department of wind energy master report

Dep

artm

ent

of

Win

d E

ner

gy

Mas

ter

Rep

ort

Structural modification of the root section of a 14.3m wind

turbine blade

Phillip Auldon Somers

DTU Wind Energy-M-0454

July 2021

Author: Phillip Auldon Somers

Title: Structural modification of the root section of a 14.3m wind turbine

blade

DTU Wind Energy-M-0454

July 2021

DTU Wind Energy is a department of the Technical University of Denmark

with a unique integration of research, education, innovation and public/private

sector consulting in the field of wind energy. Our activities develop new

opportunities and technology for the global and Danish exploitation of wind

energy. Research focuses on key technical-scientific fields, which are central

for the development, innovation and use of wind energy and provides the

basis for advanced education at the education.

Project period:

January – July 2021

ECTS: 30

Education: Master of Science

Supervisor:

Lars Pilgaard Mikkelsen

Philipp Ulrich Haselbach

DTU Wind Energy

Troels Ette

Olsen Wings A/S

Remarks:

This report is submitted as partial

fulfillment of the requirements for

graduation in the above education at the

Technical University of Denmark.

Technical University of Denmark Department of Wind Energy Frederiksborgvej 399 4000 Roskilde Denmark

www.vindenergi.dtu.dk

AbstractStructural redesign can be performed in numerous applications with varying method-ologies while constrained to a common set of design specifications. This report focusedspecifically on the structural modification of the root section of a 14.3 m wind turbineblade to enable use on an additional wind turbine type. Structural optimization wasimplemented that treated the blade materials (type, thicknesses, etc.) as fixed and in-stead varied the shape based on geometric and structural constraints. The geometricconstraints included the new reduced root blade diameter, original blade cross-sectionalgeometry at maximum chord, and the original moulding surface used in manufacturing.The primary motivation for these being adequate connection to the new turbine, preser-vation of blade performance, and reuse of existing moulds via compensating insert. Thestructural constraints included thresholds for both tower clearance and material failurewith the primary motivation for both based on avoidance of turbine operational failure.The approach utilized commercial software packages based in structural optimization(TOSCA) and finite element analysis (Abaqus CAE). A specific subset of the TOSCA(Bead) that incorporates displacement of discretized nodes was used to generate theredesigned root section of the wind turbine blade. A new feature of this subset was alsoimplemented and developed in collaboration with the software supplier Simulia for thepurpose of this report which involved utilization of the material failure criteria Tsai Wuas a design response. An arbitrarily scaled model based on the same design requirementswas used as the geometric input for the optimization where both, this model and theresultant optimal model, could then be compared to gauge performance.

It was shown for the scaled model that displacement and failure index values in-creased but were in compliance with design constraints of tower clearance and materialfailure. However, two concerns are raised in using this approach being no guarantee ofdesign requirement compliance and the best solution is often preferred compared to anacceptable solution. In the event that the scaled model violated design requirements,geometry would need to be updated based on the designer’s experience, thus becomingan arbitrary and potentially highly iterative process. In terms of the best solution, costreduction through volume minimization and increased structural margin through lowerfailure index values would both be potential outcomes in using the stated objective ap-proach. This would ultimately be of interest in the highly competitive realm of windturbine blade manufacturing where cost and quality are leveraged relative to competi-tion. Ultimately, geometric optimization in combination with the introduction of failurecriteria were shown to produce benefit to volume or strength when compared to boththe scaled root section and the original root section of the wind turbine blade.

AcknowledgementsThe curriculum provided through Danmarks Tekniske Universitet and the Wind Energydepartment was paramount in providing the necessary theory and methods in fulfillingthe objectives of the report. Lars Pilgaard Mikkelsen and Philipp Ulrich Haselbach wereinstrumental in providing constructive vantage points to the analysis and I feel fortunatefor their genuine interest in the subject matter. What began as a question regarding fail-ure criteria applicability through the open-forum in Simulia’s online community turnedinto a memorable collaboration with representatives Anton Jurinic and Claus Pedersenfrom Simulia as well. I’ll cherish the moments of success and frustration we all sharedtogether and look forward to future communication. I extend sincere gratitude to myfamily for their unwavering support in all of my pursuits in life and my friends that I’vebeen able to share new experiences with during my stay in Denmark.

ContentsAbstract i

Acknowledgements ii

Contents iii

List of Figures v

List of Tables viii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Methodology 42.1 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Composite Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Loads and boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 152.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Results and Discussion 293.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Full blade model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3 Reduced model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4 Scaled model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.5 Optimal model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Conclusions 72

Bibliography 76

A Appendix A 78A.1 Full blade FE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78A.2 Reduced FE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80A.3 Scaled FE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81A.4 Optimal FE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Contents iv

B Appendix B 84B.1 Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84B.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

List of Figures1.1 National Renewable Energy Laboratory LCOE - wind projection [1] . . . . . 11.2 Introductory figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Model discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Benchmark and model progression . . . . . . . . . . . . . . . . . . . . . . . 52.3 Element nodal positioning and DOF . . . . . . . . . . . . . . . . . . . . . . 62.4 Element overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.5 Gauss integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.6 Hourglass spurious mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.7 Lamina and Laminate diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 112.8 Blade section material diagram . . . . . . . . . . . . . . . . . . . . . . . . . 122.9 Laminate orientation and normal direction . . . . . . . . . . . . . . . . . . . 122.10 Tsai-Wu bi-axial stress effect [2] . . . . . . . . . . . . . . . . . . . . . . . . . 132.11 Loading diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.12 Reduced model loading configurations . . . . . . . . . . . . . . . . . . . . . 172.13 Reduced model loading configurations (cont.) . . . . . . . . . . . . . . . . . 172.14 Radial loading distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.15 Full blade model - loading diagrams . . . . . . . . . . . . . . . . . . . . . . . 192.16 Reduced blade models - loading diagrams . . . . . . . . . . . . . . . . . . . 192.17 TOSCA Bead characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.18 Design domain - design variable nodal selection . . . . . . . . . . . . . . . . 242.19 Design domain - geometry and response . . . . . . . . . . . . . . . . . . . . 242.20 A strictly convex (left), convex (middle), and a non-convex(right) [3] . . . . 272.21 Filter radius - checkerboard phenomenon[4] . . . . . . . . . . . . . . . . . . 28

3.1 Linear regression - blade length versus tip displacement constraint [5] . . . . 323.2 Full blade model - maximum failure index locations . . . . . . . . . . . . . . 333.3 Full blade model - maximum failure index locations (cont.) . . . . . . . . . . 343.4 Full blade model partial - Tsai-Wu and displacement- P2S loading . . . . . . 353.5 Kinematic coupling nodes - full airfoil cross-section . . . . . . . . . . . . . . 363.6 Case 1 and 2 - Tsai-Wu - P2S Loading . . . . . . . . . . . . . . . . . . . . . 363.7 Kinematic coupling nodes - web exclusion . . . . . . . . . . . . . . . . . . . 373.8 Case 3 and 4 - Tsai-Wu - P2S Loading . . . . . . . . . . . . . . . . . . . . . 373.9 Case 5 - nodes and Tsai-Wu - P2S Loading . . . . . . . . . . . . . . . . . . . 383.10 Extension - Tsai-Wu - P2S loading . . . . . . . . . . . . . . . . . . . . . . . 393.11 Mesh discretization - Tsai-Wu - P2S Loading . . . . . . . . . . . . . . . . . . 40

List of Figures vi

3.12 Full and reduced comparison - Tsai-Wu - S2P loading . . . . . . . . . . . . . 413.13 Full and reduced comparison - Tsai-Wu - T2L loading . . . . . . . . . . . . . 423.14 Full and reduced comparison - Tsai-Wu - L2T loading . . . . . . . . . . . . . 423.15 Scaling distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.16 Reduced and scaled comparison - Tsai-Wu - P2S loading . . . . . . . . . . . 443.17 Reduced and scaled comparison - Tsai-Wu - S2P loading . . . . . . . . . . . 453.18 Reduced and scaled comparison - Tsai-Wu - T2L loading . . . . . . . . . . . 453.19 Reduced and scaled comparison - Tsai-Wu - L2T loading . . . . . . . . . . . 463.20 Cantilever tube setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.21 Resultant optimal cantilever tube data . . . . . . . . . . . . . . . . . . . . . 493.22 Cantilever tube displacement . . . . . . . . . . . . . . . . . . . . . . . . . . 493.23 TOSCA.OUT - Design cycle 000 . . . . . . . . . . . . . . . . . . . . . . . . 503.24 Tsai-Wu evaluation location comparison . . . . . . . . . . . . . . . . . . . . 513.25 Element distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.26 Web transition geometric constraint . . . . . . . . . . . . . . . . . . . . . . . 533.27 Element distortion at web transition including directional constraint . . . . . 543.28 Failure reduction - Tsai-Wu objective function vs. iteration . . . . . . . . . . 563.29 Failure reduction - displacement vs. iteration . . . . . . . . . . . . . . . . . 573.30 Failure reduction - Tsai-Wu values - final iteration . . . . . . . . . . . . . . . 583.31 Failure reduction - Tsai-Wu percent differences - last and final iteration . . . 583.32 Failure reduction - displacement values - final iteration . . . . . . . . . . . . 583.33 Failure reduction - displacement percent differences - last and final iteration 593.34 Failure reduction - EQUAL_MAX case condition - nodal displacement for

final iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.35 Tsai-Wu distributions - EQUAL_MAX case condition - P2S/S2P . . . . . . 613.36 Tsai-Wu distributions - EQUAL_MAX case condition - T2L/L2T . . . . . . 613.37 Objective function condition and tip transition . . . . . . . . . . . . . . . . . 633.38 Failure reduction - displacement objective - resultant geometry and Tsai-Wu

distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.39 Volume reduction - volume objective function vs. iteration . . . . . . . . . . 663.40 Volume reduction - Tsai-Wu vs. iteration . . . . . . . . . . . . . . . . . . . . 673.41 Volume reduction - displacement vs. iteration . . . . . . . . . . . . . . . . . 673.42 Volume reduction - Tsai-Wu - last and final iteration . . . . . . . . . . . . . 683.43 Volume reduction - Tsai-Wu percent differences - last and final iteration . . . 683.44 Volume reduction - displacement - last and final iteration . . . . . . . . . . . 683.45 Volume reduction - displacement percent differences - last and final iteration 693.46 Volume reduction - nodal_015 - nodal displacement for final iteration . . . . 693.47 Tsai-Wu distributions - nodal_015 - P2S/S2P . . . . . . . . . . . . . . . . . 703.48 Tsai-Wu distributions - nodal_015 - T2L/L2T . . . . . . . . . . . . . . . . . 703.49 Displacement objective - resultant geometry and Tsai-Wu distribution . . . . 71

4.1 Filter radius influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

A.1 Full blade model displacement . . . . . . . . . . . . . . . . . . . . . . . . . . 78

List of Figures vii

A.2 Full blade model displacement (cont.) . . . . . . . . . . . . . . . . . . . . . . 78A.3 Full blade partial model displacement . . . . . . . . . . . . . . . . . . . . . . 79A.4 Full blade partial model displacement - L2T . . . . . . . . . . . . . . . . . . 79A.5 Reduced blade model displacement . . . . . . . . . . . . . . . . . . . . . . . 80A.6 Reduced blade model displacement (cont.) . . . . . . . . . . . . . . . . . . . 80A.7 Scaled blade model displacement . . . . . . . . . . . . . . . . . . . . . . . . 81A.8 Scaled blade model displacement (cont.) . . . . . . . . . . . . . . . . . . . . 81A.9 Failure reduction - optimal blade model displacement . . . . . . . . . . . . . 82A.10 Failure reduction - optimal blade model displacement (cont.) . . . . . . . . . 82A.11 Volume reduction - optimal blade model displacement . . . . . . . . . . . . . 83A.12 Volume reduction - optimal blade model displacement (cont.) . . . . . . . . 83

B.1 Supplied material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

List of Tables2.1 Moment and shear force values at maximum chord . . . . . . . . . . . . . . 182.2 Design response configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 Objective function configuration . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1 Material properties - complete . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Blade displacements - structural testing and full blade model . . . . . . . . . 323.3 Tsai-Wu - full blade model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Boundary condition parametric study . . . . . . . . . . . . . . . . . . . . . . 353.5 Section extension - load and displacement . . . . . . . . . . . . . . . . . . . 393.6 Mesh convergence - Tsai-Wu and displacement . . . . . . . . . . . . . . . . . 403.7 Blade displacements and Tsai-Wu - full blade model and reduced blade model 433.8 Blade displacements and Tsai-Wu - scaled blade model . . . . . . . . . . . . 463.9 Design cycle 000 and general static comparison and correction progression . 523.10 Failure reduction - common parameters . . . . . . . . . . . . . . . . . . . . . 553.11 Failure reduction - case condition parameters . . . . . . . . . . . . . . . . . 553.12 Failure reduction - equal_max - blade Displacements and Tsai-Wu . . . . . . 623.13 Volume reduction - common parameters . . . . . . . . . . . . . . . . . . . . 643.14 Volume reduction - case condition parameters . . . . . . . . . . . . . . . . . 653.15 Volume reduction - nodal_015 - blade displacement and Tsai-Wu . . . . . . 71

B.1 Load distribution magnitudes (target loads minus compensation and preload) 84

CHAPTER 1Introduction

1.1 BackgroundWind energy is strengthening its presence as a vital energy source based on the globaleffort to reduce carbon emissions and its capability to equal and exceed competing formsof energy in the economic domain. An important aspect to the latter is the ability forthe sector to increase efficiency both in terms of reducing costs and increasing energyproduction. A key metric in gauging this capacity is presented in terms of the levelizedcost of energy (LCOE), as shown graphically with respect to time in Figure 1.1.

Figure 1.1: National Renewable Energy Lab-oratory LCOE - wind projection [1]

It’s clear that both the GovernmentPerformance and Results Act (GPRA) tra-jectory and the actual trend values areboth decreasing relative to time. Suppliersmust keep pace with this industry bench-mark and implement strategies to reducetheir total costs, which also include thoserelated to manufacturing the various com-ponents of the wind turbine (see Figure1.2a). The primary components being thefoundation, tower, nacelle, rotor blades,and rotor hub. An effective approach insolving this challenge is to increase modu-larity in an existing component (includingits associated manufacturing equipment) opposed to it being exclusive to a single windturbine platform. One of these components that offers considerable potential in therealm of modularity is the rotor blade.

The concept of modularity can take various forms where a product can be completelyinterchangeable between applications or partially interchangeable where a portion of theproduct must be adapted for successful operation. The total quantity of applicationsmust also be considered and the cost of modularity balanced between incorporatinginterchangeability into the original design or accepting downstream costs in adaptingthe product for additional applications when the situation arises. The suppliers of suchapplications must also be considered so that adapting a product will also have effec-tive market reach. An initial indication into this last detail for blade production canbe provided by assessing the primary wind turbine original equipment manufacturers

1.2 Problem 2

(OEM’s) for the market, which is evident in Figure 1.2b. Targeting an OEM with con-siderable market share such as Vestas or Siemens Gamesa would then enable the largestopportunity for implementation through larger quantities of installed (or to be installed)turbine platforms. Considering all details, there are no shortage of challenges when incor-porating modularity for a wind turbine blade as violation of various design constraints(aerodynamic, structural, etc.) would result in determinate effects to performance andoperation.

(a) Wind turbine component dia-gram [6]

(b) Global wind turbine originalequipment manufacturer (OEM)market share [7]

Figure 1.2: Introductory figures

1.2 ProblemOlsen Wings is a wind turbine OEM that manufactures a 14.3 wind turbine rotor blade.They have identified a Vestas V-27 wind turbine as additional platform for which toinstall. However, the root section of the blade must be adapted in order to interchangewith the geometry. This creates two primary design challenges with the first being reduc-ing the blade’s root-end diameter from approximately 0.719 m to 0.573 m and the secondincluding altering the bolted interface to match that of the existing V-27 hub. The lattershall be considered out of scope for the purpose of this report with the primary focusplaced on altering the blade’s root geometry to create an acceptable geometric transitionfrom the new diameter into the original blade. The aerodynamic region of the blade isintended to remain constant which then reduces the design length for the root geometryfrom the root-most plane to maximum chord (R 2.178). Structural analysis must there-fore be implemented to ensure compliance with previous design specifications in orderfor the blade to adhere to required strength and performance. A final consideration tofurther aid in modularity is also for the root region surface to not exceed that of theoriginal tooling surface in order to reuse existing moulds. Down-scaling the existingblade in accordance with the mentioned geometric constraints will enable partial reuseof the blade design and tooling, thus serving to reduce LCOE.

