Project of the Rear Wing of a LMP3 Race Car Mechanical Engineering

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Project of the Rear Wing of a LMP3 Race Car

Gonçalo Gaspar Bentes Pimenta

Thesis to obtain the Master of Science Degree in Mechanical Engineering

Supervisor: Prof. João Manuel Pereira Dias

Examination Committee Chairperson: Prof. João Orlando Marques Gameiro Folgado Supervisor: Prof. João Manuel Pereira Dias Member of the Committee: Prof. Luís Alberto Gonçalves de Sousa

November 2018 ii To my family, who was always there for me during the hardest times. To my friends, who walked with me through the toughest challenges.

iii iv Acknowledgments

First of all, I would like to thank my supervisor Professor Joao˜ Dias with whom I have worked closely since 2013 when PSEM was revived. His belief on my skills and the freedom he gave me while developing this thesis was essential for its successful completion.

Secondly, my family. My mother, father, sister and grandmother who always supported me and be- lieved on my decisions and my ability to overcome whichever setback I was faced with without never doubting me.

I would like to thank Stephane´ Chosse, ADESS CEO, for the opportunity he gave me to work on an area I’ve loved since I was a little kid. Regarding ADESS, the team is amazing and we spent a great time working on some amazing projects. Maduro, Jose,´ Sergio,´ Andre,´ Hugo, Carlos, Marcio,´ Torsten, Jose´ Loureiro, Rui and Filipe, thank you for what you guys taught me and for the team spirit.

I could not forget about the PSEM team where I spent most of my time in Tecnico.´ Most of what I know today I learned with you, working through endless days and sleepless nights. Mario,´ Frederico, Nuno, Guilherme, Andre,´ Gerardo, Catarina, Rita, Henrique, Hugo, Alves, Dias, Pedro, Joao˜ Oliveira, Rui, Chico, Ribeira, Ines,ˆ Gonc¸alo, Ch´ıcharo and Mendes, this here is for you.

I would like to give a special thank you to Prakash from Altair who, despite not knowing me, helped me a lot through the Altair Forums, e-mails and Skype calls so I could ﬁnish my work in time.

Last but not least, I want to thank all my friends from Tecnico´ who walked this path with me, Pedro, Catarina, Beatriz, Duarte, Jose,´ Renato, Hugo, Carolina and Ricardo. A special word to Ana for her encouragement and for always being by my side to support me face my challenges and help however she could.

v vi Resumo

Esta tese acompanha todo o trabalho de actualizaçao˜ e optimizaçao˜ da nova asa traseira do Prototipo´ LMP3 ADESS-03. O trabalho desenvolvido esta´ inclu´ıdo no processo de actualizaçao˜ do carroçaria do mesmo prototipo´ para os novos regulamentos de 2019. Para começar, o modelo CAD da asa foi alterado devido a defeitos estruturais existentes no modelo anterior. De seguida, foi definido um layup standard e avaliado a sua rigidez estrutural recorrendo a estudos de elementos finitos. Com base nos resultados desses estudos, foram definidos objectivos para optimizaçao˜ da estrutura da asa de maneira a obter a maior rigidez poss´ıvel para a menor massa poss´ıvel. Recorrendo ao solver Optistruct e a um novo algoritmo desenvolvido para simplificar a forma do resultado da optimizaçao,˜ foi atingido um layup ideal que apresentava uma rigidez 73% superior apesar de ser 12% mais pesado. Com base no resultado optimizado foi analisado todo o processo de fabrico, desenhados os moldes e por ultimo,´ realizado um estudo para prever o custo relativo da peça comparativamente ao layup original. Os resultados deste estudo colocaram o layup optimizado fora do plano de fabrico devido ao custo total ser 479% superior ao layup standard. Com base no layup optimizado, foi testado um novo layup simplificado que nao˜ so´ teria melhor comportamento mecanicoˆ que o layup standard mas seria tambem´ significativamente mais barato que o layup optimizado. No final, a asa optimizada pesa 20% menos que o layup standard, e´ 54% mais r´ıgida para um aumento de custo de produçao˜ de 163%.

