reconsidered. Although it has been shown that the studied panel was not subjected to buckling, for future applications of the optimization tool, it would be beneficial to incorporate buckling investigation within the algorithm. Also other failure modes (e.g. wrinkling, delamination etc.) should be considered. This is especially important due to promising results obtained for thin carbon faces. Such design is prone to wrinkling and therefore demands a corresponding failure analysis.

90 82 It would be worthwhile to implement an algorithm that considers the out of plane deformations of the panels on the pressure and suction side. Thus, the improvement in the relative response of the panels could be observed. In the long term view different optimization algorithms could be implemented for several critical parts of the blade structure. The results could be extrapolated by an engineer designing the blade structure. Optimizing the entire blade is unrealistic using hand-tailored algorithms, like the one utilized in this thesis. Currently, ever more reliable and capable optimization engines are being implemented in commercial finite element software. Using such software the work could cover optimization of the material in the entire blade structure. Moreover, it would be an interesting to verify the optimization results presented in this thesis experimentally. Doing so was considered in an early stage of the work. However, it was decided against carrying out experiments as implementing additional layers of material was the only practicable modification of the existing blade. Finally, it could be beneficial to design, model, manufacture and test a blade that would e.g. incorporate the improvements in material layup obtained via the optimization tool accompanied by other inventions improving the structural design of the blade. Several solutions for the internal structure have lately been proposed and published by Risø (ref. [10]). Such a venture is however extremely time-consuming and financially challenging. Nonetheless it lies within the philosophy of Risø s ongoing Future Generation Blade project and thus could be beneficial to consider.

91 83 CHAPTER Bibliography [1] Allen, H. G., Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford, 1969 [2] Brøndsted, P., Holmes, J. W., Sørensen, B. F. Wind Rotor Blade Materials Technology European Sustainable Energy Review, Issue 2, 2008 [3] Cuntze, R.G. Lifetime prediction for structural components made from composite materials, NAFEMS World Congress, Crete, Greece 2009 [4] Eckold G. Design and Manufacture of Composite Structures, (1994) [5] Flower, P.C. 120m Future Generation Blade (FGB) Design for Manufacture Feasibility Study. Master thesis. Technical University of Denmark. (2009) [6] Harris B. Engineering composite materials XXX [7] Brøndsted, P., Holmes, J. W., Sørensen, B. F., Zehui Jiang, Zhengjun Sun, Xuhe Chen Evaluation of a Bamboo/Epoxy Composite as a Potential Material for Hybrid Wind Turbine Blades, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Roskilde, Denmark and International Centre for Bamboo and Rattan, Beijing, China 2008 [8] Iyengar, N. G. R., Gupta, S. K., Programming methods in structural design, Kanpur, 1981 [9] Jensen, C. Defects in FRP Panels and their influence on Compressive Strength, Master thesis. Technical University of Denmark, (2006)