1.3 Objectives 3

1.3 ObjectivesThe following learning objectives will be fulfilled in performing the structural analysis:

• Discretize existing blade geometry from computer-aided design (CAD) into ele-ments suitable for finite element (FE) analysis

• Construct FE model that incorporates existing blade mechanical material proper-ties and layup sequences

• Validate FE models through comparison of displacement and failure to existingblade structural tests

• Redesign root portion of blade from using subjective (scaling) and objective (opti-mization) methodology to include required design changes

• Perform FE analysis of new designs and demonstrate compliance with displacementand failure in addition to a comparison to gauge performance

CHAPTER 2Methodology

2.1 Finite Element ModelThe general principal of finite element analysis (FEA) is based upon the transformationfrom a physical model to a discretized representation where calculations and analysis canbe performed. This is shown visually in Figure 2.1 where the objective is to marginalizethe differences between each model to ensure numerical results are indeed representativeof the structure. The figure shows two general paths of a full or reduced representationof the original model and each path possesses an advantage to the other dependent onthe intent of the analysis. For example, a full representation brings forth the benefit ofincreased accuracy compared to a reduced model since less assumptions are made intoboundary conditions for applied loading. The latter can prove superior though in termsof increased computational efficiency if localized results are desired and less elementsare involved calculation.

Figure 2.1: Model discretization

Full and reduced presentations will be used in this study with which ultimately leadsto four primary models. These being a full blade mode (full), reduced blade model(reduced), scaled model (reduced) and a optimal model (reduced). The scaled model isbased on a partial arbitrary surface offset applied to the reduced blade model to satisfythe geometric constraints imposed by the new hub. The optimal model then being therevised scaled model based on geometric optimization. A general model progression

2.1 Finite Element Model 5

is shown in Figure 2.2 through horizontal arrows and two steps of successive benchmarking as the vertical arrows. The latter occurs first between the physical full bladeand FEA full blade model and then the FE full blade to FEA reduced blade model.This is accomplished through comparison of displacement and failure data to ensureerror inherent to domain transformations is marginalized. Model conditions beyond thereduced model are fixed with the exception of geometry to ensure continuity in theminimization of error. The models and data highlighted in green are those that wereavailable at the start of the study and required minimal processing for analysis. However,the models and studies highlighted in red are those that had to be constructed for thepurpose of this study.

Figure 2.2: Benchmark and model progression

2.1.1 Virtual workThe primary basis for FEA analysis is the fundamental relation known as the principleof virtual work, and can be expressed through the following equation [8]:∫

δϵT σdV =∫

δuT FdV +∫

δuT ΦdS (2.1)

The terms stated can be recognized as δϵ for vector of strains, σ for stress, δu forvector of displacements, F as body forces, and Φ as surface traction. In essence, thevirtual work principal relates increments of external strain energy on the left-hand sideof the equation to that of the increments of internal work shown on the right-hand sideof the equation, thus ensuring system equilibrium. To then apply this relation in a morepragmatic sense through a series of substitutions, one can then arrive at the followingrelation [8]:

[K]{D} = {P} (2.2)Where [K] represents the global stiffness matrix with size based on product of the

number of nodes and degrees of freedom (both to be explained), {D} represents theglobal displacement vector, and {P} the global load vector.


2.1.2 DiscretizationEquation 2.2 is comprised of system matrices with the degrees of freedom (DOF’s) ofeach discrete node positioned at separate indices. These nodes are created when thephysical model is discretized into an elemental model, also refereed to as a mesh, whichwas shown in Figure 2.1. The quantity and position of nodes is characteristic to the typeof element being used. DOF’s for a node can include both rotational and translationaldirections for the three principal axes. Constraints can be provided for these directionsas well which then take the form of boundary conditions. A classic case relevant toblade analysis and for this study is that of a cantilever beam where the DOF’s for theroot-most nodes would be fixed to eliminate translational and rotational displacement,thus resulting in a clamped condition.

Figure 2.3: Element nodal positioning and DOF

Figure 2.3 shows discretization in greater detail in which a bounding geometry issplit into four elements, each containing four corner nodes, with each node possessingrotational and translational degrees of freedom about the 3 principal axes. This resultsin a total of 6 DOF’s for each node, where the maximum dimension for the total systemmatrices would be the product of this and total number of system nodes (9), thus equalto 54. This is relevant to computation and accuracy since discretization of the originalbounding geometry into a greater number of four-node elements will increase the totalnumber of system nodes and the system matrices’ size, thus increasing the quantity ofcomputations. However, this would provide potential benefit of increased accuracy as alarger quantity of nodes would be more representative of the geometry.

2.1.3 Element TypeAn important aspect to discretization involves the element type which will contributeto the placement of nodes as well as how stress and strain are calculated. There arenumerous types available in FEA analysis but can be separated between solid or shellelements for the purpose of this study. Literature from ABAQUS software provides threekey guidelines for this decision in the case of selecting solid over shell elements:

• When the transverse shear effects are predominant. [9]


• When you cannot ignore the out-of-plane normal stress. [9]

• When you require accurate interlaminar stresses, such as near localized regions ofcomplex loading or geometry. [9]

The shell thickness of the reduced root model is relatively small compared to thegeometry of the model so shear effects are not assumed to be dominant. The out ofplane normal stress of the shell surface is assumed to be marginal due to larger longitu-dinal and transverse stresses expected through the applied bending load. Interlaminarfailure is also excluded from the analysis based on lack of strength data for interlaminarshear stress and the reasonable degree for homogeneity in blade materials. This could beproblematic in the case of a more heterogeneous laminate where significant differences instiffness can exist between two materials such as carbon and glass fiber lamina. However,the material layup consists of fiberglass predominantly oriented in the same directionin addition to few ductile / low-modulus materials so interlaminar stress would not beexpected as a dominant failure mode.

An additional consideration rests upon deciding between linear and quadratic el-ements (see Figure 2.4b below). The primary advantage in choosing the latter is theability for element to deform to the curvature through addition of mid-edge nodes, wherethe linear elements are only able to form straight edges between nodes and therefore in-crease discretization error in curved geometry. A planar geometry would therefore bebetter suited for linear elements while quadratic elements will be used for this studybased on the significant curvature in the blade root section.

(a) Abaqus shell elements [10](b) Linear and quadratic elementrepresentation [11]

Figure 2.4: Element overview

Lastly, a determination into whether conventional shell vs. continuum shell elementsmust be established. These elements are shown graphically below (see Figure 2.4a) wheredifferences are evident both in terms of DOF’s and geometry. Conventional shells areshown to posses 6 DOF’s (rotational and translational) while continuum with 3 (onlytranslational). Geometry is also different through conventional shells defined only froma reference surface while continuum through an an inner and outer surface. Regardlessof these differences, both element types are suitable for thin-shell bending applications.The full blade FE model was originally constructed with continuum shell elements which


creates justification to continue for later models in terms of continuity. However, aprimary driver for not selecting continuum shells is its absence as a supported elementtype for optimization routine (explained in subsequent sections). Conventional shellquadratic elements (eight total nodes) will therefore be the preferred element to beincluded in all reduced models.

2.1.4 Element IntegrationThe element integration scheme, or the quantity of integration points, must also beestablished in selection of elements. Integration can be categorized as full or reduced,and the total quantity of points is determined by this determination coupled with thetype of element. For example, a fully integrated quadratic element correlates to an ordern equal to 3, which results in 9 total integration points shown in the right-most figure ofFigure 2.5a. Reduced integration is one order lower with n equal to 2, which results in 4total points (left-most figure of Figure 2.5a). The significance of these integration pointsis based in calculation of element stiffness [ke]. Gauss integration is commonly used indetermining such stiffness where each point is a location where stiffness is calculated tothen form an aggregate [ke]. This is repeated for all elements where [ke] is assembledinto the global stiffness matrix [K]. The specific element coordinates of such points arealso presented in Table 2.5b where they can be matched to the order magnitudes statedprior. Weighting factors are also presented that are used for each point in the calculationof stiffness. Ultimately, reduced integration will be the preferred scheme for the 8-nodequadratic elements, otherwise denoted as S8R elements.

(a) Gauss integration point loca-tions [12]

(b) Integration points values [12]

Figure 2.5: Gauss integration

The diagrams and detail provided above correlate to a single planar surface butconventional shell elements also require integration point quantities to be establishedin the thickness direction for each point location. A default value of 3 will be used forthe purpose of this report that correlates to the top, middle, and bottom plane of theshell element. Simpson’s rule as opposed to Gauss is used by default within Abaqusto perform such integration. The total quantity of integration points then becomes theproduct of planes (3) and planar integration points (4), thus equal to 12.


Figure 2.6: Hourglass spurious mode

Computational efficiency can be gainedin selecting reduced integration comparedto full integration based on the reduc-tion in total points. Full integration mayprovide increased accuracy for integrationthough also produce stiffer solutions incomparison as well. However, reducedintegration can lead to spurious modesor element displacements that are non-representative of the true structural response. These occur when an element has noresistance to the nodal loads that tend to activate the spurious mode [12]. In the caseof an 8-node quadratic element, the primary mode is known as hourglass and is showngraphically in figure 2.6. These tend to be less problematic than other spurious modesthrough the concept of communicability, where an hourglass mode is thought to be non-communicable. That is, “there is no way that adjacent elements can both display thismode while remaining connected” [12].

2.1.5 ResolutionAn important consideration when selecting initial values for element quantity and typeis that the concept of virtual work will result in an approximate solution with largerpotential energy than that of the true solution. This results in a structure with higherrigidity than that of the true structure, which can then present an underestimate oftrue displacement and stress. However, the approximate solution has the capacity toconverge close to the exact solution within a marginal difference. Both the element typeand quantity will contribute to this convergence to different orders depending if theresult is displacement/compliance or stress/strain.

e ∼ Chq−r (2.3)This is shown numerically in equation 2.3 [13] where e represents the total error

and it being a product of the element type C, element size h, polynomial order q, andr scalar unique to error for displacement/compliance (r=0) or stress/strain (r=1). Itwould appear that an optimal setting should be applied to all values to then arriveat a converged solution, but in practice choosing an element size infinitesimally smallwould still achieve convergence, as commonly performed in a mesh convergence study.However, optimal values for all parameters may result in greater computational efficiencyby requiring lower resolutions. This would be a greater importance in applications wherea high resolution is a baseline requirement (e.g. localized stress analysis) but less criticalwhere low resolutions are accepted. Therefore, mesh convergence will be the preferredmethod to reduce error in this study.

2.2 Composite Structure 10

2.2 Composite Structure

2.2.1 LaminaComposite structures are constructed from constituent layers known as lamina, whichare comprised of matrix and fibers. These would inherently be thought of as anisotropic,where unlike isotropic materials, material properties vary in all directions. However,lamina are often treated as orthotropic, where 3 planes of symmetry exist for characteri-zation of material properties. These are based in a local coordinate system with principaldirections 1,2, and 3 (see Figure 2.7a) where the fibers are coaxial with the 1 direction.These can then be offset relative to a global coordinate system X,Y, and Z (includedlater for laminate) to achieve varied mechanical characteristics. A lamina is assumed tobe thin, so that a state of plane stress exists. Through making this assumption, Hook’slaw can be applied to each layer to provide the following relation during applied loading(equation 2.4 [14]):

σ1σ2τ12

= 1(1 − v12v21)

E1 v21E1 0v12E2 E2 0

0 0 G12(1 − v12v21)

ϵ1

ϵ2γ12

(2.4)

Where σ3 = τ23 = τ31 = 0

Stresses are denoted as normal stress σ1 and σ2, along with shear stress τ12. Strainare denoted as normal strains ϵ1 and ϵ2, along with shear strain γ12. The mechanicalproperties are characterized through 5 engineering constants of modulus E1, modulusE2, shear modulus G12, Poisson’s ratio on a plane normal to 1 in the direction of 2 (v12),and Poisson’s ratio on a plane normal to 2 in the direction of 1 (v21). However, onlyfour of these constants are independent through equation 2.5 [14]:

vij

Ei

= vij

Ej

(2.5)

Two additional terms are required as input for Abaqus CAE when specifying anelastic lamina material condition and include the shear modulus on plane normal to1 in direction of 3 (G13) and shear modulus on plane normal to 2 in direction of 3(G23). This is particularly useful in the case of thick shells composed of many laminawhere interlaminar stresses, or stresses between lamina, along with transverse sheardisplacement (i.e. Timoshenko beam theory) is expected to be significant.


(a) Global and local coordinate sys-tem for lamina [15]

(b) Laminate extraction from blademodel

Figure 2.7: Lamina and Laminate diagrams

2.2.2 LaminateLamina are assembled in layers that form a laminate in a global coordinate system withprincipal directions X,Y, and Z. An arbitrary section of the blade model is then shownin Figure 2.7b where varying layers, fiber angles, thicknesses, and material type of thelamina within the laminate are shown graphically. Stiffness matrices of each laminaare assembled into global laminate stiffness matrices referred to as extensional stiffnessmatrix A, extension-bending coupling matrix B, and bending stiffness matrix D. Thesecan then be used to express the overall relation for applied loading of the laminatethrough the equation 2.6 [14]:

Nx

Ny

Nxy

Mx

My

Mxy

=

[A BB D

]

ϵx

ϵy

γxy

κx

κy

κxy

(2.6)

N and M represent the load and moment per unit length in global coordinates. Newstrain terms include κ which is now the curvature, with all strain terms also now basedin global coordinates as well.

2.2.3 Model implementationThe laminate of the blade structure varies between regions in mechanical propertiesand thicknesses both in the transverse and longitudinal directions. A core advantage in


Abaqus CAE is the ability to use python scripting in order to automate the procedureof laminate assignment to the correct locations. A portion of these scripts was utilizedfrom the existing full blade model but limited to only partitioning the CAD surface.Partitioning can first be visualized through examination of Figure 2.8 where an arbi-trary section of the blade is shown with a finite longitudinal length. Material thicknessand properties for a given material category (e.g. trailing panel) is held constant withinthis section and may span multiple cells in the transverse direction to provide the bestconformance to airfoil spline. A primary task of assigning composite data to each parti-tioned area had yet to be created. Beginning with the trailing edge / suction side cornerand moving clockwise, the partitioned cells are then numbered sequentially, conclud-ing with numbering of the webs. This is completed for each cross-section of constantproperties from root to maximum chord, which results in 59 partitioned cells for eachof the 17 total cross sections. The product of these is equal 1003, or the total numberof composite layups. A complete matrix of material data which included lamina layer,lamina thickness, cross section position (i.e. 1-59), radial position (i.e. 1-17), materialassignment, and fiber angle was created from the supplied database, to then be read vianewly developed python script to be assigned to each of partitioned cells.

Figure 2.8: Blade section material diagram

Figure 2.9: Laminate orientation and nor-mal direction

The lamina and laminate must be ori-ented and defined correctly since failure todo so will result in significant variation inmechanical response to the physical model.Figure 2.9 shows the correct orientation asthe one (fiber) direction for the lamina inthis region is aligned with the longitudinalaxis of the blade. It’s also clear that thelamina normal direction is oriented intothe blade. Typically this could be assignedarbitrarily but due to the fact that theouter surface of the blade is intended tobe smooth with no transition in materialheight, this orientation must be preservedsince material is assembled in the positive normal direction. An additional setting in


Abaqus relates to the sequencing of plies via “shell reference surface and offsets” wherethe bottom surface must be selected as the start for the layup. Selection of the top wouldthen result in a correctly oriented laminate but with a reversal in layup sequence. Thiswouldn’t create an issue with a symmetric layup, or one that contains an equal numberof plies and thicknesses with equal mechanical properties, about the neutral axis. How-ever, non-symmetric layups, as in the case for regions of this model, would then exhibitan incorrect response with not having the reference surface defined correctly. Therefore,the reference surface must always be selected to be consistent with the surface normaland intended layup sequence.

2.2.4 Tsai-WuComposite material failure differs from isotopic failure in that criteria which wouldnormally account for a combined loading state, such as Von Mises, fails to account forthe differences in directional material strength (e.g. tension versus compression) thatare present in composite material. Therefore it’s necessary to include criteria unique tocomposite failure such as Tsai-Wu. The equation for such as presented from the Abaqususer manual is defined in equation 2.7 [16] where IF is the resultant failure index, σ11,σ22, and σ12 correlate to stress values in the fiber directions, transverse direction, andshear respectively. The various terms of F are then further defined below the equation asa function of the strength limits Xt, Xc, Yt, Yc, S as tension fiber direction, compressionfiber direction, tension transverse direction, compression transverse direction, and shearrespectively.