Palavras-chave: Prototipo´ LMP3, Optimizac¸ao˜ Estrutural, Materiais Compositos,´ Analise´ de Custo.

vii viii Abstract

This thesis follows all the design and optimization work of the new rear wing for the ADESS-03 LMP3 prototype. The work developed is included on the process of updating the bodywork of the prototype to comply with the new 2019 regulations. To start, the CAD model was updated due to structural defects existing on the previous model. After, a standard layup was defined and its structural integrity evaluated using FEA studies. Based on the results from those studies, objectives were defined for the wing optimization to obtain the stiffest structure possible for the least possible mass. Using Optistruct and a new algorithm developed to simplify the shape of the optimization process, an ideal layup was obtained that allowed for 73% less displacement to an increase in mass of 12%. Based on the optimized result, the whole manufacture process was analysed, the moulds were designed and finally, a study was performed to try to estimate the relative cost of the optimized layup compared to the standard layup. The results of this study placed the optimized layup outside of the manufacturing plan due to the total cost being 479% higher than the standard layup. Based on the optimized layup, a new simpler layup was tested that should have a better mechanical behaviour than the standard layup while being significantly cheaper than the optimized layup. In the end, the optimized wing weights 20% less than the standard layup, is 54% stiffer while being 163% more expensive to manufacture.

Keywords: LMP3 Prototype, Structural Optimization, Composite Materials, Cost Analysis.

ix x Contents

Acknowledgments ...... v Resumo ...... vii Abstract ...... ix List of Tables ...... xv List of Figures ...... xix Nomenclature ...... xxiii

1 Introduction 1 1.1 A Brief History of Modern Prototype Racing ...... 1 1.1.1 The LMP3 Class Introduction ...... 3 1.2 Thesis Motivation ...... 5 1.3 Regarding Composites Manufacture and Optimization ...... 7 1.4 Objective of this Thesis ...... 7 1.5 Structure of this Thesis ...... 8

2 Performance Background and Work Methodology 9 2.1 A Brief Introduction to the Concepts of Aerodynamics ...... 9 2.1.1 Mastering the Concepts and the New Standards ...... 10 2.1.2 Aero Package of a LMP Prototype ...... 12 2.2 The Old ADESS-03 Wing ...... 13 2.3 Planning for Design, Development and Manufacture ...... 15

3 The New ADESS-03 Wing 17 3.1 Modeling the New Wing ...... 17 3.2 FEA Analysis of the Standard Layup Wing ...... 21 3.2.1 Building the FEA Model – Before Meshing ...... 23 3.2.2 Meshing and Analysis ...... 23 3.2.3 Convergence Study ...... 29 3.3 Standard Layup Analysis Results ...... 31

4 Optimization Process 33 4.1 Optistruct Optimization ...... 33

xi 4.1.1 Free Size Optimization ...... 34 4.1.2 Size Optimization ...... 35 4.1.3 Shufﬂe Optimization ...... 35 4.2 Wing Optimization ...... 36 4.2.1 Free Size Optimization ...... 36 4.2.2 Ply Shape Edit ...... 40 4.2.3 MATLAB Bespoke Cleanup ...... 42 4.2.4 Cleaned Plies vs Free Size Plies ...... 46 4.2.5 Size Optimization ...... 47 4.2.6 Shufﬂe Optimization ...... 48 4.2.7 Manual Laminate Edit ...... 51 4.3 Analysis of the Optimization Results ...... 52

5 Manufacturing Planning and Analysis 55 5.1 The Wing Assembly Process ...... 56 5.2 Mould Design ...... 57 5.2.1 Top Skin Mould ...... 57 5.2.2 Lower Skin Mould ...... 59 5.2.3 Rib Mould ...... 60 5.3 Special Considerations and Manufacturing Procedure ...... 60 5.4 Costs of Manufacture ...... 62 5.5 Devising a Simplified Layup ...... 65 5.5.1 Simplified Layup Study and Optimization ...... 68 5.5.2 Simplified Layup Cost Study ...... 72

6 Conclusions 75 6.1 Achievements ...... 75 6.2 Future Work ...... 76

Bibliography 77

A Optimized Layup - Optimization Evolution 83 A.1 Plies Created After Free Size Optimization ...... 83 A.2 MATLAB Cleaned Plies Comparison - HyperMesh ...... 86 A.2.1 Ply 101200 ...... 86 A.2.2 Ply 213200 ...... 87 A.2.3 Ply 311300 ...... 88 A.3 MATLAB Cleaned Plies Comparison - MATLAB ...... 89 A.3.1 Ply 101200 ...... 89 A.3.2 Ply 213200 ...... 91 A.3.3 Ply 311300 ...... 93

xii A.4 Comparison - Cleaned Plies vs Free Size Plies ...... 95 A.5 Plies Created After Size Optimization ...... 98 A.6 Plies Created After Shufﬂe Optimization ...... 101 A.7 Laminates After Manual Editing ...... 104