92 84 [10] Jensen, F. M. Ultimate strength of a large wind turbine blade, Risø-PhD-34(EN) (Submitted May 2008) [11] Jensen, F. M., Falzon, B.G., Ankersen, J., Stang, H. Structural testing and numerical simulation of a 34m composite wind turbine blade, Composite Structures 76, 2006 [12] Jensen, F.M., Weaver, P.M., Cecchini, L.S., Stang, H., Nielsen, R.F., The Brazier effect in Wind-Turbine Blades and its Influence on Design, November 2008 [13] Jones R.M. Mechanics of composite materials 2 nd edition, 1999 [14] Kallesøe, B. S. Global Blade Deflections Effect on Local Airfoil Deformation and Performance a part of: Research in Aeroelasticity EFP-2007-II, Risø National Laboratory for Sustainable Energy, Roskilde, 2009 [15] Kam, T. Y., Lai, F.M., Chao T. M Optimum design of laminated composite foamfilled sandwich plates subjected to strength constraint, Solids and Structures 36 (1999) [16] Knill, T. J.. The Application of Aeroelastic Analysis Output Load Distributions to Finite Element Models Of Wind Turbine Blades Master thesis. Technical University of Denmark, (July 2004) [17] Libove, C., Batdorf, S. B., A general small-deflection theory for flat sandwich plates, NACA Report 899 (1948) [18] Lopes, J. C. O. Material selection for aeronautical structural application, Ciência & Tecnologia dos Materiais, Vol. 20, 2008 [19] Lund, E., Kühlmeier, L., Stegmann, J. Buckling Optimization of Laminated Hybrid Composite Shell Structures using Discreet Material Optimization, 6 th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, 2005 [20] Madsen, K., Nielsen, H. B. Introduction to Optimization and Data Fitting, DTU informatics IMM, Technical University of Denmark, August 2008 [21] March, H. W., Smith, C. B. Buckling Loads of flat sandwich panels in compression.various types of edge conditions. Mimeo no.1525, Forest Products Lab,1945 [22] Matsunaga, H. Assessment of a global higher-order deformation theory for laminated composite and sandwich plates, Composite Structures V. 56 (2002) [23] Plantema, F. J. Sandwich construction, John Wiley & Sons, New York, 1966 [24] Reddy, J. N Mechanics of laminated composite plates and shells, 2 nd edition (2004) [25] Roczek, A., Sieradzan, T. Structural behaviour of trailing edge panels in a SSP34m wind turbine blade, February 2009 [26] Robinsson, J. R. The buckling and bending of orthotropic sandwich plates with all edges simply supported, Aero. Quart., Vol. 6, No 2, 1955 [27] Skvortsov, V., Bozhevolnaya, E. Deformation and global stability of shallow single-curved sandwich panels Aalborg University, Report no. 71, August 1996 [28] Stegmann, J., Lund, E. Discreet Material Optimization of Laminated Composite Shell Structures using Local Strain Criteria, 6 th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, 2005

93 85 [29] Sørensen B.F., Jørgensen, E., Debel, C. P., Jensen, F. M., Jensen, H. M., Jacobsen, T. K., and Halling, K., 2004, "Improved design of large wind turbine blade of fibre composites based on studies of scale effects (Phase 1). Summary report". Riso-R-1390(EN) [30] Timoshenko S., Woinowsky-Krieger, S., Theory of plates and shells, 2 nd ed. London, 1959 [31] S. Timoshenko and J. Gere. Theory of Elastic Stability. McGraw-Hill Book Company, New York, pp , New York, [32] Thomsen, C.L., Eisenberg, Y. Blade test SSP34#2 Edgewise and Flapwise Final Static test. Risø-I-2083(EN). [33] Zenkert, D., Battley, M. Foundations of Fibre Composites 2 nd edition for Technical University of Denmark, Kgs. Lyngby, Denmark, 2006 [34] Zenkert, D. An introduction to Sandwich Construction London, 1995

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95 87 CHAPTER Appendices 12.1 Definitions, symbols, abbreviations Useful definitions Blade root: Part of the rotor blade that is closest to the hub Box girder: Primary, lengthwise structural member of a wind turbine rotor blade Design loads: Loads that the turbine is designed to withstand: obtained by applying the appropriate partial load factors to the characteristic values Edgewise: Direction that is parallel to the local chord of the blade FEM: Finite Element Method Flapwise: Direction that is perpendicular to the surface swept by the non-deformed rotor blade axis LTT: Leading Towards Trailing edge direction Trailing edge: Aft portion of a blade normally pointed TTL: Trailing Towards Leading edge direction Ultimate strength: Measure of the maximum (static) load-bearing capacity of a material or structural element

96 88 Symbols A Extensional stiffness a Plate length, B Bending-extension stiffness coupling b Plate width D Bending stiffness, Flexural rigidity E Young s modulus G Shear modulus K Shear correction factor, Stiffness M Moment N Normal Force, Number of layers q Pressure, load Q Shear force, Reduced stiffness S Shear strength t Plate Thickness u,v Displacement W, w Displacement coefficient x,y Coordinate z Coordinate δ ε φ κ γ ν,µ ζ Lateral displacement Strain Rotation Curvature Shear strain Poisson s ratio Stress Abbreviations BC CLPT CPU FE FEA FEM FRP FSDT GFRP SS UD Boundary Condition Classic Laminate Plate Theory Central Processing Unit Finite Element Finite Element Analysis Finite Element Method Fibre Reinforced Plastic First-Order Shear Deformation Theory Glass Fibre Reinforced Plastic Simply Supported Unidirectional Nomenclature MSC.Patran MSC.Marc Pre and Post processing finite element software Solver for finite element applications

97 Profile normalization to XFOIL needs coordinate system Figure 86. Normalisation procedure. The profile should be placed in range x[0,1]. Figure 87. Orientation of the point numbering defining aerofoil profile.