IF = F1σ11 + F2σ22 + F11σ211 + F22σ

222 + F66σ2

12 + 2F12σ11σ22 < 1 (2.7)

F1 = 1Xt

+ 1Xc

, F2 = 1Yt

+ 1Yc

, F11 = − 1XtXc

, F22 = − 1YtYc

, F66 = − 1S2

F12 = f ∗√F11F22

Figure 2.10: Tsai-Wu bi-axial stress effect[2]

A notable term is that of F12 that in-cludes the unique term f ∗ (referred toas cross product term coefficient (CP)),where a range of −1 ≤ x ≤ 1 is com-mon accepted and a default value of 0 isassigned. The physical representation ofthis term is shown graphically in the Fig-ure 2.10 where the outline of the ellipsoidrepresents material failure or a Tsai-Wuvalue equal to or greater than 1. f ∗ beingequal to 0 would assume an ellipsoid cen-tered about the origin, while 1 and -1 would indicate +45◦ and −45◦ shift of the ellipsoidand the subsequent shift in combination of longitudinal and transverse stress at material


failure. This all being due to the change in composite material strength during expo-sure to a combined stress state. F12 can be calculated through an additional equationif the bi-axial stress at failure is known, but due to lack of material testing, then thiscalculation shall be neglected and a default value of 0 used for f ∗.

Differentiation between classical the Tsai-Wu failure index as presented prior and thevalue produced in Abaqus CAE must be established. The resultant value for the latteris equal to a scaling factor which all stress states (σ11, σ22, σ12) need to be divided bysimultaneously in order to produce IF = 1 for each state (see equation 2.8 [16]).

σ11

R,σ22

R,σ12

R⇒ IF = 1 (2.8)

Each of these terms can be inserted back into equation 2.7 with the inclusion of thenew scaling factor where IF = 1 and the following quadratic formulation presented inequation 2.9:

R = − 2[F1σ11 + F2σ22][F1σ11 + F2σ22] ±

√[F1σ11 + F2σ22]2 + 4[F66σ2

12 + 2F12σ11σ22](2.9)

Both the traditional Tsai-Wu value and the scaling factor R would be equal to 1 atfailure. However, a user-defined subroutine will instead be implemented for all analysis(denoted as UVARM) that is based on the traditional interpretation. Arguments canbe made for and against this technique but the core of such rests in ensuring greatercontinuity to literature and avoiding ambiguity for failure threshold values as they arecompared to design specifications.

2.2.5 Failure Criteria ApplicabilityThis report is based upon Tsai-Wu as the primary failure response both for model vali-dation and optimization. Questions may arise as to why additional failure criteria arenot being considered and the reason why Tsai-Wu is the preferred method among alter-natives. One must first consider that a full comparison could be presented to includemaximum stress, maximum strain, Tsai-Hill, etc. but would also be highlighting a trendthat is already established in literature for composite mechanics. For example, a studyknown as the “World-wide Failure Exercises” [17] examined the performance of variousfailure methods with respect to different loading cases. One of the main conclusionsto the report stated “The 12 models employed in the Part A of the WWFE-III variedin their complexity, maturity and their treatment of final failure. No two models gaveidentical predictions for any of 13 Test Cases” [17]. This means differences could alreadybe expected by using additional criteria with no clear insight into accuracy.

A common approach in design is to include numerous criteria knowing this trendand to incorporate the lowest index values for a conservative estimate. Based on this,

2.3 Loads and boundary conditions 15

justification shifts to how this failure index is being used. The intent with model vali-dation and optimization is based on precision rather than accuracy. Or in other words,the intent with model validation is to show consistency in magnitude (thus resultingin model confidence) while in the case of optimization to then compare the differences,both irrespective of the value accuracy. Of course, accuracy is of interest when indexvalues approach a threshold value of 1, which should then be included in later discussionif such a case is presented. Based on the precision, this means a sole criteria would besufficient for this application with the selection of such becoming rather arbitrary innature. However, Tsai-Wu still becomes the preferred method though based on the in-clusion of multi-directional loading effects (only unidirectional for max stress and strain)and to also raise awareness for bi-axial parameters (not included in Tsai Hill).

2.3 Loads and boundary conditions

2.3.1 LoadsThe loads utilized in the full blade FE models are comprised of 4 blade orientations witheach its own set of 4 discrete loads. These are derived based on safety factors applicableto the transfer from aero-elastic loading to design loads and from design to test loads.Figure 2.11a from the full blade FE model shows an example loading configuration wherethe blue vertical lines represent the discrete loads and are coaxial with the directionalvector indicated by the loading orientation. This example specially involves the pressureto suction orientation where the term pressure indicates the starting surface and suctionas the ending surface of the blade for the directional vector. These surfaces in additionto others can be visualized in Figure 2.11b and form the basis for the 4 blade orientationsfor loading (shown as red arrows in same figure) with the following nomenclature:

• Pressure to suction (P2S)

• Suction to pressure (S2P)

• Leading edge to trailing edge (L2T)

• Trailing edge to leading edge (T2L)


(a) Load orientation - S2P (b) Blade surface orientation

Figure 2.11: Loading diagrams

An additional detail into static testing involves the definition into net applied loadsfor these are the true loads applied during testing. These loads include compensation forthe weight of the clamps that the discrete loads are applied through which then differwith respect to the original target loads as derived from the design. The process formeasuring displacement prior to measurements being taken involves fixing the root ofthe blade in the test stand, installing the clamps, and then imposing a preload of 200N to stabilize any vibration that would compromise measurement. The final loads usedtesting and in all FE models will therefore be equal to the net applied loads reduced bysuch preload, thus ensuring that target loads are not exceeded in the analysis. Theseare included in appendix B through Table B.1 along with the respective radius for whicheach load is applied.

The value measured by devices used for recording blade displacement during testingis set to 0 following application of the pre-load so all recorded displacement from thestatic test will therefore capture the displacement of the final loads. However, a notableeffect of this procedure is the exclusion of the effect due to gravity. It’s assumed tobe acceptable based on the marginal difference in displacement that could be expectedto account for the blade mass in addition to the difficulty in capturing a true zero po-sition for the blade prior to mass displacement. In practical terms, this means thatdisplacement may indeed be marginally greater in the T2L and L2T loading configura-tions during normal operation since gravitational loading is acting in the same directionas such loads during normal operation. This is also means that observation into failureduring the test is a marginal overestimation for the P2S and S2P loading configurationssince the gravitational load applied during testing is not acting in the same directionas such loads during normal operation. These aren’t significant concerns since towerclearance, which is the sole displacement constraint, is not applicable for T2L and L2Tloading and additional failure margin for P2S and S2P loading would typically be abenefit.

The loads from the full blade model must then be translated into coupled bendingmoment and point loads for all reduced models. This is accomplished by applying a


moment and force vector to a referent point coincident with the center axis and tip-most plane of the reduced models. Figures 2.12a - 2.13b show this visually where theforce vector shown in yellow is oriented by the nomenclature loading direction. Whilethe moment vector in purple is oriented in direction of the axis of rotation to produce aresultant moment in the nomenclature loading direction as well (i.e. right-hand rule).

(a) P2S (b) S2P

Figure 2.12: Reduced model loading configurations

(a) L2T (b) T2L

Figure 2.13: Reduced model loading configurations (cont.)

Bending moment and shear force diagrams are first calculated based on the full bladeloads as a function of blade length and are shown graphically in Figure 2.14a and Figure2.14b. Values are then extracted at maximum chord length (shown by green verticalline) which are then summarized in Table 2.1. These in turn all used for all models inthe reduced blade state which include the reduced, scaled, and optimal models.


(a) Bending moment distribution (b) Shear force distribution

Figure 2.14: Radial loading distributions

Orientation Moment @ Max Chord (kNm) Shear Force @ Max Chord (kN)

S2P 141.1 21.43P2S 190.9 32.33T2L 34.24 5.343L2T 25.38 3.761

Table 2.1: Moment and shear force values at maximum chord

2.3.2 Boundary ConditionsOnce the loads have been established, one of the next decisions to undertake is how nodesare constrained on both the tip and root-most planes. In terms of the full blade model,the root section is bolted in place during testing which is assumed to constrain bothtranslational and rotational degrees of freedom. The load is also kinematically coupledto the surface nodes of the blade due to the load saddle used during static testing. Bothof these conditions are shown graphically in Figures 2.15a and 2.15b.


(a) Root boundary conditions (b) Load coupling

Figure 2.15: Full blade model - loading diagrams

In terms of the reduced blade models, the load reference node in the tip as wellas a reference node in the root are kinematically coupled to all available nodes in therespective cross-sections (see Figure 2.16a). Translational and rotational degrees offreedom are also constrained for the root nodes based on the assumed clamped conditionfrom the full blade model (see Figure 2.16b).

(a) Root boundary conditions (b) Load coupling

Figure 2.16: Reduced blade models - loading diagrams

A challenge exists for the case of the applied load for the reduced models in thatassumptions that prove valid for the full blade model may no longer be valid where thetip plane is expected to exhibit different behaviour due to it being a free edge. Referringback to Figure 2.15b, three key factors for the reduced blade models must be consideredto better mimic the behaviour of the physical saddle that applies load during testing forthe full blade model:

• The quantity of nodes from those available in the cross-sectional plane

• The total number of cross-sections

• The constrained degrees of freedom through those available in kinematic coupling

2.4 Optimization 20

Establishing the correct parameters for the reduced model will therefore take theform of parametric study to presented in the results section. The full blade model willbe used as the target baseline and an arbitrary load orientation as the pressure to suction(P2S) load case.

2.4 Optimization

2.4.1 GeneralThe goal of optimization in general terms is directed at achieving the best outcome.In the context of a structural design problem, this means maximizing or minimizing anobjective function comprised of state and design variables, subject to various constraints.Detailed definitions are as follows:

Objective function: A function that produces a value representative of the goodnessof the design. Tsai-Wu and volume are both examples relevant to this report thatwill be minimized to provide the best solution.

State variable: A vector or function of indicative of the structural response. Alsoreferred to as design response.

Design variables: A vector or function representing the parameters that can bealtered in order to induce change to the objective function. This can includemodification to geometry such as nodal position which is relevant to this report.

Constraints: Bounding values imposed on state or design variables.

An optimal value is known to be located at the maximum (in case objective max-imization) or minimum (in case of objective minimization) to a function or where thederivative is equal to 0. This forms of the foundation of sensitivity-based optimizationthat relies upon calculation of the objective function (e.g. Tsai-Wu) and constraint (e.g.displacement) derivatives with respect to the design variables (e.g. nodal positions).This is accomplished through the adjoint sensitivity method where the following generalexpression can be written for the objective function in equation 2.10 [3]:

g = g(u(x), x) + λ([K]{U} − {P}) (2.10)New terms include g as equal to the objective function value, g(u(x),x) for g as func-

tion of displacement u(x) and the design variable x, and λ as set of Lagrange multipliers.The gradient of g with respect to x can then be expressed through equation 2.11 [3]:

dg

dx= ∂g

∂x+ ∂g

∂u

du

dx+ λT [∂[K]

∂x{U} + [K]du

dx] (2.11)

λ is strategically chosen for reduction of terms and is shown in equation 2.12 [3]:

2.4 Optimization 21

λ = [K]−1 ∂g

∂u

T

(2.12)

This results in the reduced form of equation 2.11 as shown in equation 2.13 [3]:

dg

dx= ∂g

∂x+ λT [∂[K]

∂x{U}] (2.13)

2.4.2 TOSCAThe primary software intended for the optimization routine is that of TOSCA. A newstate variable or design response will be utilized to introduce failure criteria Tsai-Wuthat was previously not available. The governing function is based on stress, which thenmust be included in the partial derivatives and coupled to ∂g

∂ufrom equation 2.12 as

shown in equation 2.14 below. Also, to ∂g∂x

from equation 2.13 as shown in equation 2.15below as well.

∂g

∂u= ∂g

∂σ

∂σ

∂u(2.14)

∂g

∂x= ∂g

∂σ

∂σ

∂x(2.15)

In the case of Tsai-Wu (TW) as the objective g, this requires partial derivatives ofTsai-Wu with respect to stress tensors to be defined as follows:

∂TW

∂σ11= F1 + 2F11σ11 + 2F12σ22

∂TW

∂σ22= F2 + 2F22σ22 + 2F12σ11

∂TW

∂σ33= 0

∂TW

∂τ12= 2F66σ12

∂TW

∂τ23= 0

∂TW

∂τ13= 0

(2.16)

Values are null for σ33, τ13, τ23 as they are not included in calculation of Tsai-Wuwhich also highlights this criteria is exclusive to plane stress where values are null fromequation 2.4. These derivatives are then be included in the newly created user-definedsubroutine along with calculation of the Tsai-Wu term. Although the visibility into thealgorithm architecture for TOSCA is limited, it could then resemble a generic flow chart

2.4 Optimization 22

[18] specific to this report below. Terms presented include Imax as the maximum num-ber of iterations allowed from the routine, {NP} as nodal position (design variables),dT WdNP

equal to the derivative of the objective function TW (Tsai-Wu) with respect to de-sign variables (objective function gradient analogous to dg

dxpresented in equation 2.11),

and ϵ as a sufficiently small threshold. The primary intent of the routine being to up-date nodal position until the new value derived from the change in gradient is less than ϵ.

for i = 1:Imax

{NPold} = {NP}Solve [K]{D} = {P} (including {NP} in new formulation of [K])Calculate gradient vector(s) dT W

dNP

Find {NP} by bi-section method (as function of {NP}old and gradient vector(s))If ||{NP}old - {NP} || <ϵ ||{NP}||break

2.4.3 TOSCA BeadThere are several packages within the parent category of TOSCA that include topology,sizing, shape, and bead. Each of these possess strength and weaknesses when com-pared against the other and must be matched to objective function, design responses,constraints, and overall intent for the optimized structure in order to achieve adequateresults. There are three primary consideration that provide justification for selectingTOSCA Bead:

• Nature of nodal displacement

• Objective function selection

• Tsai-Wu implementation

The nature of nodal displacement can be linked to the overall degrees of freedom ofthe optimal blade structure. Material layup in this case is chosen to be held constant(mechanical properties, quantity and thickness of layers, etc.). This would mitigate po-tential risks in manufacturing since new layups often require iterative refinement in thevacuum infusion process to eliminate surface defects (e.g. air voids). The choice of objec-tive functions in volume and displacement are then closely tied to effective cross-sectionsize through this laminate constraint. Bead optimization is particularly efficient in alter-ing the cross-section geometry (and subsequent sectional modulus / bending stiffness)through surface beads (see Figure 2.17a). This effectively means nodal displacement isimposed uniformly through the laminate rather than unequal amounts between the innerand outer surface, thus complying with the material layup constraint. Tsai-Wu design re-sponse through a user-defined subroutine is also a feature supported on limited versionsof TOSCA and included in the case of bead. This then enables a comprehensive analy-sis into the potential benefits that a failure criteria can provide to an optimization study.

2.4 Optimization 23

The user can choose between a controller-based and sensitivity-based algorithm inwhich the latter will be utilized. It’s clear in the Figure 2.17b below that sensitivity-based algorithm enables a greater range of objective and constraint values comparedto controller-based. Displacement and stress (to formulate Tsai-Wu) are two primaryintended responses that are not included for controller-based, which then forms the basisfor selecting sensitivity-based.

(a) Resultant geometric displace-ment [19]

(b) Sensitivity and controller-basedcomparison [19]

Figure 2.17: TOSCA Bead characteristics

2.4.4 TOSCA Bead Definition2.4.4.1 Design domainThe design domain is based on the scaled blade model geometry. One of the choicesthat must be initially implemented is the selection of design variables or the nodesallowed to displace. These shall include all available nodes excluding three cross-sectionalplanes of nodes at the start and end of the blade section (see Figure 2.18a), along withremoving those of the webs as well (see Figure 2.18b). The motivation for excludingthe mentioned planes is too ensure a smooth transition into the root-most and tip-mostconstraints. Also, in the case of the root, the root inserts require a perpendicular lengthapproximately equal to the length of the bolts to ensure connection to the hub. However,the quantity of planes is arbitrarily selected and can be further refined based on laterrequirements. The webs nodes have also been removed since it’s assumed the webs shallremained in the same position in the transverse and longitudinal directions. The sharednodes between the web nodes and blade surface remain free which then means the websare allowed to displace in height. This also forces the surface area of the web elements

2.4 Optimization 24

adjacent to the shared nodes to vary while the remaining elements on the web remainconstant.