B Material Cost for Optimized Layup 107

C Simpliﬁed Layup - Optimization Evolution 110 C.1 Plies Created After Free Size Optimization ...... 110 C.2 Plies Created After Size Optimization ...... 112 C.3 Plies Created After Shufﬂe Optimization ...... 114 C.4 Laminates After Manual Editing ...... 116

D Material Cost for Simpliﬁed Layup 118

xiii xiv List of Tables

3.1 Wing parameters for downforce calculation...... 23 3.2 Mechanical properties of Standard Modulus Plain Weave carbon ﬁbre fabric...... 26 3.3 Layup sequence for the standard wing laminates...... 27 3.4 Pressure loading values...... 29 3.5 Computer hardware for calculations ...... 30 3.6 Mechanical behaviour of the standard layup...... 31

4.1 Example of plies created after the free size analysis...... 34 4.2 Mechanical properties of high modulus unidirectional carbon ﬁbre fabric...... 36 4.3 Layup sequence for the super ply wing laminates...... 37 4.4 Comparison between free size results with UD reinforcements at 45o and 79,5o...... 37 4.5 Plies created for the Top Skin laminate after the free size optimization...... 39 4.6 Mechanical behaviour and mass comparison between the standard layup and the free size layup...... 40 4.7 OSSMOOTH effects on the free size model after multiple analysis with varying area ratios and iterations...... 41 4.8 Scoring system for the MATLAB square size value...... 44 4.9 Mechanical behaviour and mass comparison between the free size layup and the cleaned free size layup...... 46 4.10 Mechanical behaviour and mass comparison between the standard layup and the cleaned free size layup...... 47 4.11 Sample of some plies with their upper boundaries edited...... 47 4.12 Lower skin laminate after size optimization...... 49 4.13 Mechanical behaviour and mass comparison between the standard layup and the size layup...... 49 4.14 Mechanical behaviour and mass comparison between the standard layup and the shufﬂe layup...... 50 4.15 Lower skin laminate before and after the manual edit...... 51 4.16 Mechanical behaviour and mass comparison between the standard layup and the edited layup...... 53

xv 5.1 Example of laminate material cost from ply area with top skin laminate...... 63 5.2 Table with assumptions made regarding work cost and manufacturing time...... 65 5.3 Cost of the manufacture of each of the individual laminates for the optimized layup. . . . . 66 5.4 Optimized layup total cost...... 66 5.5 Cost of the manufacture of each of the individual laminates for the standard layup. . . . . 67 5.6 Standard layup total cost...... 67 5.7 Comparison between total cost of standard layup and optimized layup...... 68 5.8 Occurence of each direction of reinforcement on each of the laminates...... 68 5.9 Superplies used for the optimization process of the new simplified layup...... 69 5.10 Final laminates obtained for the new simplified layup...... 70 5.11 Results from the static analysis of the new simplified layup...... 70 5.12 Mechanical behaviour differences of the new simplified layup compared to the previous optimized layup...... 71 5.13 Mechanical behaviour differences of the new simplified layup compared to the standard layup...... 71 5.14 Cost difference between simplified layup and optimized layup ...... 72 5.15 Cost difference between simplified layup and standard layup...... 73

A.1 Top skin laminate plies after free size optimization ...... 83 A.2 Lower skin laminate plies after free size optimization ...... 84 A.3 Rib laminate plies after free size optimization ...... 85 A.4 Comparison between top skin plies before and after cleaning...... 95 A.5 Comparison between lower skin plies before and after cleaning...... 96 A.6 Comparison between rib plies before and after cleaning...... 97 A.7 Top skin laminate plies after size optimization...... 98 A.8 Lower skin laminate plies after size optimization...... 99 A.9 Rib laminate plies after size optimization...... 100 A.10 Top skin laminate plies after shuffle optimization...... 101 A.11 Lower skin laminate plies after shuffle optimization ...... 102 A.12 Rib laminate plies after shuffle optimization...... 103 A.13 Top skin laminate plies after manual editing...... 104 A.14 Lower skin laminate plies after manual editing...... 105 A.15 Rib laminate plies after manual editing...... 106

B.1 Material cost for top skin laminate...... 107 B.2 Material cost for lower skin laminate...... 108 B.3 Material cost for rib laminate...... 109

C.1 Top skin laminate plies after free size optimization...... 110 C.2 Lower skin laminate plies after free size optimization...... 111

xvi C.3 Rib laminate plies after free size optimization...... 111 C.4 Top skin laminate plies after size optimization...... 112 C.5 Lower skin laminate plies after size optimization...... 113 C.6 Rib laminate plies after size optimization...... 113 C.7 Top skin laminate plies after shuffle optimization...... 114 C.8 Lower skin laminate plies after shuffle optimization...... 114 C.9 Rib laminate plies after shuffle optimization ...... 115 C.10 Top skin laminate plies after manual editing...... 116 C.11 Lower skin laminate plies after manual editing...... 116 C.12 Rib laminate plies after manual editing...... 117