98 Information on the blade and experimental equipment The blade was manufactured by SSP Technology A/S. The one tested in the current experiment was cut at distance 25m from the root. The blade weights approximately 4200kg including the equipment mounted on it. The FE-model weight 4178kg (only the part up to 25m from the root). Strain Gauges Strain gauge is a device that measures elongation by means of the electrical resistance. A coil of certain resistance is attached to the examined part. When a strain occurs, the length of the coil changes and so does resistivity. Simple, uni-axial strain gauges measure the relative strain only in one direction. In order to measure both directions, the system of two perpendicular gauges was applied. The third class of gauges are rosettes, which measure the elongation in 0, 45, 90 degree directions. By means of such a measurement, the whole strain field may be determined. Fig. a Fig. b Fig. c Figure 88. a) Unidirectional strain gauge scheme. b) Bi-axial strain gauge. c) Rosette. It measures displacement in three directions. ASM Inside the blade, in between the webs, measurements of the main chamber take place. For this purpose, ASMs (Length Transducer from ASM Cable actuated positions sensors) are used in the number of 3 for most important cross- sections. The principle of action of an ASM deals with the resistivity dependent on length of the wire pulled out. Three kinds of ASMs were used, differing in range of the measurement, starting from 100mm up to 4000mm. however inside we use only 100mm because the variations are within the range at all times. Figure 89. ASM length transducer As a substitution for the centre plane, adjustable bars were used. External ASMs measure global deformation of the whole blade under applied loading conditions. As the blade is going to be loaded in two different directions, the placement of the equipment has to compensate special behaviour of the blade e.g. twisting due to bending.

99 91 Figure 90. Scheme of the measuring devices placed at 4m from the root section. The equipment varies between sections. For details regarding other sections, visit future data reports for the ongoing experiment. Local displacement - LT Another type of measuring equipment used in the experiment is the LT- Length Transducer. The range of a transducer which was used is 100mm. It is used for measurements of the local blade deflection while buckling. It is attached to the metal frame, which is fastened to the blade with a stripe. The force in stripes cannot be too high in order to prevent the deformation of the blade. Figure 91. LT- NT, Length Transducer from NovoTechnik Adjustments of the LTs were made by means of the mounts on the frames attached to the blade. The zero position enabled movement of the measuring rod in both directions. The direction measured was not ideally aligned with the flapwise direction. However, for the purpose of this project, they were assumed coherent.

100 92 Frame holding NT sensor Fig. a Fig. b Figure 92. a) Picture showing position of LT-NT sensors on the trailing edge panel mounted on the blade in Risø DTU s new test center for blade structure. b) Schematic description of the measuring devices placed at m from the root section. DIC Digital Image Correlation ARAMIS ARAMIS is the deformation measuring system used for recording an object under load. It uses two (or more) CCD (Charge Couple Device) cameras to detect the difference in the measured pattern. For each & every stage of load, this system calculates 3D coordinates of the object surface on the basis of digital image processing delivering the 3D displacement and the strain. ARAMIS sourced from GOM, Germany is a non-contact measuring system for measuring 3-dimensional deformation and strain distributions of real components under static or dynamic load. Figure 93. The results of the optical DIC (Digital Image Correlation) measurements. A spectral pattern is painted on the blade so the system can measure the out of plane deformation. The different salient features of ARAMIS used in the testing included: - Large measuring area from small to large objects (1 mm up to 1000 mm) - High data point density