(a) Full view (b) Partial view including webs

Figure 2.18: Design domain - design variable nodal selection

An alternative to this method would be to include the web nodes into the total designnodes, and then impose directional geometric constraints (e.g. ∆ X = 0). However,initial analysis showed instabilities occurring where elemental areas exhibited a non-uniformity in scaling as the web height varied between iterations. The removal of webnodes then helped to stabilize such areas and decrease risk of element distortion andpremature termination in the optimization routine. A similar method could have alsobeen used for the root and tip-most planes by imposing geometric constraints ratherthan removing the nodes. The latter proves desirable simply due to the gained efficiencyin removing nodes that are intended to be static rather than defining an additionalconstraints to achieve the same outcome.

(a) Original and penetration surfacecross-sections

(b) Design response elements

Figure 2.19: Design domain - geometry and response

Constraints must nevertheless be considered and imposed (if necessary) on the se-lected design nodes. A penetration surface constraint shall be imposed where such nodaldisplacement is constrained to not exceed or penetrate a defined surface. The airfoil cross

2.4 Optimization 25

sections for both the scaled model and the original model are shown in Figure 2.19a,where the penetration surface is later generated by creating a lofted surface betweenthe larger airfoil splines. The nodal displacement for the scaled model, with startinglocations on the smaller splines in the figure, can then be defined to not penetrate thissurface during the optimization. The region(s) of the blade for which to calculate de-sign responses must also be established. These are shown in Figure 2.19b where unlikenodes, all available elements are selected. The primary motivation for implementinga penetration surface constraint is that existing manufacturing blade moulds can thenbe potentially reused since material can simply be added to the existing mould surface,thus reducing overall capital expenditure cost for implementing the root reduction. Oth-erwise, material may then need to be removed from the mould thus compromising itsintegrity and ultimately requiring new moulds to be manufactured. An alternative tothis constraint could have been to define a maximum nodal growth per airfoil sectionbut this would have proven to be inefficient as a unique value would need to be assignedto each section in the region of the linear ramp.

2.4.4.2 Design response configurationThere are several parameters to define in the configuration of the design responses whichare included as the following:

DEF_TYPE - provides access to analysis database values (e.g. stress, displace-ment, etc.).

LIST - specifies output of values.

TYPE - specifies the type of variable from established responses or user-defined.

(EL/ND)_GROUP - specific group for which the response is based.

GROUP_OPER - selection criteria for response value.

LC_SET - analysis type, load case, and sub-step definition.

Explicit design response values for these categories are provided in Table 2.2 below.It’s evident that unique design responses are provided for each loading case as in thecase of displacement and Tsai-Wu design response. A maximum value is also used forthese values since a constraint violation is based on a single rather than aggregate term.

2.4 Optimization 26

DRESP DEF_TYPE LIST TYPE (EL/ND) GROUP LC_SETLIST GROUP OPER LC_SET

Volume SYSTEM NO_LIST VOLUME ALL_ELEM SUMDisplacement L2T SYSTEM NO_LIST DISP_X_ABS Load Node MAX ALL,1,ALLDisplacement P2S SYSTEM NO_LIST DISP_Y_ABS Load Node MAX ALL,2,ALLDisplacement S2P SYSTEM NO_LIST DISP_Y_AB Load Node MAX ALL,3,ALLDisplacement T2L SYSTEM NO_LIST DISP_X_ABS Load Node MAX ALL,4,ALL

Tsai-Wu L2T SYSTEM NO_LIST USER_DRESP ALL_ELEM MAX ALL,1,ALLTsai-Wu P2S SYSTEM NO_LIST USER_DRESP ALL_ELEM MAX ALL,2,ALLTsai-Wu S2P SYSTEM NO_LIST USER_DRESP ALL_ELEM MAX ALL,3,ALLTsai-Wu T2L SYSTEM NO_LIST USER_DRESP ALL_ELEMS MAX ALL,4,ALL

Table 2.2: Design response configuration

2.4.4.3 Objective configurationConfiguration for the objective function is achieved in a similar fashion and examplevalues are provided in Table 2.3. Default values of 1 are assigned to the weighting factors(WF) which represents a scalar with which to multiply the resultant design response.The selection of MIN for target implies that the objective function seeks to minimize alldesign response terms as opposed to an alternative setting as MINMAX which wouldthen base the objective function on the design response of largest magnitude. The impactof varying the objective target and weighting factors will be investigated further whenTsai-Wu is used as the objective. This is not possible for volume as the objective due toit being the only term.

Objective DRESP WF TargetVolume Volume 1 MINTsai-Wu Tsai-Wu L2T 1 MIN

Tsai-Wu P2S 1Tsai-Wu S2P 1Tsai-Wu T2L 1

Table 2.3: Objective function configuration

2.4.4.4 Load CasesAll analysis excluding optimization has been based upon separate FE models for eachloading case (P2S, S2P, etc.). A singular general, static step is created within eachmodel which is then linked to the specific loading values. The optimization shouldinclude all loading cases in the same model in order to ensure the solution is globallyand not locally optimal. There are two directions to accomplish either through specifyingmultiple general, static steps or a singular static, linear perturbation where a load caseset containing all load cases can then be linked. The primary difference between thesetwo is the overall number of steps to accomplish the design intent. The choice to usegeneral, static steps requires intermediate steps as loads equal and opposite to that ofthe prior step in order to return the geometry to its original base state. Failing to doso will apply loading sequentially onto the prior step when the loads are intended to

2.4 Optimization 27

be independent. This is done automatically for a static, linear perturbation step whereeach load case is applied relative to the base geometry at the start of the step. Thisis turn results in a lower overall number of steps and thus selected as the preferredmethod based on the gain in computational efficiency. However, this creates a separatechallenge in being able to view the detailed distribution of Tsai-Wu values generated fromthe UVARM subroutine. Such distribution is not inherent to the resultant optimization.odb file since UVARM subroutine is not compatible with linear perturbation steps. Inother words, a post-processing analysis must be made where the model used for staticanalysis that contains a general, static step is updated with the optimal nodal positionsin order to view the revised distribution of Tsai-Wu values generated from the UVARMsubroutine.

2.4.4.5 Additional ParametersNodal move - a scalar selected between 0.0 and 1.0 (default value = 0.1). This ismultiplied by the maximum allowable displacement (i.e. distance between nodesand restriction) in order to generate the nodal displacement limit per iteration.

Nodal update - can selected as normal or conservative and is linked to controlof the method of moving asymptotes (MMA). In order to understand the latter,a general comprehension of convexity must be established and the nature of thestructural problem. Figure 2.20 illustrates the curvature of convexity in which afunction, where a line drawn between x1 and x2, is said to be convex when theline lies above (or below for concave) or on the function plot. This condition isviolated then for a non-convex function where the drawn line is above and belowbased on observed intersections. It’s understood in literature that “most problemsin structural optimization are nonconvex” [3], and based on the inherent difficultyin solving nonconvex problems, convex approximations are used to solve these.One of the primary challenges to overcome when using this approach is rate ofconvergence where the MMA approach mentioned prior (via nodal update) canserve to resolve this through introducing asymptotes that vary during iterationsand alter such approximations.

Figure 2.20: A strictly convex (left), convex (middle), and a non-convex(right) [3]

2.4 Optimization 28

A normal opposed to conservative setting for nodal update would then result inmore rapid convergence. A larger nodal move can also serve the same benefit butsetting both too aggressively can also risk forcing the the solution to an undesiredlocal minima.

Filter radius - a setting used to modify sensitivities as ”weighted averages of thesensitivities in mesh-independent neighborhoods” [4]. This is intended to avoid“checkerboard” patterns (see Figure 2.21) patterns in the resultant optimal geom-etry where are high and low values in elements produce the same result comparedto a more homogeneous solution. A larger value for the radius would include agreater number of neighboring elements used in the weighted average calculation.A default value of 4 is used for the purpose of this study and specified as a relativevalue to medium edge length.

Figure 2.21: Filter radius - checkerboard phenomenon[4]

CHAPTER 3Results and Discussion

3.1 Material

3.1.1 PropertiesAn initial task performed prior to generating results was establishing a baseline set ofmechanical properties and orientations and ensuring this set was consistently definedin all FE models. This was especially pertinent in the case of the original full bladeFE model where material strength data was discovered to be incomplete due to designspecifications based in maximum strain instead of maximum stress. Consequently, con-siderable variation in location and magnitude for failure index values would be created,thus leading to poor conclusions and determinations when comparing models. Multipletables of material properties were first assessed and only one of which seemed to themost comprehensive in at least containing partial data for all material (see Figure B.1bin Appendix B). This table in addition to one specific to core (see Figure B.1a in Ap-pendix B) was then used in generating the baseline data for all models but also createdopportunity for assumptions to be made. Complete data is provided in Table 3.1 belowto include all materials and their respective mechanical properties along with detailedbackground into assumptions provided after.

Mechanical PropertyE1 E2 NU12 G12 G13 G23 11-T 11-C 22-T 22-C 12 CP

MATERIAL MPa MPa MPa MPa MPa MPa MPa MPa MPa MPaUNIAX 37800 11100 0.24 3270 3270 3270 360 257 25 64 17 0.00BIAX 9550 9550 0.62 19100 3270 3270 69 65 69 65 56 0.00TRIAX 18700 10900 0.55 7720 3270 3270 186 152 31 52 42 0.00CORE 49 49 0.40 29 29 29 3 1 3 1 1 0.00GLUE 3009 3009 0.30 3009 3009 3009 ∗ ∗ ∗ ∗ ∗ 0.00GELCOAT 2000 2000 0.30 2000 2000 2000 ∗ ∗ ∗ ∗ ∗ 0.00CHOP 13600 13600 0.32 5130 5130 5130 56 56 56 56 24 0.00COMBI 21100 19800 0.18 4030 3270 3270 69 65 69 65 56 0.00UD90 11100 37800 0.24 3270 3270 3270 25 64 360 257 17 0.00

Table 3.1: Material properties - complete

3.1.2 AssumptionsMechanical properties are often derived through experimental methods and the inclusionof such can pose an issue if time scales are compressed. This was the case in terms of theOlsen combi material where compressive, tensile, and shear strength were absent from

3.1 Material 30

supplied data. The construction of this material involves a biax and CSM (chop strandmat) layered together. A conservative assumption was first used for values based off firstply failure which a single ply in a laminate will fail when it’s strength is exceeded by theloading. The conservative portion being to treat the material’s overall strength, insteadof laminate in this case, by the lowest strength properties in each direction betweenthe UD (oriented in 0° and 90°) and CSM. However, initial analysis revealed excessivefailure in this material for the full blade model which indicated the approach was tooconservative considering no failure was present in the structural test. Therefore, thestrength properties of biax were used, which are greater and based on the assumption ifthe CSM ply fails, the biax can still carry the load.

Two additional materials in gel coat and glue also lacked defined strength values.Fibers in composites are the primary load carrying members, which are absent in thesematerials. This fact combined with their low thickness provides the basis for the as-sumption that they do not contribute to the strength of the structure. For this reasonthe strength values are then set equal to one order of magnitude larger than the higheststrength in the other materials, subsequently producing a low Tsai-Wu index value. Thislarge number is denoted as ∗ within the table to indicate its exclusion from the analysis.Apart from strength, the shear modulii G13 and G23 also were missing in the case of allmaterials. These values for uniaxial, biaxial, triaxial, Olsen combi, and UD90 were allset equal to the shear modulus G12 for a uniaxial laminae as a reasonable approximationsince they all share the same constituent materials with orientation being the differingfactor. Fiber directions are constrained to in-plane variation which should then maintainuniform properties out-of-plane as in the case with G13 and G23. In the case of materialassumed to be isotropic (glue, gelcoat, core, chop), these values were then equal to theshear modulus G12 for each material.

A final detail to review concerning mechanical properties concerns material orienta-tion. This is only pertinent in the case of the webs where instead of the fiber directionfor the material aligned with the longitudinal axis of the blade, the direction is typicallyoriented with a 45° offset. This is intended to align the shear forces between the twoshells with the web fiber direction and subsequently increase stiffness. This was discov-ered to be set in original full blade FE model to 0° which then prompts the question intothe specification for lamina orientation. Properties can be defined in global coordinatesfor lamina but provides no explicit indication to whether the fibers are positioned at0°/90° or -45°/45° relative to the X direction. It’s only through hand calculation thatthe answer can be provided in place of detailed material data sheets. Equation 3.1 [14]shows the relation between the resultant modulus in axial direction Ex, and the laminamodulii E/G and Poisson’s ratio v with respect to the longitudinal (L) and transversedirections (T).

1Ex

= 1EL

cos4θ + (−2vLT

EL

+ 1GLT

)sin2θcos2θ + 1ET

sin4θ (3.1)

Based on the material properties for biax included in appendix B along with an input

3.2 Full blade model 31

of 45°, the resultant axial stiffness equates to 22.4 GPa which is much greater than 9.6GPa for the same direction from the material properties. If the lamina were positioned at0°/90°, then a 45° offset should result in a lower stiffness due to the fibers no longer beingin alignment with the axial direction. This proves the fibers are indeed at +45°/-45°since a 45° shift aligns the fibers with the axial direction and creates a larger modulus asshown in the calculation. The webs are then defined with a 0° alignment for all models.

3.2 Full blade modelThe first benchmark of comparing structural test and numerical data must be achievedto gain confidence in the full blade FE model. The key findings from the structural statictest include both displacement and the physical observation of failure (crack formationand sound). Actual values for tip displacement will be compared to evaluate the model’saccuracy but all failure values are instead assumed to be less than 1 since no failure wasreported during the test and explicit values are not possible to obtain.

3.2.1 Displacement and Tsai-WuIn terms of displacement, the comparison is presented in Table 3.6 below with detailedplots available for reference in appendix A through Figure A.1a - A.2b. The differenceappears to vary both in the positive and negative direction between both models. How-ever, all tip displacements are of the same sign and with a maximum of increase of 28.33% from the full blade to structural test. This may then imply that the physical bladepossessed a greater stiffness than what is calculated by the full blade FE model. Mate-rial properties (actual vs. expected modulus) and manufacturing conditions (e.g. fibervolume fraction, orientation, position, etc.) are both viable categories that can impactstiffness. It’s known that additional reinforcement layers beyond those documented inmanufacturing drawings are often incorporated into Olsen Wing’s manufacturing processand would also create significant influence to this property. Apart from material, thequality of measurements can also be called into question given the substantial variationin magnitude and sign between the four loading cases at R3.5 and R6.1. Positioningof loads and mass compensations (clamps and preload) can also be factor if loading isplaced further toward the tip of the blade or if the mass was over-estimated relativeto the values actually used in testing. A sole source may not explain the percent dif-ference in its entirety but the probability increases with respect to the aggregate total.Consequently, the goal of presenting these potential sources of error is to show that thedisplacement for the full blade model is indeed reasonable and can be used for furthermodel validation.


DisplacementLoad Orientation R3.5 R6.1 R10 R13 R14.3

Structural Test S2P 0.014 0.076 0.482 1.029 1.288 (m)P2S 0.023 0.066 0.583 1.273 1.592 (m)T2L 0.003 0.011 0.038 0.073 0.088 (m)L2T 0.003 0.008 0.029 0.056 0.066 (m)

Full Blade Model S2P 0.013 0.080 0.522 1.198 1.515 (m)P2S 0.018 0.106 0.681 1.516 1.910 (m)T2L 0.003 0.011 0.042 0.084 0.103 (m)L2T 0.002 0.008 0.033 0.068 0.085 (m)

Percent Difference S2P (-) 8.57 (+) 4.61 (+) 8.28 (+) 16.41 (+) 17.60 %(Full : Test ) P2S (-) 23.83 (+) 60.34 (+) 16.89 (+) 19.09 (+) 19.99 %

T2L (+) 2.37 (-) 0.78 (+) 0.74 (+) 14.46 (+) 16.48 %L2T (-) 26.08 (+) 0.52 (+) 12.96 (+) 22.30 (+) 28.33 %

Table 3.2: Blade displacements - structural testing and full blade model

Figure 3.1: Linear regression - blade lengthversus tip displacement constraint [5]

A detail to be considered later for opti-mization concerns the magnitude of maxi-mum tip displacement in both sets of datarelative to the allowable. This can bechallenging to determine since the bladedesign is not driven by a global tip con-straint, but instead the capability to be in-stalled on various turbines. In other words,the end-user will treat tip displacement asan inherent characteristic to the blade andin the case of P2S loading, will match theblade to a turbine with sufficient towerclearance. However, in the case of opti-mization, margin identification is critical so an over-constraint condition is avoided andthe optimal solution is representative of the true design domain. Methods exist for de-termining an approximation into global tip constraints and is highlighted in Figure 3.1,where again in the case of P2S loading and tower clearance, a linear regression is con-structed based on a separate case study of various turbine lengths versus local end-usertower clearance. The subsequent equation generated by such fit then results in a towerclearance of 3.1 m as its applied to the 14.3 m blade included in this report. This meansthe blade is using 51% and 62% of the allowable tip clearance for the structural test andfull blade model respectively. A greater challenge exists in arriving at an approxima-tion for other loading conditions since there’s a lack of physical barrier as in the towerthat constrains the magnitude. Given this fact and the considerable under-utilizationof the P2S loading constraint, a conclusion can be made that tip displacement (or rootdisplacement to be discussed later) could increase while creating minimal risk to bladeusability.