D.1 Material cost for top skin laminate...... 118 D.2 Material cost for lower skin laminate...... 119 D.3 Material cost for rib laminate...... 119

xvii xviii List of Figures

1.1 Group C Legend Poster...... 2 1.2 BPR Global GT Series race start...... 3 1.3 Le Mans 24h start in 2006...... 3 1.4 Side proﬁle of GTE and LMP3...... 4 1.5 ADESS-03 carbon ﬁbre kit...... 6 1.6 Nissan Zeod RC and Lotus T128 LMP2...... 6

2.1 1938 Mercedes Benz W125 Record Car...... 10 2.2 Michel May’s Porsche 550 Spyder...... 10 2.3 Chaparral 2C at Nassau, 1965...... 11 2.4 1969 Spanish Grand Prix...... 12 2.5 Contemporary study of aerodynamics on racing cars...... 12 2.6 LMP aerodynamic devices...... 13 2.7 Wing bounding box...... 13 2.8 Current ADESS-03 wing...... 14 2.9 Current wing detailed stress point...... 14 2.10 Current wing with no top skin...... 15 2.11 Development process ﬂuxogram...... 16

3.1 Pininfarina H2 Speed 2018 at the 2018 Geneva Motor Show...... 17 3.2 New rib and lower skin design...... 18 3.3 New wing conﬁgurations...... 18 3.4 Wing aluminium inserts...... 19 3.5 Side proﬁle of the new wing...... 19 3.6 New wing...... 20 3.7 Detail of new wing assembly...... 20 3.8 Wing adjusment from aero guide...... 20 3.9 Nico Rosberg at the 2016 Chinese Gran Prix...... 21 3.10 Autodromo´ do Estoril telemetry ...... 22 3.11 Rib defeature comparison...... 23 3.12 Automesh menu...... 24

xix 3.13 Local edge reﬁnement...... 24 3.14 Quality index menu...... 25 3.15 Elements normal and direction...... 25 3.16 Plain weave carbon ﬁbre fabrics...... 26 3.17 Zone vs ply based modelling...... 27 3.18 HyperMesh laminates menu...... 28 3.19 Wing pressure distribution...... 28 3.20 Mapped loads...... 29 3.21 Bonding areas...... 30 3.22 Results of the convergence analysis...... 30 3.23 Results from the standard layup static analysis...... 31

4.1 Optistruct’s composite optimization process...... 34 4.2 Wing diagonal angle...... 38 4.3 Output ﬁle...... 40 4.4 OSSMOOTH plies...... 42 4.5 Picture from HyperWorks Help explaining how the bulk data on the .fem ﬁle is separated. 43 4.6 Ply cleanup process ...... 43 4.7 Element numbering...... 44 4.8 Ply cleanup MATLAB output ...... 45 4.9 Ply cleanup on HyperMesh...... 45 4.10 Ply cleanup on laminate...... 45 4.11 Time to execute the MATLAB code for ply cleanup...... 46 4.12 Deleted ply during manual edit...... 52 4.13 New top skin laminate ...... 52 4.14 Shifting of the maximum displacement zones...... 53 4.15 Optimized layup failure...... 53

5.1 Iteration difference on ply geometry ...... 55 5.2 H2 Speed wing bondind instructions ...... 56 5.3 Top skin mould add-on details ...... 58 5.4 Add-ons attachment details ...... 58 5.5 Exploded top skin mould ...... 59 5.6 Top skin mould ...... 59 5.7 Lower skin mould ...... 60 5.8 Rib mould ...... 61 5.9 Vacuum bagging cutout ...... 61 5.10 Carbon waste diagram ...... 64 5.11 Results from the static analysis of the new simpliﬁed layup ...... 71 5.12 Final H2 Speed wing ...... 73