101 displacement [mm] 93 - Highly efficient and flexible system due to a compact measurement set-up - Good understanding of the component behaviour by the use of graphical representation of the measuring results The ARAMIS system finds applications in material testing, characterization of creep and aging processes, component dimensioning, examination of non-linear behaviour, strength assessment etc Additional study of the experimental data 13 Distance from the root Full-scale test 51% FEM scaled to 51% % difference 22m 240mm 256mm 6% 16m 134mm 140mm 4% 10m 58mm 55mm -5.5% Table 8. Comparison of experimental and numerical results for global deformation in edgewise direction. The deformation values were compared at 51% of the load since this was the highest load for which experimental results were obtained. The model was compared to the full-scale test results also at the level of global trailing edge validation. Figure 94 presents global deflection of the blade trailing edge in flapwise direction. It is noticeable that here, the data are not as ideally coinciding Comparison of experimental and numerical results for global displacement of the trailing edge in flapwise direction 0% 20% 40% 60% 80% 100% FEM - 22m Test - 22m FEM - 10m load [% of ultimate load] Test - 16m Test - 10m Figure 94. Comparison of experimental and numerical results for global deformation in flapwise direction measured at the trailing edge. The exact data for the plots presented above are given in Table 9. Analogically to the displacement in edgewise direction, the data was scaled to enable direct comparison. Distance from the root Full-scale test FEM % difference 22m 41mm 41mm 1% 16m 25mm 29mm 14% 10m 7mm 8mm 12.5% Table 9. Comparison of experimental and numerical results for global deformation of the trailing edge in flapwise direction. The deformation values were compared at 51% of the load.

102 strain [µs] strain [µs] Figure 95. Strain in the edgewise direction in the midpoint of suction side trailing edge panel compared a to the result of experimental testing, Strain in z-direction at 4m suction side Figure 96. Strain in the longitudinal direction in the midpoint of suction side trailing edge panel compared a to the result of experimental testing, 12.5 Material layups Original layup Strain in x-direction at 4m suction side 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% load [% of ultimate load] % 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% load [% of ultimate load] layer 1 layer 8 experiment -inside experiment -outside layer 1 layer 6 layer 12 experiment - inside experiment - outside The material is composed starting from the outside, i.e. layer 1 in the tables below is the most outer layer. Figure 97. Material data for pressure side trailing edge panel in the considered region. The material was internally for the model called LM_Shell_trail_L.2, with orientation angle: Overall thickness is 20.45mm.

103 95 Fig. a Fig. b Figure 98. Material data for the composite of which the above pressure side trailing edge panel is composed Fig. a: YE900HRC. Fig. b: EGL1600. For comparison, also suction side is presented: Figure 99. Material data for suction side trailing edge panel in the considered region. The material was internally for the model called LM_Shell_trail_up.4. This panel is more than twice thicker than the pressure side panel (its thickness is 47.3mm) Figure 100. The layup obtained by dismantling the triax layers. The material was designed to imitate the behaviour of the original one.

104 96 Layup for optimized material For a reader acquainted with FEM-software used, the original and improved layups may seem virtually the same. However, in the original layup, property called angle of orientation was additionally set to almost 90 degrees and this is the rotation of the layup. The only change applied to the original, triax layup after optimization, was removing the angle of orientation for elements in the panel. Thus, no tables are presented. Figure 101 presents a scheme of the change in fibre plies orientation suggested by the optimization algorithm and implemented in Finite Element Model confirmed significantly improvement of the local deformation. Figure 101. Scheme presenting change in fibre orientation in the sandwich panel. Figure 102. The layup obtained by rearranging the orientation of plies in the free layup and adding one additional layer of thick UD. The material was originally redesigned to imitate the behaviour of the original one.

105 97 Figure 103. The layup obtained by rearranging the orientation of only thick UD plies. Note lower thickness of sandwich faces than in the original layup. In Figure 104, the change in thickness in finite element modelling software is presented. There is no offset for shell element type used. The shell elements represent the midplanes of modelled material thickness. This ensures corresponding method of calculation of the mechanical properties for a sandwich element. Figure 104. Sudden change in material thickness Initial Finite Element Analysis Root section Figure 105. View of the root section between distances 3m and 5m from the root. This fringe shows global displacement (considering all directions translation). Here, also webs are subjected to some localised phenomena. That is however not the scope of this project.

106 98 In order to more conveniently analyse and visualise the considered out of plane deformation, a local coordinate system was introduced for the plate. In Figure 106, the local displacement of the plate section where the deformation reaches maximal amplitude is presented. Figure 106. Local displacement of the plate section where the deformation reaches maximal amplitude, i.e. 4.25m. The results are presented on the deformed shape and the undeformed section is shown with the local coordinate system depicted in orange. Strains In broad view for the root section, it is clearly visible that a local behaviour occurs on the pressure side trailing edge panel (circled). This will be analysed in more details. Other local behaviour visible in the fringes is not within the project scope and therefore should not draw Reader s attention. Figure 107. Strains in root section in edgewise (left) and longitudinal (right) direction (inner layer). It is clearly visible that a local behaviour occurs in pressure side trailing edge panel (circled).other local behaviour visible in the fringes are not within the project scope. As presented in below, it revealed nonlinear behaviour of the bending, which could indicate influence of buckling.