It’s also important to investigate failure criteria values since as no observable failurewas evident during structural testing which means failure index values should be lessthan 1. Table 3.3 shows such resultant global maximum Tsai-Wu values. One of the


trends that’s most apparent is values indicate that failure exists for the P2S loadingconfiguration with IF = 1.022 exceeding the failure threshold of 1. The table presentedprior indicated that the full blade model resulted in larger displacements than that ofthe structural test, which would increase the likelihood of Tsai-Wu values being over-estimated. The value is also marginally exceeding failure so a decrease in Tsai-Wu basedon smaller displacements in the structural test would then have higher probability offalling below the failure threshold, which is then confirmed through no observable failurein the structural test.

Load Orientation Maximum Tsai-WuS2P 0.559P2S 1.022T2L 0.076L2T 0.107

Table 3.3: Tsai-Wu - full blade model

Closer inspection into the maximum failure index location for P2S loading (see Figure3.2b) reveals it being localized near the tip. This is important considering the geometricchange will involve the root portion of the blade, thus showing capacity for this regionto experience larger loading without exceeding failure. This also creates justification toassume that material can remain constant based on the required geometric change asopposed to larger failure values which may then require geometry, stiffness, and strengthof the laminate to be altered to ensure failure is not exceeded. Plots for other loadingorientations also show a similar trend with maximum values located away from the rootregion (see Figures 3.2a - 3.3b), thus placing further confidence into success for themodification.

(a) S2P (b) P2S

Figure 3.2: Full blade model - maximum failure index locations

3.3 Reduced model 34

(a) T2L (b) L2T

Figure 3.3: Full blade model - maximum failure index locations (cont.)

Further investigation could also be placed into the correlation between the maximumindex locations and those where loads are applied. Load coupling constraints can createlocalized stress concentrations and such maximum locations appear to local and close tothe approximate locations. However, this report will focus on validation of new modelsrather than existing models, but highlights the importance of investigating load couplingconstraints as it applies to the reduced blade model in the next section.

3.3 Reduced modelOnce the first benchmark was completed through the structural test comparison, areduced model was created that was based with the conventional shell elements describedin section 2.1.4 (S8R) and the extracted loading stated in section 2.3.1. The non-linearoption NLGEOM was also enabled to be consistent with the full blade model. A seriesof studies are performed with respect to the P2S loading case to reduce complexityand gain confidence into parameter selection. A mesh based on 0.09 m global seedingwas initially used for such studies but will will also be further verified through meshconvergence. The second benchmark of all loading cases from the reduced to full blademodel are then presented at the conclusion of this section.

3.3.1 Boundary conditionsDisplacement and Tsai-Wu index values of the reduced model could then be comparedto the full blade model by creating a cross-sectional cut of such model at the maximumchord radius position, thus serving as the second benchmark. An immediate result ofthe study was the substantial edge effect that produced excessive stress concentrationsand large subsequent Tsai-Wu values. Often IF would be greater than 1 which is deemed


unreasonable as no failure was detected during the structural testing. Therefore a para-metric study was performed to investigate the three factors described in section 2.3.2.An overview of the study is presented in Table 3.4 below with detailed explanation intothe the conditions in later sections. To provide a clear comparison into the distributionbetween the full blade and reduced blade model, the maximum Tsai-Wu index from thefull blade model for each desired loading case was used as a contour limit.

Study Nodes Kinematic coupled DOF’s

1 Full Translational / Rotational2 Full Translational3 Web exclusion Translational / Rotational4 Web exclusion Rotational5 Web exclusion / Node extension Translational / Rotational

Table 3.4: Boundary condition parametric study

3.3.1.1 BaselineThe Tsai-Wu distributions and maximum displacement magnitudes shall only be com-pared (for P2S loading) in the studies which excludes displacement distribution entirelybased on minimal observable deviation of such plots. However, a comparison can bemade for these distributions between the full blade model and those of the reducedmodel based on the final preferred boundary condition by comparing Figures A.3a - A.4to Figures A.5a - A.6b in appendix A respectively. The maximum displacement valuesprovided in the studies below can also be matched to the maximum value shown in suchplots. A maximum Tsai-Wu index of IF = 0.225 is shown in the case of the full blademodel for the P2S loading case with the largest value located centrally on the suctionside (see Figure 3.4a). The maximum tip displacement being 6.5 mm with consistentpropagation from root to tip (see Figure 3.4b).

(a) Tsai-Wu (b) Displacement

Figure 3.4: Full blade model partial - Tsai-Wu and displacement- P2S loading


3.3.1.2 Case 1

Figure 3.5: Kinematic coupling nodes - fullairfoil cross-section

The conditions imposed for this study in-clude fully coupled transitional and rota-tional degrees of freedom through the kine-matic coupling constraint. All availablenodes in the tip cross section are also usedon both the outer airfoil and web surfaces(see Figure 3.5). Figures 3.6a shows the re-sults of the study where there appears tobe no propagation at the free edge in Tsai-Wu values exceeding the maximum base-line value. The maximum displacement isalso calculated to be 4.6 mm (not shown). The overall distribution in failure index valuesappear to be similar to the full blade model with the exception of the max location withit being an isolated location near the tip on the the pressure side.

3.3.1.3 Case 2The conditions imposed for case 2 include only coupled transitional degrees of freedomwhere those of rotational remain free. All available nodes in the tip cross section arealso used on both the outer and web surfaces in accordance with the figure from theprevious case. Figures 3.6b shows the results of the study where there appears to bepropagation at the free edge in Tsai-Wu values exceeding the maximum baseline value(shown in white/grey), as well as marginal gain to the maximum displacement of 4.8mm. Apart from the free edge, the failure index distribution appears to be similar tothe full blade model where stress concentrations exist on the mid-pressure side of theblade.

(a) Case 1 (b) Case 2

Figure 3.6: Case 1 and 2 - Tsai-Wu - P2S Loading


3.3.1.4 Case 3

Figure 3.7: Kinematic coupling nodes - webexclusion

The conditions imposed for case 3 includefully coupled transitional and rotationaldegrees of freedom through the kinematiccoupling constraint. However, not allavailable nodes in the tip cross section areused where the web surfaces are excluded(see Figure 3.7). Figures 3.8a shows theresults of the study where as in case 1there appears to be no propagation at freeedge in Tsai-Wu values exceeding the max-imum baseline value. The maximum dis-placement as also 4.6 mm. The distribution appears to be similar to full blade modelwith the exception being two isolated locations near the tip of the pressure side and alsono the free edge of the section side.

3.3.1.5 Case 4The conditions imposed for case 4 include only coupled transitional degrees of freedomwhere those of rotational remain free. Once again, the same nodes in the tip crosssection are used as shown in the figure from the previous case. Figures 3.8b shows theresults of the study where like case 2, appears to be greater propagation at the free edgein Tsai-Wu values exceeding the maximum baseline value (shown in white/grey). Themaximum displacement is also calculated to be 5.2 mm. Apart from the free edge, thefailure index distribution appears to be similar to the full blade model.

(a) Case 3 (b) Case 4

Figure 3.8: Case 3 and 4 - Tsai-Wu - P2S Loading


3.3.1.6 Case 5The conditions imposed for case 5 include fully coupled transitional and rotational de-grees of freedom through the kinematic coupling constraint. However, not all availablenodes in the tip cross section are used where the web surfaces are excluded (see Figure3.9a). In addition, multiple layers of nodes are used to attempt to minimize potentialstress concentration on the free edge. Figures 3.9b shows the results of the study whereunlike the prior studies, failure values are minimized on the free edge but have shiftedlarger magnitudes to the root-most coupled nodes, thus creating a similar region to theoriginal free edge. The maximum displacement is is calculated to be 4.7 mm. The dis-tribution also appears to be similar to the full blade model excluding two locations nearthe tip of the pressure side.

(a) Kinematic coupling nodes - web exclusionand extension

(b) Case 5

Figure 3.9: Case 5 - nodes and Tsai-Wu - P2S Loading

3.3.1.7 DiscussionIt appears that enabling rotational degrees of freedom results in an increase in displace-ment, and thus closer to that of the full blade model. However, this creates the adverseimpact of increasing the surface area of stress concentration on the free edge opposedhaving these restricted. In terms of impact, stress concentrations at the free edge wouldhave a greater detrimental impact to the later optimization study since less marginexists for failure values as opposed to displacement. This means an underestimationinto displacement would not influence the optimal design opposed to an over-estimationfor Tsai-Wu where the free edge would then be driving the design based on inaccuratevalues. Therefore, either case 1 or 3 are the most suitable with respect to this concern.The maximum Tsai-Wu value for case 1 is IF = 0.44 compared to IF = 0.85 for case 3.Considering the same value for the baseline is IF = 0.32, then case 1 is the most suitableloading condition.


3.3.2 Section ExtensionThe analysis thus far has been based on applying the loading at maximum chord loca-tion. To add further confidence into the validity of this approach, the final section wasextended by 0.250 m and 0.500 m with the loading applied to the new tip-most nodes.The bending moment was reduced due to the distance reduction to applied loading. Theshear force remained the same due to the extension not violating the position of the firstapplied load. This new loading set is shown below in Table 3.5.

Load Orientation Extension length (m) Moment @ Tip Nodes (kNm) Shear Force @ Tip Nodes (kN)

P2S 0.250 182.8 32.330.500 190.9 32.33

Table 3.5: Section extension - load and displacement

Figures 3.10a and 3.10b below show the Tsai-Wu distribution for the 0.250 m and0.500 m extension respectively. Regardless of the extension, a cross-sectional cut wasmade to only include the original geometry up to maximum chord. The distributionsseem to differ from the original reduced model in that the distance from the tip-mostnodes to the maximum Tsai-Wu location appears to increase with each progressive in-crease in length. The overall magnitude also displays a similar trend. Overall, thestudy doesn’t show an improvement to the distribution and an adverse impact to thetotal Tsai-Wu magnitude, thus the original assumption of applying loading at maximumchord location will be used.

(a) 0.250m extension (b) 0.500m extension

Figure 3.10: Extension - Tsai-Wu - P2S loading

3.3.3 Mesh convergenceA mesh convergence study is performed in accordance with the discussion from section2.1.5 in interest of reducing error. Figures 3.11a and 3.11b below show the Tsai-Wu


distribution for 0.02 m and 0.045 m approximate global seeding size respectively. Asmaller seeding size increases the total number of nodes and thus also the mesh resolution.It’s evident that the distribution is consistent with the original seeding configurationalthough the maximum values and location differ. In the case of .045 m seeding, themagnitude increases and but remains in the same location. In the case of 0.02 m seeding,the magnitude then decreases to that of the original configuration but then shifts locationfrom the pressure to suction side. Displacement also appears to remain constant throughall cases. 0.09 m seeding will therefore be used as the default mesh size for subsequentreduced models based on the following conclusions:

• Inconsistency in developing proportionality between mesh size and Tsai-Wu value

• Marginal difference in magnitude between maximum Tsai-Wu value for full blademodel (see IF = 0.225 in next section) compared to IF = 0.255 for reduced blademodel

• Increase computational efficiency with using a lower resolution

• Maximum size achievable before noticeable discretization error was observed rela-tive to original CAD surface

(a) Fine mesh (b) Medium mesh

Figure 3.11: Mesh discretization - Tsai-Wu - P2S Loading

Mesh Global Seed Size Element Quantity Element Type Maximum Tsai-Wu Displacement

Course 0.09 (m) 1898 S8R 0.255 0.0043 (m)Medium 0.045 (m) 6325 S8R 0.261 0.0043 (m)

Fine 0.02 (m) 22140 S8R 0.255 0.0043 (m)

Table 3.6: Mesh convergence - Tsai-Wu and displacement


3.3.4 Displacement and Tsai-WuOnce all studies had been conducted and updated parameters implemented for the re-duced blade model, the comparison was then be made from the full blade to the reducedblade model for the remaining load configurations. A table containing explicit magni-tudes for failure index and displacement values is provided at the end of this sectionwith Tsai-Wu plots presented prior to this. The P2S configuration is not covered due toit’s prior use in performing the mentioned studies.

3.3.4.1 S2PS2P loading case is shown below where it’s evident the max location is indeed consistentbetween models (see Figures 3.12a and 3.12b). It may same unusual for an abrupttermination in the max location as evident in the transverse and longitudinal directions.However, thickness investigation reveals that uniax contains the largest Tsai-Wu valueswhich then correlates to the abrupt distribution based on this material tapering to 0thickness in the longitudinal direction and transfers to an entirely different layup in thetransverse direction.

(a) Full blade model (b) reduced blade model

Figure 3.12: Full and reduced comparison - Tsai-Wu - S2P loading

3.3.4.2 T2LThe T2L loading cases provides greater variation between the two models in terms ofthe maximum Tsai-Wu location where such value is located on the TE pressure sidefor the full blade and on the trailing edge for the reduced blade (see Figures 3.13aand 3.13b). However, both models appear to have concentrations in roughly the samelocations to different magnitudes. Perhaps the choice of boundary conditions provide agreater benefit to the P2S and S2P loading confirmations in terms of uniformity. This isthen an adverse impact to limiting the studies to only the P2S loading condition whereaccuracy may be gained when preferred conditions are representative of all loading cases.The concentration location does appear reasonable though for the reduced model giventhis location would be further from from the neutral axis for bending (for T2L loading)and closer to the root where bending stresses are greater.


(a) Full blade model (b) Reduced blade model

Figure 3.13: Full and reduced comparison - Tsai-Wu - T2L loading

3.3.4.3 L2TThe conclusion from the T2L loading case can be made for the L2T loading cases whereroughly the same magnitudes and distributions are shown for maximum Tsai-Wu (seeFigures 3.14a and 3.14b).

(a) Full blade model (b) Reduced blade model

Figure 3.14: Full and reduced comparison - Tsai-Wu - L2T loading

3.3.4.4 DiscussionTable 3.7 below shows the complete overview for maximum Tsai-Wu and displacementvalues. The sign convention and magnitude for displacement percent difference appearto be consistent in the range from -33.3% to -36.4%. This would imply that the reducedmodel is stiffer than the full blade model. Tsai-Wu values are also consistent in signconvention with slightly greater variation in magnitude from a range of +11.2% to+27.9%. A noteworthy observation is typically lesser displacement should lower stressand lead to lower failure index values which is contradictory to what is recorded. In termsof such index values, these could be attributed to the tendency for stress concentrationsto accumulate in a conventional shell model versus continuum shell model. Ply thicknesschanges form sharp transitions in a conventional shell model instead of being controlledin a smooth contour as would be the case with a continuum shell model where the both

3.4 Scaled model 43

surface splines of the laminate are defined. In terms of displacement, the uncontrolledoffset of conventional shells from the original reference surface also creates overlap inmaterial that can create differences in material properties in transition regions suchas the web to shell interface, ultimately impacting the bending stiffness of the section.These values are therefore viewed as accepted and thus ensuring validity in using thesame model parameters for the scaled model.

DisplacementLoad Orientation R2.178 Maximum Tsai-Wu

Full Blade Model S2P 0.0047 (m) 0.169P2S 0.0065 (m) 0.225T2L 0.0015 (m) 0.052L2T 0.0011 (m) 0.043

Reduced Blade Model S2P 0.0031 (m) 0.188P2S 0.0043 (m) 0.255T2L 0.0010 (m) 0.064L2T 0.0007 (m) 0.055

Percent Difference S2P (-) 34.0 % (+) 11.2 %(Reduced : Full) P2S (-) 33.8 % (+) 13.3 %

T2L (-) 33.3 % (+) 23.1 %L2T (-) 36.4 % (+) 27.9 %

Table 3.7: Blade displacements and Tsai-Wu - full blade model and reduced blade model

3.4 Scaled model

Figure 3.15: Scaling distribution

The scaled model was created by assigning an ar-bitrary geometric scaling to the existing reducedblade model in order to then provide comparisonto the results generated through the later optimiza-tion routine. The scaling is shown graphically inFigure 3.15 in terms of percentage to the originalairfoil sections. The root diameter is held constantfor an equal number of cross sections as the originalreduced model, and then increased linearly to theconstraint of the maximum chord geometry. Theentirety of the reduced model excluding the geome-try (loads, boundary conditions, material, etc.) areheld constant.