xx 5.13 Produced wing moulds ...... 74

A.1 Ply 101200 before MATLAB cleanup...... 86 A.2 Ply 101200 after MATLAB cleanup...... 86 A.3 Ply 213200 before MATLAB cleanup...... 87 A.4 Ply 213200 after MATLAB cleanup...... 87 A.5 Ply 311300 before MATLAB cleanup...... 88 A.6 Ply 311300 after MATLAB cleanup...... 88 A.7 Ply 101200 before MATLAB cleanup...... 89 A.8 Ply 101200 after MATLAB cleanup...... 89 A.9 Ply 101200 comparison before and after MATLAB cleanup...... 90 A.10 Ply 213200 before MATLAB cleanup...... 91 A.11 Ply 213200 after MATLAB cleanup...... 91 A.12 Ply 213200 comparison before and after MATLAB cleanup...... 92 A.13 Ply 311300 before MATLAB cleanup...... 93 A.14 Ply 311300 after MATLAB cleanup...... 93 A.15 Ply 311300 comparison before and after MATLAB cleanup...... 94

xxi xxii Nomenclature

Greek symbols

ν12 Major Poisson’s Ratio.

ρ Density.

Roman symbols

D Downforce.

o E1 Young’s Modulus angle 0 .

o E2 Young’s Modulus angle 90 .

F Lift Coefﬁcient. f (x) Objective Function.

G12 In Plane Shear Modulus. x ik Thickness of the i − th super-ply of the k − th element.

H Chord. hp Horsepower.

NE Number of Finite Elements.

Np Number of super plies.

S Ultimate In-plane Shear Strenght.

V Velocity.

W Wingspan.

o Xc Ultimate Compressive Strength 0 .

o Xt Ultimate Tensile Strength 0 .

o Yc Ultimate Compressive Strength 90 .

o Yt Ultimate Tensile Strength 90 .

xxiii xxiv Glossary

ACO = Automobile Club De L’Ouest CAD = Computer Aided Design Can-Am = Canadian-American Challenge Cup CFD = Computational Fluid Dynamics DRS = Drag Reduction System F1 = Formula 1 FEA = Finite Element Analysis FIA = Fed´ eration´ Internationale de l’Automobile FSTOSZ = Free Size to Size GSM = Grams per Square Meter GT = Grand Touring GTE = Grand Touring Endurance GTE - AM = Grand Touring Endurance - Amateur GTE - PRO = Grand Touring Endurance - Professional HM = High Modulus Plain Weave Carbon Fibre Fabrics LMP = Le Mans Prototype LMP1 = Le Mans Prototype 1 LMP2 = Le Mans Prototype 2 LMP3 = Le Mans Prototype 3 LMP675 = Le Mans Prototype 675 LMP900 = Le Mans Prototype 900 LMPGT = Le Mans Prototype Grand Touring NACA = National Advisory Committee for Aeronautics Prepreg = Pre-Impregnated Fibre SM = Standard Modulus Plain Weave Carbon Fibre Fabrics SZTOSH = Size to Shufﬂe TMANUF = Manufacturable Thickness UD = Unidirectional

xxv xxvi Chapter 1

Introduction

On this chapter is presented a brief introduction to prototype racing and LMP3 racing cars so it is possible to better understand the scope of this thesis. The motivations behind this work, its objectives and the overall structure are also presented.

1.1 A Brief History of Modern Prototype Racing

Le Mans Prototypes (LMP) were first used in the 1992 24h of Le Mans. Group C Prototypes, some of them shown in Figure 1.1 on a slot car poster, were one of the most famous racing categories ever. With their golden age coming to an end after the introduction of the 3.5L Engine Rule in 1991 [1] and looking at a reduced grid for the 1992 season [2], the Automobile Club De L’Ouest (ACO) decided to introduce a new class of prototype racing cars to complement the existing Group C cars. Since this new class was not immediately a success and new entrants were scarce, for 1993 and for the first time in seven years, Grand Touring (GT) cars were allowed to take part in the 24h of Le Mans. These new GT cars would have to be based on existing road cars and comply with a set of rules including minimum production numbers of their street legal variant. Competing alongside the new GT and the old Group C, the LMP cars were off to a slow start. Compared to GT cars, the Group C cars were expensive to maintain so they quickly disappeared. The first entrants of the LMP class were mostly modified Group C chassis to comply with the LMP regulations. The costs associated of running a dedicated prototype racing car along with the success of the new GT class meant that until 1999, the racing scene was dominated by the GT class cars. Notable entrants on the LMP class between 1993 and 1999 are few and overshadowed by the feats of GT cars like the McLaren F1 GTR, Porsche 911 GT1 and the Mercedes-Benz CLK GTR LM that can be seen in Figure 1.2. The ones that are mostly remembered now are due to the exploitation of loopholes on the regulations [4] or curious circumstances [5]. With the development of the GT class cars mostly due to heavy factory support from brands like Porsche, Mercedes-Benz, McLaren, Nissan and Chrysler, these cars quickly became too fast.