107 strain [µs] strain [µs] Strain [ S] Strain [ S] Strain [ S] Strain [ S] Strains in X direction (edgewise) in midpoint at 4.25m from the root - optimized layup load [% of the ultimate load] layer 1 layer Strains in X direction (edgewise) in midpoint at 4.25m from the root after taking away membrane strain - optimized layup layer load [% of the ultimate load] Figure 108. Comparison of FEM results for strain in X (edgewise) direction at 4.25m section also after taking away the membrane average strain. layer Strains in Z direction (longitudinal) in midpoint at 4.25m from the root - optimized layup Strains in Z direction (longitudinal) in midpoint at 4.25m from the root after taking away membrane strain - optimized layup layer 1 layer layer 1 layer load [% of the ultimate load] Figure 109. Comparison of FEM results for strain in Y (flapwise) direction at 4.25m section also after taking away the membrane average strain load [% of the ultimate load] Strain in x-direction at 3.5m pressure side layer 1 layer 6 0% 20% 40% 60% 80% 100% load [% of ultimate load] Strain in x-direction at 4.5m pressure side layer 1 layer 6 0% 20% 40% 60% 80% 100% Figure 110. Comparison of FEM results for strain in X (edgewise) and Y (flapwise) direction at 3.5 and 4.5m section at the pressure side Strain in z-direction at 3.5m pressure side 0% 20% 40% 60% 80% 100% load [% of ultimate load] layer 1 layer 6 Strain in z-direction at 4.5m pressure side 0% 20% 40% 60% 80% 100% layer 1 layer 6

108 Y dir X dir Y Y dir Distribution of the loading and boundary conditions. The following presents milestones of the derivation of distribution of the forces applied to the plate considered in the algorithm. First, the angle of orientation of the plate in FE XY-plane was found, see figure below. 3m section, α y = x R² = X dir y = x R² = m section, α Figure 111. View of the considered region of trailing edge panel. Then, the angle of orientation of the plate in XZ- and YZ-plane was found: X dir y = 0.128x R² = Trailing edge, β y = 0.125x R² = Z dir Figure 112. View of the considered region of trailing edge panel Trailing edge, γ y = x R² = Z dir Here, the jump at 4m is caused by change of element orientation. The trend (orientation of the plate) is however not changed between the region 3-4m and 4-5m. Full transformations are omitted. The derived formulae are as follows: N x =F z N y =F x cosβ F y cosγ at the web N y =F x cosγ F y cos β at the trailing edge q=f x sin α F y cos β Next, the strains were transformed via mechanical properties and the panel s dimensions to obtain the following distributions (approximated through the thickness).

109 q - x axis for the plate m 1.2 y = 70982x x x R² = m Poly. (5m) Linear (3m) Poly. (3m) Figure 113. The plots present distribution of the lateral (to the plate) force on the 3m and 5m edges of the considered trailing edge panel y = 46935x R² = Figure 114. The plots present in-plane forces averaged for two opposite sides of the plate giving a common approximated distribution. The trends present approximations (linear and third order) of the force distribution.. On basis of these results, an approximation was created in relation to the plate dimensions: Nx = 46935y Ny = 39204x q= x Nx (f(fz)) For the lateral load distribution, a linear distribution was also chosen for the simplicity. The overall behaviour is to mirror the original and not be precisely identical. And the forces applied to the plate were: 5m 3m Ny (f(fx, Fy, β,γ)) average Linear (average) Poly. (average) y = 39204x R² = y = x x x R² = Nx=47000y Ny=40000x q= x in Section 5.2. which is presented in the algorithm in the form derived

110 102 In the Figure below, the connections of the trailing edge panel to the web and the suction side panel is presented. The connection to the web is flexible. This is a result of material change from a sandwich to a very thin laminate, which decreases the bending stiffness dramatically and facilitates deformation and rotation of the panel plate at this joint. At the other side, the panel is connected to a significantly thicker sandwich. This causes it to be more prone to deformations at that point of a sudden material change. In order to avoid influence of the connection-related behaviour, the plate considered was bounded no exactly at the joints. Trailing edge Box girder Edge of the studied plate Figure 115. The blade pressure side trailing edge panel model. Connections that allow deformation are marked Derivation of the plate deformation formula Solving the above system (****) for A mn, B mn and C mn gives; For in-plane forces in all directions, (****-3) takes the form: From (****-3) it yields: Substituting that into (****-1) we obtain: it can be transformed into:

111 103 What substituted into (****-2) gives: Splitting A and q components: omitting the terms reducing each other and performing several mathematically trivial, yet altogether complex, transformations we obtain:

112 104 Which, substituted back to: to the one given in ref. [26] and [34]: gives the final solution analogical Where: The above derivation was performed for needs of this project and gives exact solution to the considered loading and boundary conditions. It was implemented in Matlab with utilization of several simplifications giving convenience in programming. Also fact that the core in the considered case is isotropic, and therefore D Qx =D Qy, was used. Load distribution The following gives derivation of the load distribution formula.

113 Additional results for the optimization Stacking sequence rearrangement only Figure 116. Deformation of the optimized plate with additional layers introduced. Added layers Deflection (Matlab) Improv ement LOCAL deflection Improve ment in local defl INITIAL 5.6 mm Optimized with poor 4.4mm starting point - Optimized 4.21mm 30% 8.39mm 42.2% face 1 0 face 2-1 layer 3.6 mm 40% face 1 1 layer face 2-1 layer 2.9 mm 52% 5.72mm 60.5% face 1 1 layer face 2-2 layers 2.55 mm 57% face 1 2 layers face mm 47% face 1 2 layers face 2-1 layer 2.55 mm 57% face 1 2 layers face 2-2 layers 2.25 mm 63% 4.15mm 71.4% face 1 1 layer face 2-0 face 1 0 face 2-2 layers SUBTRACTED Face 1 1 Face mm 35% 3.26mm 42% 9.26mm -66% The force distribution applied in the algorithm is an approximation resulting from several transformations described in Section 5. Such distribution is not perfectly reliable and therefore, the forces have been adjusted to more accurately mirror the initial shape and amplitude of the plate deformation obtained at the entire blade model. The deformation distribution for the adjusted forces applied is presented.

114 106 Figure 117. Deformation of the optimized plate for the adjusted force distribution. The vertical axis is corresponding to the blades longitudinal direction (Z), whereas the horizontal one represents the edge at 3 and 5m respectively. The forces applied in the algorithm were then adjusted in order to more accurately approximate initial shape and amplitude of the plate deformation. This force adjustment, however, did not influence the obtained results significantly. The optimized stacking sequence was the same. That is because the loading cases were virtually the same (the adjustment was mainly scaling). Free layup optimization Initial Face 1: [ ] Face2:[ ] Matlab % improve. FEM - LOCAL (FEM)% improve. Improved added 0 and added 3 and added 3 and added 0 and added 6 and added 3and added 6 and added 0 and added 9 and added 6 and added 3 and added 9 and added 6 and added 9 and added 9 and added 3 and 3 without stronger UD

115 107 Figure 118. Out of plane deflection in 4.25m section for optimized layup with added 2 layers in each face. The deformation is scaled 5 times for better visualization of the deformation. Fig. a Fig. b Figure 119. Fringe of flapwise displacement in the considered plate region for optimized free material layup with one additional layer of thick UD fibres added at the inner side and Fig. a: 3 sublayers (equivalent to one layer) added at each face. Fig. b: 6 sublayers (equivalent to two layers) added at each face Figure 120. Fringe of flapwise displacement in the considered plate region for optimized free material layup applied in the region from 3 to 6m.

116 Strain [ S] Strain [ S] Strain [ S] Strain [ S] 108 Figure 121. Fringe of flapwise displacement in the considered plate region for optimized free material layup with one layer oriented by 90 degrees in each face. The material is applied in the region from 3 to 5m. The additional deformation is decreased, but the amplitude of the main deformation concerned is 4 times larger than for the corresponding UD solution. The double wave has not been avoided in this solution. Strain analysis In the following, the strain behaviour is studied to investigate nature of the deformation for the improved material layup. The plots below show strain at the point of the highest deformation amplitude. Results for the initial and optimized layup without added material are compared Strains in edgewise direction after taking away membrane strain - original layup layer 1 layer 6 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Strains in edgewise direction after taking away membrane strain - improved layup layer 1 layer 6 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Figure 122. Strain in edgewise (left) and longitudinal (right) direction at the point of maximal displacement amplitude for the original (top) and the improved layup (bottom).here, the membrane strains taken away to present the nature of bending Strains in longitudinal direction after taking away membrane strain - original layup 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Strains in edgewise direction after taking away membrane strain - improved layup 600 0% 20% 40% 60% 80% 100% load [% of the ultimate load] layer 1 layer 6 layer 1 layer 6