3.4.1 Displacement and Tsai-WuThe resultant Tsai-Wu distributions are then shown below with displacement distribu-tions again located in appendix A in Figures A.7a to A.8b. A summary table is providedat the conclusion of the section. Failure index distributions for the reduced blade model

3.4 Scaled model 44

are once again presented as duplicates to aid in the side-to-side comparison to the newscaled model distributions.

3.4.1.1 P2SThe overall distributions for P2S loading appear to be same with the exception for themaximum value location (see Figures 3.16a and 3.16b). This was isolated near the tip ofthe pressure side for the reduced model but has shifted to the trailing edge transition forthe scaled model. Such behaviour would be more problematic if the location possesseda greater coverage area but since both are small and isolated, the probability of thesebeing an erroneous stress concentration is greater, therefore requiring lesser focus intothe difference.

(a) Reduced blade model (b) Scaled blade model

Figure 3.16: Reduced and scaled comparison - Tsai-Wu - P2S loading

3.4.1.2 S2PThe overall distributions for S2P loading are once again similar and unlike the priorloading configuration, the coverage area for maximum location is greater but also locatedin the same location near the middle of the pressure side (see Figures 3.17a and 3.17b).

3.4 Scaled model 45


Figure 3.17: Reduced and scaled comparison - Tsai-Wu - S2P loading

3.4.1.3 T2LThe overall distribution also appear to be similar for T2L loading and also have thesame locations for maximum value at the trailing edge transition region with significantcoverage area (see Figures 3.18a and 3.18b).


Figure 3.18: Reduced and scaled comparison - Tsai-Wu - T2L loading

3.4.1.4 L2TThe overall distribution also appears to be similar and have the same locations formaximum value at the trailing edge transition region with significant coverage area (seeFigures 3.19a and 3.19b).

3.4 Scaled model 46


Figure 3.19: Reduced and scaled comparison - Tsai-Wu - L2T loading

3.4.1.5 DiscussionThese plots show a consistent trend that scaling has produced marginal impact to failureindex concentrations. Explicit values for Tsai-Wu and displacement can be found in thetable below. It’s clear that the scaling results in greater displacement values and thoseof Tsai-Wu as well. The latter values are all less than 1 which indicates that the scalingfulfills the design intent of no failure. Also, based on the discussion from section 3.2.1,an increase of 69.8% or 3 mm when compared to the reduced model would not presenta violation for tip displacement in terms of tower clearance. It’s also worth noting thespecific percentage increases for Tsai-Wu since it’s clear that the T2L value differs by afactor of 2 relative to the remaining loading conditions. This shows that failure indexvalues for different loading cases possess varying sensitivities to changes in geometry andare not uniformly impacted.


Scaled Blade Model S2P 0.0052 (m) 0.217P2S 0.0073 (m) 0.302T2L 0.0015 (m) 0.078L2T 0.0011 (m) 0.065

Percent Difference S2P (-) 67.7 % (+) 15.4 %(Scaled : Reduced) P2S (-) 69.8 % (+) 18.4 %

T2L (-) 50.0 % (+) 53.1 %L2T (-) 57.1 % (+) 18.2 %

Table 3.8: Blade displacements and Tsai-Wu - scaled blade model

Overall, these results can be viewed from two primary vantage points as fulfillingdesign intent with no further redesign or in the fact that these results are coincidental.The latter creates the opportunity for a methodology that will guarantee compliancein the future studies (assuming problem is not over-constrained) while also providingthe best solution for this problem. Such a solution can be viewed from two vantagepoints where either a stronger blade is desired, in which case the sectional moduluswould need to increase with the intent to lower displacement and failure values. The

3.5 Optimal model 47

second being that the scaled geometry can be seen as over-dimensioned considering themaximum value for loading cases is IF = 0.302 relative to an absolute failure thresholdof 1, in which case the volume can be decreased. Both cases present the opportunity foroptimization and the basis for the subsequent analysis.

3.5 Optimal model

3.5.1 Performance comparisonConfidence must be achieved for correct use of TOSCA Bead in generating an optimalgeometry. An initial study was performed to compare results from the intended beadoptimization routine to that of the built-in matlab optimization function Fmincon. Acantilever tube exposed to a gravitational load (see Figure 3.20a) was selected as thebase geometry in order to isolate diameter as the primary design variable. The intentwould be then for a clear transition in diameter where maximizing such value, and thesubsequent sectional modulus, would no longer benefit the objective function but providean adverse impact due to the increased mass moment. The beam is also discretized intoN number of sections with the gravitational load calculated about the mean radius foreach section. The beam properties can be found in Table 3.20b below.

(a) Discretization and load diagram

Length (m) N ρ ( kgm3 ) twall (m) E (Pa)

0.500 34 8050 0.010 200E9

(b) Geometric and material data

Figure 3.20: Cantilever tube setup


The optimization routine details are as follows:

Objective: δ (at tip node)Design variables: DT ube

Constraints: Dmini = 0.09 m, Dmin

i = 0.130 m, twall = 0.01 mMathematical expression:

(SO)nf

minimize δ(N)Dtube ∈ RN

s.t.{[Dmin

i ≤ Di ≤ Dmaxi ]

The objective function is formulated by first calculating curvature k for each meanradius through equation 3.2 where M is equal to the moment about the radius, and EI isthe flexural rigidity, both of which found in previous sections. The calculated curvaturesk are then stored as a vector for subsequent calculation.

k = M

EI(3.2)

The angle θ at each mean radius can then be calculated through equation 3.3 wherermean is the mean radius, and the values (i+1) and (i) refer to the next and previousradius respectively. The value of i is equal to the total number of radii.

θ(i + 1) = θ(i) + 12

(k(i + 1) + k(i))(rmean(i + 1) − rmean(i)) (3.3)

The displacement u at each mean radius can then be calculated through equation3.4 with terms previously defined.

u(i+1) = u(i)−θ(i)[rmean(i+1)−rmean(i)]−[16

k(i+1)+13

k(i)][rmean(i+1)−rmean]2 (3.4)

As an additional benchmark, the static displacement was calculated in both programsas a function of position. The max displacement at the tip using beam theory (seeequation 3.5) was also used for comparison where is P is the load due to gravity, a isequal to half the beam length, E the modulus of elasticity, I the moment of inertia of atube, and l equal to the beam length.

δ = Pa2

6EI(3l − a) (3.5)

The results for static displacement can be found in Figure 3.21a below where thereappears to be deviation in values, where the analytical method using beam theory isroughly an average between Abaqus and the discretized method. These differencesmay warrant further investigation upon assessing the results of the optimization routine.However, as evident in Figure 3.21b, there appears to be a strong correlation in resultsbetween the diameter generated in the vertical direction and that of the routine fmincon.


The results generated from TOSCA are shown graphically in 3.22b where the displace-ment distribution and magnitude can be compared with the default configuration in3.22a.

The question remains for the difference in values compared to the diameters gen-erated in the X direction but further proves the effectiveness of TOSCA Bead wheredisplacement of nodes is primarily directed toward those which have the highest impactto the section modulus. This inevitably would be those that increase the thickness ordiameter in Y direction, analogous to increasing the moment of inertia to a rectangularbeam where height produces an increase 2 orders larger than that to width. The designresponse in fmincon could be altered so that Dtube becomes N(x,y) but would marginalvalue given the strong correlation in the Y direction and reasonable understanding ofthis preliminary study.

(a) Static displacement (b) Diameters

Figure 3.21: Resultant optimal cantilever tube data

(a) Default shape (b) Optimal shape

Figure 3.22: Cantilever tube displacement


3.5.2 Design response verification

Figure 3.23: TOSCA.OUT - Design cycle000

Confidence must also be achieved in suc-cessful integration of the new user-definedsubroutine. The optimization routine pro-vides a text file record of each design cyclewhich includes the status of the the ob-jective function, constraints, and stoppingcriteria. This also serves to validate theaccuracy of the values being used withinthis routine by comparing such to a gen-eral, static case. For example, in the de-sign cycle 000 in which no nodes have beendisplaced, the results should be equal inmagnitude. Figure 3.23 shows such anoverview of the optimization values withthe second row of Table 3.9 providing thedetailed comparison in terms of percent-age to design cycle 000. However, throughfurther examination, there’s two key differences between the calculation for Tsai-Wu inthe optimization routine and that of the standard Abaqus CAE platform which includethe depth and position for which the values are calculated.

The difference between integration point and section point must first be established.The quantity of integration points is the quantity of equally spaced surfaces in the thick-ness direction of the lamina to be included in analysis. A quantity of 3 would correlateto the top, middle, and bottom of a lamina. A section point is what is defined in afield output request which controls which of these surfaces are to be included in thefinal output. The optimization routine for TOSCA will use every section point availableby default, which is equal to the number of integration points specified per compositelayer, thus equating to three. In Abaqus CAE, this is accomplished by explicitly spec-ifying the section point position or accepting the default when creating a field outputrequest. However, the default setting in CAE is not set to every available section pointper layer, so in order for the results to match, multiple field outputs must be createdwith sequencing 1,2,3,... up to the maximum number of layers multiplied by the quan-tity of integration points. The maximum number of lamina for blade laminate is 57, sofield outputs must include all 171 positions. Otherwise, the maximum value for a givenoptimization design cycle may be differ as it is calculated from a greater range of valuesthrough the laminate thickness.

There is also an automatic adjustment made in the Abaqus CAE contour view whenselecting max envelope for a field output of interest. The max envelope being a settingthat can be selected which enables all available section points to be used when displayingresults. The result shown not only includes all such points but also the extrapolated


values at the corners of the element, whereas this is limited to the element integrationpoint locations in the optimization. Unless stress tensors are perfectly uniform throughan element, this creates the potential for differences in the max value since two differentsets of nodes are being used for calculation that can vary in quantity and location. Thesettings for the optimization are unable to be altered, therefore results from reducedmodel are post-processed to compare. This is accomplished by creating a script toextract raw data from the .odb file and calculating the global max. The raw datafollows the same principle from the optimization in that it’s based on the integrationpoints rather than the extrapolation. Both this extrapolation difference and that ofsection points are shown graphically in Figure 3.24.

Figure 3.24: Tsai-Wu evaluation location comparison

Calculation are made based on these corrections and are shown in the remaining rowsin Table 3.9. It’s apparent that these highlighted differences are not without merit sinceit’s evident that the absolute value of percent differences relative to TOSCA decrease byimplementing these changes. A range of 4.92 - 25.4% is initially observed for Tsai-Wuvalues based on no corrections but implementation of both then yields a range of 0% to3.42%. This ultimately shifts focus away from performance or user-defined subroutinerelated issues in TOSCA to that of how data is ultimately presented, thus ensuring va-lidity in the optimization routine.


MaximumCategory Load Case Displacement Tsai-WuTOSCA S2P 0.0052 (m) 0.1924

P2S 0.0072 (m) 0.2409T2L 0.0015 (m) 0.0962L2T 0.0011 (m) 0.0684

Percent Difference S2P (-) 0.24 % (+) 12.78 %(Scaled : TOSCA) P2S (+) 0.82 % (+) 25.38 %

T2L (+) 0.33 % (-) 18.49 %L2T (+) 0.38 % (-) 4.92 %

Scaled - Section point (SP) increase S2P 0.0052 (m) 0.2192P2S 0.0073 (m) 0.3279T2L 0.0015 (m) 0.0984L2T 0.0011 (m) 0.0704

Percent Difference S2P (-) 0.24 % (+) 13.9 %(Scaled - SP increase : TOSCA) P2S (+) 0.82 % (+) 36.1 %

T2L (+) 0.33 % (+) 2.3 %L2T (+) 0.38 % (+) 3.0 %

Scaled - SP increase / Remove corner nodes S2P 0.0052 (m) 0.1924P2S 0.0073 (m) 0.2491T2L 0.0015 (m) 0.0966L2T 0.0011 (m) 0.0686

Percent Difference S2P (-) 0.24 % (+) 0.00 %(Scaled - SP increase - remove corner nodes : TOSCA) P2S (+) 0.82 % (+) 3.42 %

T2L (+) 0.33 % (+) 0.43 %L2T (+) 0.38 % (+) 0.35 %

Table 3.9: Design cycle 000 and general static comparison and correction progression

Displacement and failure index values provided in subsequent analysis are split be-tween two domains. The first being the TOSCA domain which include a greater numberof section points and exclude nodal extrapolation. However, the second being the gen-eral, static domain where final contour plots are presented from the optimal geometrythat include a lesser number of section points and include nodal extrapolation, thus en-suring continuity to prior models. The TOSCA domain will only be used for subsequentparametric studies while the general, static domain will be used for all final analysis andconclusions.

3.5.3 Additional considerationsSeveral initial studies were completed that provided a basis for model refinement. Muchof this was focused on implementing geometric revision and constraints to avoid elementdistortion and areas that approached zero that caused the optimization to fail. It’simportant to note these problems were not necessarily mutual between volume and Tsai-Wu as the objective where they were primarily used in the case of volume. This couldbe attributed to the characteristic nature of volume reduction where elements wouldconverge and therefore place greater stress on elements boundaries and areas.


3.5.3.1 Element areas

Figure 3.25: Element distortion

Element areas calculated to be zero poseda reoccurring issue. Closer examinationinto the location revealed elemental col-lapse (see collapsed element in Figure3.25). An important factor beyond thescope of the optimization algorithm is theamount of partitions originally defined inthe reduced blade model. A potential miti-gation would be to then decrease the num-ber of partitions in the failure region toresult in larger element areas which wouldbe less prone to collapse. These were origi-nally included in the model as separate re-gions of same material and layup properties (as discussed prior) but further investigationalso showed that the adjacent regions in the area of interest shared the same propertiesand could be combined without sacrificing quality. Therefore, a virtual topology tech-nique via Abaqus CAE was performed where such regions regions were combined (region13-15 in the same figure) where longitudinal partitions were eliminated while preservingtransverse so material properties on a radial basis could once again be assigned.

3.5.3.2 Element transitionsElement transitions also were cause for element distortion and were located betweenthe blade surface and web (see Figure 3.26a). The elements indicated in red appear tobend immediately before the transition as a result of nodal displacement. A geometricconstraint which restricts movement in transverse (X direction) was therefore imposedto prevent such bending.

(a) Element distortion at web transition (b) Node selection

Figure 3.26: Web transition geometric constraint


3.5.3.3 Additional nodal displacement

Figure 3.27: Element distortion at web tran-sition including directional constraint

Figure 3.27 shows the effect of imposingthe directional constraint stated prior inthat bending is eliminated near the webtransition. However, distortion still existswhich was suspected to be caused by thelarge relative nodal displacement to thestarting geometry. To mitigate this issue,a maximum allowable nodal displacement(into the blade) was introduced. The samefigure indeed includes this as well but onlyfor a 0.02 m constraint where element dis-tortion still exists. It was only after limit-ing displacement to 0.015 m could distor-tion then be completely removed. A validargument could be presented that imposing such a constraint then essentially makes vol-ume reduction a function of the nodal constraint. Ultimately, this technique highlightsthe necessity for further development in controlling element distortion while at the sametime providing a conservative estimate into volume reduction.

3.5.3.4 Mesh RefinementInitial studies also often led to erroneous nodal displacements. Extensive effort wasused for a parameter study for nodal update, nodal move, and constraint magnitudes.These did indeed impact the final solution but not to the extent of complete removalof undesired displacements. It was presented prior that mesh refinement was marginalin the case of a general, static analysis. However, this trend appears to be broken inthe case of optimization where creating additional nodes through a finer discretizationin select cases led to smoother transitions during nodal displacement. Therefore, anadditional mesh size was used (medium mesh from Table 3.6) for the studies below.

3.5.3.5 Tsai-Wu sensitivitiesIt was discovered during these initial studies that a revision was required for the develop-mental software used in this report with respect to results generated from user-definedsubroutines for multi-layer cases. This revision was also relevant to prior versions of soft-ware as well but required unique problem construction for detection to occur. TOSCABead has typically been used for isotropic analysis which meant this was also normallyused in single-layer structural cases, thus not exposing the issue as it applies to multi-layer cases common to composite structures. This was initially suspected by viewingexcessive magnitudes for objective function sensitivities in the output report. Furtherindication was provided by using an arbitrary reduction scaling through the user-definedsubroutine for Tsai-Wu partial derivatives which then produced more reasonable results.


A correction was indeed implemented and the results presented below are indicative ofsuch.

3.5.4 Failure ReductionTable 3.10 contains parameters used for all studies targeting a failure index reductionin the blade. The first row will be used for a parametric study where Tsai-Wu is im-plemented as the objective function. The optimal settings from the parametric studytogether with those shown in the second row will then be used in an additional studywhere displacement replaces Tsai-Wu as the objective function. This being done tocompare performance in developing Tsai-Wu as a design response compared to the pre-existing software capability.