1 Figure 1.1: Slot.it poster with some of the available Group C miniatures for slot car racing. With almost 10 years of racing and 53 entrants per year on the Le Mans 24h, the diversity of manufacturers and the colours of the liveries stay to this day on the minds and hearts of the aﬁcionados. Retrieved from [3].

The original road like designs were being exploited with huge wings, enlarged wheel arches and advanced aerodynamic solutions. With the increase in speed of the closed GT cars, the ACO published a new set of rules for 1999: this new set of regulations contemplated two types of LMP cars – the LMP Prototypes similar to the ones existing so far and the new Le Mans Prototype Grand Touring cars (LMPGT).

The new LMPGT class consisted mostly of the evolutions of the previous leading GT class cars that were deemed too advanced and too fast to be considered a simple GT car.

The main difference between these LMP and the LMPGT cars were their cockpit design: the LMP cars were open-top vehicles while the LMPGT cars were closed-top vehicles.

Changes were made once again to the LMP regulations in 2000 redeﬁning the existing two classes of prototype cars: LMP900 and LMP675 with the numbers of each referring to the minimum weight of the prototype. These changes were kept until 2005 when the “current” LMP prototypes were introduced.

2 Figure 1.2: BPR Global GT Series race at Brands Hatch in 1996. Even today, these cars are instantly recognizable by their incredible looks and performance. Retrieved from [6].

For 2005, the ACO introduced the new two classes of LMP prototypes – the LMP1 and the LMP2 cars. The LMP1 cars were now the top class, more advanced and powerful than their LMP2 siblings. Due to this difference, LMP2 cars are incapable of competing for wins while racing against LMP1 cars so major manufacturers where encouraged to move to the LMP1 class while leaving the LMP2 class mainly for privateers.

Figure 1.3: Le Mans 24h start in 2006. The ﬁrst two cars on the grid were the then new Audi R10 TDI. The ﬁrst diesel powered car to win the toughest race in the world. Retrieved from [7].

With a few changes throughout the years including the addition of diesel engines, ﬁrst introduced in the 2006 Le Mans 24h with the Audi R10 TDI shown in Figure 1.3, and hybrid propulsion systems, 2015 arrives with the prototype class main features unchanged.

1.1.1 The LMP3 Class Introduction

Arriving in 2015 [8], a new class of prototypes was introduced: the LMP3 Prototypes. Until 2015, endurance racing had four main categories: the leading LMP1 prototypes, usually backed by leading manufacturers, LMP2 prototypes used mainly by privateers and lastly, Grand Touring Endurance - Pro- fessional (GTE - PRO) and Grand Touring Endurance - Amateur (GTE - AM).

3 The last two classes, GTE - PRO and GTE - AM both use GTE class cars which are GT cars based on existing road going models. The difference between the two [9] is the number of professional drivers allowed on each race with the GTE - PRO teams consisting of only professional drivers and the GTE - AM consisting of a maximum of one professional driver (each teams consists of three drivers). Also, the GTE - PRO teams are usually backed by the manufacturer of the car. Notable teams include Aston Martin, Ferrari, Corvette, Ford and Porsche. With this in mind, the natural progression of performance on endurance is: GTE, then LMP2 and finally LMP1. The problem with this is that there is a huge gap of performance between the GTE cars and the LMP2 cars. Reduced weight, more horsepower, improved braking and improved downforce translate not only on much quicker lap times but also a completely different driving style. This gap made stepping out of a GT car on to a LMP2 car a difficult experience and getting used to the LMP2 came with a steep learning curve. The LMP3 prototypes arrived to made climbing the ladder from GT racing to prototype racing easier. With performance levels close to a GT car, displayed in Figure 1.4, a LMP3 car, also displayed in Figure 1.4, resembles a smaller LMP2 prototype. The main goal while defining the regulations for the LMP3 class was to make the car as easy to use and maintain as possible. With this in mind, a number of constraints were introduced: all LMP3 cars have the same engine and gearbox and the sale price of a new car must not exceed 206 000e [10].

(a) Ferrari 488 GTE. Retrieved from [11].

(b) Ligier JS P3 LMP3. Retrieved from [12].

Figure 1.4: From the side proﬁles of both cars it’s easy to see the resemblance of a GTE car with their road going counterpart. The LMP3 prototype meanwhile is a much more focused machine.