117 Strain [ S] Strain [ S] Strain [ S] Strain [ S] 109 The plots below show present the strain for the layup with the most significant decrease of the local deformation. Not only the value of ultimate strain is decreased significantly but also the nonlinearity is less pronounced for the panel with altered orientation of plies Strains in X direction (edgewise) at the point of the highest deformation amplitude - optimized layup with faces material nearly doubled 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Fig. a layer 1 layer 10 Fig. b Figure 123. Strain at the midpoint of trailing edge panel for the optimal layup with 2 layers added at each face. Fig. a: edgewise direction Fig. b: longitudinal direction Strains in Z direction (longitudinal) at the point of the highest deformation amplitude- optimized layup with faces material nearly doubled 0% 20% 40% 60% 80% 100% load [% of the ultimate load] layer 1 layer 10 For strain plots, presenting results for the longitudinal direction, improvement can be also observed in significant decrease of the strain amplitude. Moreover, the nonlinearity present in the original panel was decreased or even eliminated, see figure below. This confirms a real improvement, not only in the local deformation amplitude but also in its character Comparison of the strains in the edgewise direction at the point of the highest deformation amplitude after taking away membrane strain outer layer- original layup 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Comparison of the strains in the longitudinal direction at the point of the highest deformation amplitude after taking away membrane strain 0% 20% 40% 60% 80% 100% load [% of the ultimate load] inner layer - original layup outer layer- optimized layup inner layer - optimized layup outer layer - original layup inner layer - original layup outer layer - optimized layup inner layer - optimized layup Figure 124. Comparison of the strains at the point of the highest deformation amplitude after taking away membrane strain. Top: the edgewise direction. Bottom: the longitudinal direction. As it is demonstrated, the local out of plane behaviour of trailing edge pressure side panel was improved significantly by rearranging the stacking sequence of plies in sandwich faces.

118 Strain [ S] Strain [ S] Strain [ S] Strain [ S] 110 Not only was the local deformation s amplitude decreased dramatically, but also the nonlinear characteristic of the bending was linearized. The above deliberations were performed for material currently used in manufacturing. It gives a great potential in performance improvement without additional costs. In the following section, improvement possibilities will be explored for different materials Strains in X direction (edgewise) - optimized layup with with the use of bamboo 0% 20% 40% 60% 80% 100% load [% of the ultimate load] layer 1 layer 6 Strains in Z direction (longitudinal) - optimized layup with with the use of bamboo 0% 20% 40% 60% 80% 100% layer 1 layer 6 load [% of the ultimate load] Strains in X direction (edgewise) after taking away membrane strain - optimized layup with with the use of bamboo 0% 20% 40% 60% 80% 100% load [% of the ultimate load] Strains in Z direction (longitudinal) after taking away membrane strain - optimized layup with with the use of bamboo 0% 20% 40% 60% 80% 100% load [% of the ultimate load] layer 1 layer 3 layer 1 layer 3 Figure 125. Strain in edgewise (top) and longitudinal (bottom) direction at the point of maximal displacement amplitude (left) for the layup entirely built of bamboo with poplar veneer. The figures to the right present results with the membrane strains taken away to present the nature of bending Flapwise and combined loading FLAPWISE (PTS) LOAD CASE Fig. a Fig. b Figure 126. Comparison of results of global displacement for original (Fig. a) and improved layup (Fig. b) in pressure side trailing edge panel in the root region for PTS load.

119 111 Figure 127. Fringes present displacement in X, Y and Z direction on the plate considered. COMBINED LOAD CASE Figure 128. Results of global displacement for the root region for combined load. Here, the original material layup is used in pressure side trailing edge panel.

120 112 Figure 129. The root section fringe presenting global displacement magnitude, X (edgewise), Y (flapwise), and Z (longitudinal) direction for the original material layup. Figure 130. Root view for the improved material applied. The fringes present displacement in X, Y and Z direction.