NODAL NODAL FILTERUPDATE MOVE CONSTRAINT DVCON DRESP OBJ RADIUSNORMAL 0.05 D (REL) ≤ 1.0 ∆Nodes = 0.01m TW (S2P/P2S/T2L/L2T) TW 4

∆Nodes = −0.075m D (S2P/P2S/T2L/L2T)NORMAL 0.05 ∆Nodes = 0.01m D (S2P/P2S/T2L/L2T) D 4

∆Nodes = −0.075m

Table 3.10: Failure reduction - common parameters

Three case conditions are used for the parametric study where weighting factors andobjective target were altered. A baseline case of equal weighting factors and a maxcondition for objective target was first used, and then the effect of weighting equalityand objective target could then be isolated relative to this condition. Varied weightingfactors can be chosen to alter the inherent variation and create beneficial or adverseimpacts to objective terms. The values are selected as a scaling factor to create equalityin magnitudes since it’s observed that the L2T / T2L failure index values are less thanthat of P2S / S2P by an approximate factor of 4. Weighting factors could alternatively bebased on normalization as a more accurate approach but may be once again compromisedfollowing the first iteration. The objective target creates a similar effect where only thelargest failure index value for all load cases will be used in the minmax condition wheremax uses all values from all cases.

Case Condition WEIGHTING FACTOR (S2P P2S L2T T2L) OBJECTIVE TARGET1 1.0 / 1.0 / 1.0 / 1.0 MAX2 1.0 / 1.0 / 4.0 / 4.0 MAX3 1.0 / 1.0 / 1.0 / 1.0 MINMAX

Table 3.11: Failure reduction - case condition parameters

A summary of the resultant Tsai-Wu and displacement values for the parametricstudy are plotted with respect to iteration cycle in Figure 3.28 and 3.29 respectively.The plots are separated by loading case and case conditions presented prior.


Figure 3.28: Failure reduction - Tsai-Wu objective function vs. iteration

Several key findings can be made for the case of Tsai-Wu values and include thefollowing:

• All plots show reasonable convergence but differences exist in the total number ofrequired iterations to reach the default convergence criteria

• Plots with the same objective target (max) but varying weighting factors showmarginal variation as opposed to those in which the objective target is changed.The plots of the latter show a significant increase in Tsai-Wu with the exceptionbeing the P2S loading case.

• Overall the P2S loading case shows the least variation among all three case con-ditions but also the largest magnitude in Tsai-Wu. This means that it’s alwaysactive and influencing nodal displacement unlike the other conditions that fail tobe reduced in a minmax condition due to their relative lower magnitudes.


Figure 3.29: Failure reduction - displacement vs. iteration

Notable discoveries can also be made in the case of displacement (see Figure 3.29and include the following:

• Values are not fully converged as in the case of Tsai-Wu. This could in large partbe driven by the stopping criteria linked to changes in the objective function ratherthan constraints. Although convergence isn’t achieved, the relative gaps betweenthe plots appear to be consistent which may implies that additional iterations willimpact accuracy rather than precision of the final displacements.

• The magnitudes for the S2P/P2S and L2T/T2L loading cases show marginal vari-ation through overlapping plots.

• All case conditions produce a reasonable degree of displacement variation for theP2S/S2P loading cases.

• A similar trend is present for the L2T/T2L loading cases, but with significantincrease in displacement for the minmax case condition.

• The displacement constraint appears to be conservative or influencing the result inthat no displacement values are exceeding the threshold of 1 through all iterations.

Explicit resultant values are then extracted from these plots and then calculated asa difference percentage to the original values. The additional case where displacementis used as the objective function is added as well denoted as NO_TSAI. In the case ofTsai-Wu values, magnitudes are presented in Figure 3.30.


Figure 3.30: Failure reduction - Tsai-Wu values - final iteration

Difference percentages are then shown in Figure 3.33 below. It’s clear that equalityfor weighting factors and the max objective target results in the largest mean reduction(+ = decrease) of 33.1%. The additional case condition by using only displacement as aconstraint then result in the largest increase as well of -176.7%. Difference percentagesfor the EQUAL_MINMAX case condition also support the adverse and beneficial trendspresent in the previous plots where the largest mean reduction is occurring for the P2Sloading of 19.3% with a significant adverse impact to the L2T loading case of -38.1%.

Figure 3.31: Failure reduction - Tsai-Wu percent differences - last and final iteration

For the case of displacement values, detailed magnitudes are provided in Figure 3.32with difference percentages presented in Figure 3.33. It’s evident that largest decreasesin displacement occur for EQUAL_MAX and NO_TSAI case conditions equal to 11.1%.The EQUAL_MINMAX condition then results in the smallest decrease in displacementof 4.4%.

Figure 3.32: Failure reduction - displacement values - final iteration


Figure 3.33: Failure reduction - displacement percent differences - last and finaliteration

Based on the results above, the EQUAL_MAX case condition produces the mostdesirable results based on the mean decrease in Tsai-Wu and displacement. Therefore,this condition will be closely evaluated with respect to nodal displacement and failureindex distributions. Figures 3.34a and 3.34b show the resultant geometry where thepositive direction is into the blade and negative in the outward direction. It’s clearthat the maximum positive displacement is equal to 10.0 mm, which shows that thisis being limited by the nodal growth constraint. It’s also positioned on the pressureand suction side of the tip-side trailing edge. The maximum negative displacement isequal to 58.3 mm and is located on the trailing and leading edge side of the root. Anegative displacement could then be associated with an increase in sectional modulusto lower bending stresses and Tsai-Wu values, which then occurs at location of Tsai-Wuconcentration for the L2T/T2L loading cases. A positive displacement would appearcounter-intuitive to produce a beneficial impact to the objective function but the locationdoesn’t match that of any stress concentration for all loading cases. This could thenaid in load transfer through change in curvature rather than a pure increase to stiffness,thus still potentially aiding the objective function.


(a) View 1 (b) View 2

Figure 3.34: Failure reduction - EQUAL_MAX case condition - nodal displacement forfinal iteration

Figures 3.35a through 3.36b show the resultant Tsai-Wu distributions and can becompared to the reduced and scaled plots presented for the scaled blade model. Thefollowing observations and for the maximum value location:

• P2S - A shift back to the original location for the reduced model and minimalpropagation from the isolated location.

• S2P - A shift to a new region near the suction-root face that’s non-coincident withthe boundary condition but also split into two locations near partitioned edges.

• T2L - Significant reduction in surface area for the Tsai-Wu concentration from thescaled model but split into several isolated locations along the trailing edge. Themaximum of which located on the boundary condition.

• L2T - A similar trend to T2L but with less concentrated maximum locations.


(a) P2S (b) S2P

Figure 3.35: Tsai-Wu distributions - EQUAL_MAX case condition - P2S/S2P


Figure 3.36: Tsai-Wu distributions - EQUAL_MAX case condition - T2L/L2T

Explicit values can also be extracted from these plots and are presented in Table 3.15below. These values are extracted from contour plots where magnitudes will differ fromthose in the parameter study based on reduced section points and corner node inclusion.Displacement plots are also included as Figures A.9a - A.10b in appendix A. It’s shownthat displacement and maximum Tsai-Wu both decrease relative to the scaled modelwith a mean of 11.9% and 23.9% respectively. This is partially preserved with respectto the reduced model where there is a mean increase in displacement of 42.3% and stilla reduction in Tsai-Wu but to a lesser maximum magnitude of 9.8%.



Percent Difference S2P (-) 7.7 (-) 24.3 %(Optimal: Scaled) P2S (-) 8.2 (-) 25.6 %

T2L (-) 13.3 (-) 31.3 %L2T (-) 18.2 (-) 14.3 %

MEAN (-) 11.9 (-) 23.9 %Percent Difference S2P (+) 54.8 (-) 12.7 %

(Optimal: Reduced) P2S (+) 55.8 (-) 11.9 %T2L (+) 30.0 (-) 15.8 %L2T (+) 28.6 (+) 1.3 %

MEAN (+) 42.3 (-) 9.8 %

Table 3.12: Failure reduction - equal_max - blade Displacements and Tsai-Wu

Several conclusions that can be made from these results that first include the lackof ability for the optimization to reduce isolated locations as in the the P2S loadingcase. This could imply that these stresses are not directly due the coupling betweengeometry and load, but more so with the construction of the model (e.g. conventionalvs. continuum shell elements). Therefore, there rests a lack of ability for a routinebased in nodal displacement to then reduce this effect. The S2P loading case exhibiteda larger distribution of Tsai-Wu in the original reduced and scaled models which hasbeen reduced significantly and shifted to a location of larger bending stresses near theroot. The edge effect may be influenced again by the same factors for the P2S loadingcases since these edges represent a difference in material thickness, which may create astress concentration in the case of conventional shell elements.

These trends continue with the L2T and T2L loading cases where larger distributionsof stress are marginalized with residual isolated locations. The location for T2L couldbe called into question since stresses located on the boundary condition are susceptibleto error which would mean the routine has been driven by a non-representative Tsai-Wuvalue and a sub-optimal solution. However, two considerations must be made in thatthe overall Tsai-Wu reduction along the trailing edge is similar to that of L2T whichdoesn’t possess an edge location. Also, the maximum location isn’t completely isolatedin that there’s a degree of propagation (although not of the same value) leading into thelocation. Both of these facts show the location didn’t hinder the larger concentrationfrom being reduced and that this location may indeed possess significant Tsai-Wu mag-nitude.

Figures 3.38a and 3.38b for the P2S loading condition provide an opportunity to alsoinvestigate the behaviour of Tsai-Wu distribution in the case of using only displacementfor the objective function. The table presented prior show a significant increase in Tsai-Wu values with these figures showing an example of the source for the increase. It’sknown that the tip-most nodes are constrained but with displacement as the objective,nodes immediately beyond this constraint are displaced to the upper limit to maximizebending stiffness. However, this abrupt change creates a stress concentration which isotherwise reduced through a smooth transition in using Tsai-Wu as the objective.


(a) Displacement objective (b) Tsai-Wu objective

Figure 3.37: Objective function condition and tip transition

Figures 3.38a and 3.38b show the resultant nodal displacement and Tsai-Wu dis-tribution for the case of P2S loading respectively. These are generated with respectdisplacement as the objective mentioned prior. Variation is evident in the maximumand minimum nodal displacement compared to Tsai-Wu as the objective where newmagnitudes include -47.8 mm and 0 mm. This shows that the routine was driven bya pure increase to bending stiffness since no displacement occurred into the blade. Toaid in comparison, the max countour limit has been changed to equal the magnitudein iteration 0 (IF = 0.246) in order to have a clear indication for distribution since themaximum is much larger relative to the remaining values. It’s clear that the severalnew concentrations have been created relative to the scaled P2S contour plot. Thisalso shows that additional effort placed in resolving the step effect (apart from Tsai-Wu as objective) in the figures above would not be sufficient in completely eliminatingconcentrations from the model.


(a) Nodal displacement (b) P2S distribution

Figure 3.38: Failure reduction - displacement objective - resultant geometry and Tsai-Wudistribution

3.5.5 Volume ReductionTable 3.13 contains parameters used for all studies targeting a volume reduction in theblade. The first row will be used for a parametric study where Tsai-Wu is implementedas a constraint. The second will replicate the most suitable setting from the parametricstudy but exclude Tsai-Wu as a constraint.

NODAL NODAL FILTERUPDATE MOVE CONSTRAINT DVCON DRESP OBJ RADIUSNORMAL 0.05 D (REL) ≤ 5.0 ∆Nodes = −0.075m TW (S2P/P2S/T2L/L2T) VOL 4

TW (ABS) ≤ 1.0 D (S2P/P2S/T2L/L2T)NORMAL 0.05 D (REL) ≤ 5.0 ∆Nodes = −0.075m D (S2P/P2S/T2L/L2T) VOL 4

Table 3.13: Volume reduction - common parameters

Nodal update, nodal move, and filter radius are consistent with the previous studies.However, differences exist for constraints and geometric constraints with the first be-ing a relative constraint of 5.0 used for displacement. Volume and displacement wouldbe thought of as opposing mechanical characteristics since a volume reduction wouldincrease the likelihood of a decrease to the blade cross-section, which is then directlylinked to a decrease in bending stiffness and increased displacement. Exceeding suchvalue instead by an arbitrary factor of 5 may prove detrimental to the overall blade tipdisplacement constraint since the starting displacement magnitude, and the subsequentscaled value would be relatively small. For example, the largest displacement is 7.3 mmfor P2S loading, which then equates to a 36.5 mm by applying the relaxed constraint.By referring back to the discussion on allowable tip clearance for Figure 3.1, one cancalculate a difference of 1.19 m between such value and to the resultant from the fullblade model. The blade structure is preserved outside of the root region which means


the increased tip displacement at the root through constraint relaxation would be equalto the increase in tip displacement. Subsequently, one can then conclude that 36.5mmis significantly less than the allowable, therefore eliminating potential risk in increasingthis constraint.

An absolute constraint value of 1 is used for Tsai-Wu which then creates the questionwhy failure would then be acceptable. One must consider that safety factors have beenincluded into the pre-existing design loads, which means 1 will still include marginrelative to failure. Assigning additional margin would be an arbitrary practice butcould of course be included for future design studies. This could also be of interestin considering the original discussion in using only Tsai-Wu among the various multi-directional failure criteria since additional margin may account for potential differences.Table 3.14 contains parameters used in the parametric study. These are strategicallyselected as values equal to or exceeding 0.02 m were determined to cause excessiveelement distortion which terminated iterations prematurely.

CASE DVCON1 ∆Nodes = 0.01m2 ∆Nodes = 0.015m3 ∆Nodes = 0.02m

Table 3.14: Volume reduction - case condition parameters

Figure 3.39 contains the resultant volume for the three different cases. It’s evidentthat convergence is not achieved for 0.02 nodal growth which is indicative of the elementdistortion causing the routine to fail. The maximum converged reduction is equal to0.1886 m3, or a 3.43% percentage reduction from 0.1953 m3. There also appears to beminimal variation in the plots for 0.01 nodal growth between including and excludingTsai-Wu as a constraint.


Figure 3.39: Volume reduction - volume objective function vs. iteration

Resultant Tsai-Wu values are also presented in Figure 3.40. It’s evident that P2S/S2Ploading cases show a larger sensitivity to volume changes rather than L2T/T2L. Thiscould be attributed to a general larger cross-sectional dimension in the X direction thanY, where the first would be the dominant factor for bending stiffness for L2T/T2L load-ing cases and the latter for P2S/S2P loading cases. A reduction via nodal displacement(shown to be reasonably uniform in later plot) common to all loading cases would there-fore have a much greater impact for the P2S/S2P loading cases in terms of bendingstress, thus resulting in larger Tsai-Wu values. The IF for P2S loading also appears toapproach 1 in the case of the 0.015 nodal growth. This indicates that Tsai-Wu mayindeed be limiting the design instead of element distortion as presented in the volumeplot. In other words, solving element distortion would not lead to substantial additionalreduction in volume since Tsai-Wu is shown to increase with nodal growth and is closeto violating the constraint at 0.015 nodal growth.


Figure 3.40: Volume reduction - Tsai-Wu vs. iteration

Resultant displacement values are shown in Figure 3.41. It’s clear that P2S/S2Pnormalized values are greater than L2T/T2L in all cases. This also supports the notionthat a constant nodal displacement will impact bending stiffness for a P2S/S2P to agreater extent.

Figure 3.41: Volume reduction - displacement vs. iteration

Once again, explicit resultant values and difference percentages to the original valuesare presented in Figures 3.42 and 3.43 below. An additional case condition used for


comparison is added as well by replicating the same optimization study but removingthe Tsai-Wu constraint denoted as NO_TSAI.

Figure 3.42: Volume reduction - Tsai-Wu - last and final iteration

The largest mean percentage increase (shown as negative) occurs for the NO_TSAIcondition as 141.6% while the smallest for the NODAL_01 condition as 60.2%.

Figure 3.43: Volume reduction - Tsai-Wu percent differences - last and final iteration

For the case of displacement values, detailed magnitudes are provided in Figure 3.44with difference percentages presented in Figure 3.45. It’s evident that largest increaseoccurs for NODAL_015 as 19.8% while the least for NODAL_01 as 11.6%. A notablefinding is that the absence of Tsai-Wu as a constraint produces a displacement increasenearly equal to NODAL_01. This supports the trend presented earlier with resultantvolume where both of these conditions appeared to be equal in value, which then providesjustification for equal displacement.