The powertrain of the LMP3 cars consists of a Nissan 5 litre naturally aspirated V8 engine with 420 hp and a six speed X-Trac gearbox. All the LMP3 cars have a closed cockpit design with a carbon ﬁbre monocoque and a steel roll cage. The 420 hp of the engine may not seem much when compared to the GT cars that have around 500 hp, variable, but when coupled with the low weight of 930 kg, 315 kg less than the minimum weight required by the Fed´ eration´ Internationale de l’Automobile (FIA) for GTE cars [13], the LMP3 is able to match the performance of a GT car with higher cornering speeds and smaller braking distances.

4 With the before mentioned characteristics, the LMP3 stepped in as the necessary step between GT racing and prototypes racing. Homologated to race on national and international events such as V de V, Michelin Le Mans Cup, European and Asian Le Mans Series, the class was received with great success. After three seasons of LMP3, in 2018 the new regulations for 2020 were announced. Four manufacturers were allowed to continue to produce and sell LMP3 prototypes: Duqueine Engineering, previously Norma, Ligier, Ginetta and ADESS AG. Since the regulations state that an evolution for the car may only be homologated every three years, the new 2020 regulations present a good opportunity to improve the performance of the existing prototypes.

1.2 Thesis Motivation

The first homologation of the ADESS-03 prototype was overweight by around 30 kg, actual deficit depends on the chassis specification. In order to overcome this obstacle, the best solution was to develop a new bodywork layup. In order to keep costs down, the first ADESS-03 prototypes all had a glass fibre bodywork so, an easy way to reduce the weight of the car was replacing the glass fibre by carbon fibre. Through the course of two months, new ply books were devised to allow the manufacture of the new bodywork parts. With no data available, Computational Fluid Dynamics (CFD) studies for example, to improve every single part using optimization software and little time to complete this project, empirical data was collected from the cars that were competing along with knowledge from the mechanics that had assembled the previous chassis to define a standard layup for every single part. This standard layup was then updated if a part had behaved improperly on previous occasions. In the end the new parts, all of which are displayed in Figure 1.5, were successfully installed and allowed the car to be underweight, which in turn allowed to changes on the whole setup of the car for better performance. Although lighter, these new parts are now much stiffer than their glass counterparts and will hopefully work as intended.

The Rear Wing

Among all the bodywork parts updated, one part needed special attention. From the data gathered from the working cars, the rear wing was prone to fail during races due to a design ﬂaw. This failure was easily detected to be due to a design failure that prevented the loads created from being correctly distributed through the whole width of the wing. Although fairly rigid while static, this ﬂaw rendered useless the mechanical properties of the material from which the wing was manufactured so, a complete redesign was needed. This proved to be the ideal set up for this master thesis since an updated layup and manufacturing plan was already under way, the need to design a whole new part presented the perfect opportunity to completely follow the design and manufacturing stages of a new composite component.

5 Figure 1.5: The ADESS-03 carbon ﬁbre bodywork kit consists of 48 individual components, not including parts that are symmetric regarding the middle plane of the car.

About ADESS

Advanced Design and Engineering Systems Solutions (ADESS) is a motorsport company created in Munich in May 2012 [14]. Among its projects are the Lotus T128 LMP2 Prototype, the Nissan Zeod RC Garage 56 experimental prototype, both of them showed in Figure 1.6, and of course, the ADESS-03 LMP3 Prototype.

ADESS moved to Portugal on January 2017 to better expand its production and engineering activi- ties.

(a) Nissan Zeod RC. Retrieved from [15]. (b) Lotus T128 LMP2. Retrieved from [16].

Figure 1.6: The Nissan Zeod RC and the Lotus T128 LMP2 are two of the cars developed within ADESS- AG.

6 1.3 Regarding Composites Manufacture and Optimization

Although production started in the 1950’s, carbon fibre widespread use did not appear until the end of the 1960’s with Rolls Royce using it to manufacture blades for jet engines [17]. Although light, these new blades did not have the expected impact due to their vulnerability to damage from bird strikes among others, revealing one of the setbacks of designing with carbon fibre reinforced composites [18]. The first use of carbon fibre in motorsport was in 1981 with the McLaren MP4/1 Formula 1 car [19]. This car boasted the first ever carbon fibre monocoque. Developed by McLaren with the help of Hercules Composites, an american aerospace company, the carbon fibre monocoque proved to be not only lighter, but also stiffer and safer [20] than its aluminium counterparts. These first carbon fibre monocoques used sandwich panels of nomex honeycomb core and carbon fibre skins bonded together with structural adhesive [21]. Although revolutionary for the time, they lacked the structural integrity of contemporary carbon fibre monocoques [22] . The flexibility modern composites provide regarding design solutions and mechanical properties make their use ideal for almost any application on motorsport and aeronautics, among other, where lighter and stiffer components are sought after, most of the times with little to no regard to the final cost [23]. In order to extract the best performance with the least possible mass, optimization of structural parts is one of the tools that can be used to do it. Composite optimization as seen a great development in recent years as described in the work published by Altair’s current director of software development [24] [25] [26]. With the advances in recent years regarding finite element analysis (FEA), free size optimization [27] was improved and added to commercial software as an alternative to other optimization methods [28].