Figure 3.44: Volume reduction - displacement - last and final iteration


Figure 3.45: Volume reduction - displacement percent differences - last and finaliteration

Based on the results above, the NODAL_015 case condition will be used for furtheranalysis. Figures 3.46a and 3.46b below show resultant nodal displacement which showsa maximum inward displacement of 16.5 mm and outward as 7.4 mm. Although amajority of the nodal growth appears to be uniform in magnitude and into the blade,there is a portion on the pressure trailing edge side accounts for the outward displacementof nodes.


Figure 3.46: Volume reduction - nodal_015 - nodal displacement for final iteration

Figures 3.47a through 3.48b show the resultant Tsai-Wu distributions. Once again,these are intended to be compared to prior plots for the scaled or reduced. All casesseem to be showing the same trend where the maximum Tsai-Wu location is shiftedtoward the tip next to the transition from constrained to free nodes. It’s evident thatTsai-Wu also exceeds the failure threshold with a value of IF = 1.194 in the case ofP2S loading. Normally this would indicate a constraint violation but the tosca domainvalue from the prior table is IF = .881 which is the true value coupled to the constraintin the optimization. The argument can be made that due to Tsai-Wu being inactiveup to the value of the constraint, an aggressive transition has been created that would


have otherwise become smooth as in the case when the comparison was made betweendisplacement and Tsai-Wu objectives in the prior study. The Tsai-Wu constraint couldtherefore be reduced to force it to be active in controlling the step effect. This would inturn also have a marginal impact on the remaining geometry since it’s evident that allother locations are less than the failure threshold which would also present a marginalimpact to the volume.

(a) P2S (b) S2P

Figure 3.47: Tsai-Wu distributions - nodal_015 - P2S/S2P

(a) T2L (b) L2T

Figure 3.48: Tsai-Wu distributions - nodal_015 - T2L/L2T

Explicit values are extracted from these plots and are presented in Table 3.15 below.Displacement plots are also included as Figures A.11a - A.12b in appendix A. It’s shownthat displacement and maximum Tsai-Wu both increase relative to the scaled modelwith a mean of 20.8% and 153.5% respectively. Values with respect the reduced modelare a mean increase in displacement of 95.1% and Tsai-Wu 198.9%.



Percent Difference S2P (+) 26.9 (+) 253.5 %(Optimal: Scaled) P2S (+) 24.7 (+) 295.4 %

T2L (+) 13.3 (+) 39.0 %L2T (+) 18.2 (+) 26.2 %

MEAN (+) 20.8 (+) 153.5 %Percent Difference S2P (+) 112.9 (+) 308.0 %

(Optimal: Reduced) P2S (+) 111.6 (+) 368.2 %T2L (+) 70.0 (+) 70.3 %L2T (+) 85.7 (+) 49.1 %

MEAN (+) 95.1 (+) 198.9 %

Table 3.15: Volume reduction - nodal_015 - blade displacement and Tsai-Wu

Figures 3.49a and 3.49b show the resultant nodal displacement and Tsai-Wu distri-bution (P2S loading) for excluding Tsai-Wu as a constraint. Variation is evident inthe maximum and minimum nodal displacement compared to the inclusion of Tsai-Wuwhere new magnitudes include -11.6 mm and 0 mm. This shows that the routine wasdriven by a pure decrease to volume since no displacement occurred out of the blade.Also, in that that the outward displacement of nodes from the inclusion of Tsai-Wu inthe previous displacement plot is directed at constraining such magnitude. To aid incomparison for distribution, the max contour limit again has been changed to equal themagnitude in iteration 0 (IF = 0.246) based on the excessive maximum magnitude. It’sclear that the several new concentrations have been created relative to the scaled P2Scontour plot. The maximum value of IF = 2.170 for Tsai-Wu also indicates how thesuch constraint was active in the previous case of limiting the total magnitude (compareto IF = 1.194).

(a) Nodal displacement (b) P2S Tsai-Wu distribution

Figure 3.49: Displacement objective - resultant geometry and Tsai-Wu distribution

CHAPTER 4Conclusions

4.0.1 OverallTwo different routes for structural optimization were completed that ultimately resultedin an increase to strength and decrease to volume when compared to a model that ex-cluded this technique (arbitrarily scaled). In terms of failure reduction, the new optimalgeometry generated through TOSCA Bead showed that Tsai-Wu magnitudes were re-duced by a mean value of 23.9% relative to arbitrarily scaled model and 9.8% to thatof the original root section contained in the reduced model. However, all values for thescaled and reduced models were under the failure threshold, thus showing the decreasesserved to increase margin relative to failure rather than for prevention. Comparisonsto both models are provided because the introduction of an orthotropic failure criteria(Tsai-Wu) as design response is a new feature which assumes this was likely not includedin the existing design. Therefore, these values show the value created when applied tooriginal and modified geometries.

It’s also shown that displacement decreases relative to the scaled model with a meanof 11.9% and increases with respect to the reduced model with a mean of 42.3%. Thedisplacement magnitude of 6.8 mm for P2S loading, which is the only load case governedby a displacement constraint (tower clearance), is estimated to significantly less than theallowable increase. This being based by first calculating the difference to the reducedmodel (4.3 mm) of 2.5 mm, and then comparing the difference between the allowabletip clearance (3.1 m) and tip displacement (1.91 m), which is 1.19 m. The displacementincrease shows that new geometry is not able to compensate for the reduced sectionalmodulus produced from the required geometric reduction, which would in turn result ingreater displacement. This shows displacement and failure are not always proportional,where a decrease to Tsai-Wu is still possible when coupled with increased displacementdue to the reduction of failure index concentrations. The contour plot comparison fromthe new geometry relative to the scaled and reduced models provided justification intothis conclusion when viewing the reduction on display in the TE transition and mid-pressure side regions.

The parametric study involving weighting factor and objective target variation alsoprovides insight into the effect these have in a multi-objective case. Negligible differencesexist between an equal and unequal case which highlight the minor effect of this param-eter. However, opposite to this, using a minmax for objective target creates significantadverse impacts to all objectives values that are less than the maximum used. While at

4 Conclusions 73

the same time resulting in roughly the same percent difference for the maximum valueused compared to other conditions. This shows deviation from an equal, max conditionwill likely result in less than or equal to this condition for objective values.

In terms of volume, it was shown that the optimal geometry produced a 3.43% reduc-tion compared to the scaled model (no value in comparing to reduced model since volumereduction is already expected in reducing root diameter). This then resulted in meanincrease to displacement and Tsai-Wu of 20.8% and 153.5% respectively in comparisonto the scaled mode. Mean increases of 95.1% and 198.9% were calculated in comparingto the reduced model. These values may appear significant but simply highlight theexcessive starting margin between constraint and response. In terms of constraints, themaximum Tsai-Wu value occurred for P2S loading which increased to the approximatevalue of 1 for the absolute failure constraint (IF = 0.881 tosca domain vs IF = 1.194contour domain). The increase for P2S loading relative to the allowable displacementonce again is first determined by the difference of the reduced model displacement (4.3mm) and that of the increase (9 mm). This results in 4.7 mm which is significantly lessthan the allowable increase of 1.19 m.

It’s also important to note that several versions of TOSCA were released during thisinvestigation based on preliminary results. An initial finding was the excessive computa-tional time required for completing design cycles when including failure criteria throughuser-defined subroutines. Models were constructed separate from those presented in thereport that formed the basis of studies between single and multi-layer cases to helpdemonstrate the link between layer / element quantity and computational time. Im-provements were thus made based on these in new software versions by Simulia thatreduced such time by approximately 25% of the original values. As stated prior, revi-sions were also made with objective function sensitivities which were also then includedsuch versions.

4.0.2 Future Investigation4.0.2.1 Stress ConcentrationsThere are however issues to consider for future use. One of these challenges includes newmethods for reducing isolated Tsai-Wu concentrations which were shown to be presentafter the overall reduction in larger concentrations. Differences were shown to exist indistribution of maximum Tsai-Wu locations between the full blade model that used con-tinuum shell elements and the reduced model which used conventional shell elements.However, element type may not be simple to overcome since the type is constrained byTOSCA Bead. This may shift focus toward the original model creation and laminatedefinition as mitigation. For example, creating a greater degree of uniformity in mate-rial thickness and properties could then reduce abrupt transitions in geometry and stress

4 Conclusions 74

which would may lead to a reduction in concentrations.

4.0.2.2 Failure CriteriaVolume reduction is currently limited by the maximum nodal displacement and Tsai-Wuconstraint. Utilizing additional failure criteria together with solving the issue of elementcollapse may provide added benefit considering failure values are expected to approachthe upper limit. Certain failure criteria may produce lower index values which wouldprovide additional freedom for displacement but also increase risk through the inherentuncertainty of criteria accuracy. An alternative approach could then be to incorporateadditional criteria for the purpose of conservative design where several different studiesare performed and the design with the largest volume is selected as the preferred ge-ometry. This direction could also be used concerning failure reduction but provide lessbenefit given all failure index magnitudes were significantly less than threshold.

These low magnitudes also lead back to the original assumption that incorporatingTsai-Wu as the sole failure criteria was sufficient for all analysis. Additional criteria mayprovide more conservative values to be used in the design but at a lower probabilityof violating failure than if all index values were originally closer to failure. A generaltrend could therefore be established where additional criteria add the greatest value forvolume reduction where margin is expected to decrease relative to failure. A sole criteriathen is more suitable for failure reduction where the opposite is expected and marginis expected to increase relative to failure. However, the latter approach through a solecriteria would still require assessment of initial failure index values since close proximityto threshold (unlike those in this study) may shift discussion back to requiring additionalcriteria.

4.0.2.3 Parameter refinement

Figure 4.1: Filter radius influence

A general issue to consider is the differencein convergence between general FEA anal-ysis and optimization. FEA relies on errorreduction methods (e.g. reduction in meshsize) to show convergence to value that aretreated as globally representative, wherevariation of alternative parameters will ul-timately lead to the same result. How-ever, a challenging aspect to geometricoptimization is that convergence is mostlikely achieved to a local minima, and verymuch linked to the design domain of vari-ous constraints and optimization parame-

4 Conclusions 75

ters. For example, it was shown that the equal, max condition was the preferred meansfor failure reduction but performing an additional study only varying the filter radius(refer to section 2.4.4.5) from 4 to 1.3 produces a significantly different geometry (seeFigure 4.1). A parametric study could then be performed with respect to this variablein addition to many others (constraint magnitudes, nodal move, nodal update, etc.)to determine if additional improvement exists from the available range of values. Ulti-mately, timescales and the fact that structural benefit was ultimately achieved led tofixed baseline settings beyond those that were included in this report (objective target,etc.).

Bibliography[1] T. Stehly, P. Beiter, and P. Duffy, “2019 cost of wind energy review,” December

2020.

[2] L. Shuguang, E. Sitnikovaa, and A.-S. Yuning, Liang Kaddour, “The tsai-wu failurecriterion rationalised in the context of ud composites,” 2017.

[3] P. Christensen and A. Klarbring, An Introduction to Structural Optimization.Springer Science and Business Media B.V, 2009.

[4] O. Sigmund, “Morphology-based black and white filters for topology optimizations,”2007.

[5] J. Alberto and N. Martínez, “Material choice and blade design,” 2019.

[6] P. Newsroom, “Steel solutions in wind power.” https://newsroom.posco.com/en/steel-solutions-in-wind-power/. January 26, 2016.

[7] En:former, “Major wind turbine manufacturers grow market share.” https://www.en-former.com/en/major-wind-turbine-manufacturers-grow-market-share.June 6, 2020.

[8] O. Sigmund, “Notes and exercises for the course: Finite element methods (41525),”2020.

[9] “Creating solid composite layups.” https://help.3ds.com/2021/english/dssimulia_established/simacaecaerefmap/simacae-m-PrpCompositesSolid-sb.htm?ContextScope=all, 2021. Dassault Systems.

[10] “Conventional shell versus continuum shell.” https://help.3ds.com/2021/english/dssimulia_established/simacaecaerefmap/simacae-m-PrpCompositesSolid-sb.htm?ContextScope=all, 2021. Dassault Systems.

[11] “Full integration.” https://help.3ds.com/2021/english/dssimulia_established/simacaegsarefmap/simagsa-c-ctmfull.htm?contextscope=all, 2021.Dassault Systems.

[12] R. Cook, D. Malkus, M. Plesha, and R. Witt, Concepts and Applications of FiniteElement Analysis. John Wiley Sons. Inc., 2002.

[13] O. Sigmund, “Day 12: Error analysis and meshing,” 2020.

https://newsroom.posco.com/en/steel-solutions-in-wind-power/

https://newsroom.posco.com/en/steel-solutions-in-wind-power/

https://www.en-former.com/en/major-wind-turbine-manufacturers-grow-market-share

https://www.en-former.com/en/major-wind-turbine-manufacturers-grow-market-share

https://help.3ds.com/2021/english/dssimulia_established/simacaecaerefmap/simacae-m-PrpCompositesSolid-sb.htm?ContextScope=all






https://help.3ds.com/2021/english/dssimulia_established/simacaegsarefmap/simagsa-c-ctmfull.htm?contextscope=all

https://help.3ds.com/2021/english/dssimulia_established/simacaegsarefmap/simagsa-c-ctmfull.htm?contextscope=all

Bibliography 77

[14] D. Zenkert and M. Battley, Laminate and Sandwich Structures Foundations of FibreComposites. Technical University of Denmark, 2009.

[15] P. Haselbach, “Modelling and post-processing fibre composite materials,” 2020.

[16] “Plane stress orthotropic failure measures.” https://help.3ds.com/2021/english/dssimulia_established/simacaematrefmap/simamat-c-failuremeasures.htm?contextscope=all, 2021. Dassault Systems.

[17] A. Kaddoura, M. Hintonb, S. Lic, and P. Smithd, “The world-wide failure exercises:How can composites design and manufacture communities build their strength,”2014.

[18] O. Sigmund, “Day 4: Topology optimization,” 2020.

[19] “Introduction to tosca structure - lesson 11: Bead optimization.” https://eduspace.3ds.com/CompanionManager/up/?&lexType=1&lang=en&lpId=224026&cls_aud=s&utm_source=535_5_29&utm_medium=onl_crs&utm_campaign=C224026&/index.html/#/lp-content. Dassault Systems.

https://help.3ds.com/2021/english/dssimulia_established/simacaematrefmap/simamat-c-failuremeasures.htm?contextscope=all



https://eduspace.3ds.com/CompanionManager/up/?&lexType=1&lang=en&lpId=224026&cls_aud=s&utm_source=535_5_29&utm_medium=onl_crs&utm_campaign=C224026&/index.html/#/lp-content




APPENDIXAA.1 Full blade FE Model

A.1.1 Displacement - Full Model

(a) S2P (b) P2S

Figure A.1: Full blade model displacement

(a) T2L (b) L2T

Figure A.2: Full blade model displacement (cont.)

A.1 Full blade FE Model 79

A.1.2 Displacement - Partial Blade Model

(a) S2P - displacement (b) T2L - displacement

Figure A.3: Full blade partial model displacement

Figure A.4: Full blade partial model displacement - L2T

A.2 Reduced FE Model 80

A.2 Reduced FE Model

A.2.1 Displacement

(a) S2P (b) P2S

Figure A.5: Reduced blade model displacement

(a) T2L (b) L2T

Figure A.6: Reduced blade model displacement (cont.)

A.3 Scaled FE Model 81

A.3 Scaled FE Model

A.3.1 Displacement

(a) S2P (b) P2S

Figure A.7: Scaled blade model displacement

(a) T2L (b) L2T

Figure A.8: Scaled blade model displacement (cont.)

A.4 Optimal FE Model 82

A.4 Optimal FE Model

A.4.1 Failure reduction

(a) S2P (b) P2S

Figure A.9: Failure reduction - optimal blade model displacement

(a) T2L (b) L2T

Figure A.10: Failure reduction - optimal blade model displacement (cont.)

A.4 Optimal FE Model 83

A.4.2 Volume Reduction

(a) S2P (b) P2S

Figure A.11: Volume reduction - optimal blade model displacement

(a) T2L (b) L2T

Figure A.12: Volume reduction - optimal blade model displacement (cont.)

APPENDIX BB.1 Loading

Load Orientation R3.5 Load (kN) R6.1 Load (kN) R10 Load (kN) R13 Load (kN)

S2P 2.46 4.99 9.95 4.03P2S 7.58 5.51 14.71 4.53T2L 1.37 0.89 1.22 1.87L2T 1.32 0.05 0.63 1.77

Table B.1: Load distribution magnitudes (target loads minus compensation and preload)

B.2 Material

(a) Core properties (b) Material properties - partial

Figure B.1: Supplied material properties

department of wind energy master report

Documents