1.4 Objective of this Thesis

The goal of this master thesis was to provide an in depth guide on the processes and choices that go into designing the new rear wing for the ADESS-03 LMP3 Prototype. Starting by designing the wing itself, first there was the need to understand what caused the failures of the previous wing. The new design needed to reflect changes that would improve on this subject. Second, a static analysis of the standard layup defined for this component to understand what are its limitations, followed by a process of structural optimization to extract the best performance of the geometry and the materials used on the manufacture of the final part. Since cost is an important part of the LMP3 category and, a part resulting from an optimization process is not necessarily cost friendly, the total cost of the manufacture of the part was evaluated through simple calculations to understand the feasibility of the optimized component. In the end, measures to improve both the manufacturability and the total cost of the component were implemented to make sure the final result presented a good compromise between mechanical performance and total component cost.

7 1.5 Structure of this Thesis

On this first chapter, modern prototype racing was introduced by tracing the current generation prototypes origins to their roots back in the beginning of the 1990’s. The current racing hierarchy was established and the train of thought that led to the introduction of the LMP3 class was presented. A brief background regarding composite manufacture and optimization was exposed. The motivation and objectives of this thesis were also highlighted. Chapter 2 begins by tracing the origins of aerodynamics on racing cars back to its origins. Their history is briefly described and the old ADESS-03 wing is presented along with its defects. The methodology used to face the problems to be solved by this thesis is presented as well. Chapter 3 starts with the new wing being designed using CATIA to comply with the new requirements. An FEA model is built using HyperMesh to allow the study of the standard layup and all the preparatory actions are described. A convergence analysis is performed to find the ideal element size and the first results are obtained. Chapter 4 is the wing optimization chapter. The optimization process used by Optistruct is described along with its limitations. The optimization process begins with the free size optimizations and its results. A bespoke solution coded using MATLAB is devised to allow the best simplification of the results of the free size analysis. Decisions regarding the layup sequence are explained and the optimization process is completed. Before the next chapter, the final layup is edited to allow correct manufacturing. Chapter 5 consists on the planning and cost analysis of the manufacturing process for the optimized wing. The whole manufacturing process is explained beginning by the wing assembly, bonding and finally the specificities of the material used like the curing method. Moulds for all the composite components are designed and thoughts behind design choices are clarified. Finally, a cost analysis is devised to understand how much more expensive is the new optimized layup. In the end a solution is found between the standard layup that performs poorly structurally and the optimized layup that is too expensive to manufacture. Chapter 6 presents all the conclusions retired from this work, a brief analysis of the results and suggestions for the upcoming work.

8 Chapter 2

Performance Background and Work Methodology

In this chapter, the origins of aerodynamics in racing cars are introduced. The current state of aerodynamic performance on LMP prototypes is described. The old wing of the ADESS-03 prototype is analysed and its problems identiﬁed. Finally, the methodology used to design and improve the new wing is described.

2.1 A Brief Introduction to the Concepts of Aerodynamics

Auto racing appeared almost as soon as automobiles were invented with the first recorded race event taking place as early as 1867 between two cities in England [29]. The first auto racing events had what could be called the regular automobiles of the time participating. Wealthy people that could afford an automobile would race their own car against their friends in an attempt to see who was the fastest. Since the human being always thrives to be the best within a competitive environment, people sought after marginal improvements that could make their vehicle faster than the one that they were racing against. By the 1930’s, purpose built racing cars began to appear. With the increasing popularity of motor racing, manufacturers like Alfa Romeo, Auto Union, Bugatti and Mercedes-Benz began producing factory ready racing cars featuring enlarged engines and streamlined bodies, as displayed in Figure 2.1, so they could gain every margin of improvement against their competition sometimes going as far as to producing cars with no paint to save every kilogram of weight possible [30]. Although the principles of fluid mechanics have been established for more than two hundred years, a profound knowledge of how they can be of used to improve the performance of an automobile has only been acquired on the past thirty to forty years. Automotive engineers first noticed the effects of aerodynamics on a car when they started experimenting with streamlined bodyworks in the 1920’s. When the norm to reach a higher speed was to increase the size of the engine, the use of a streamlined body allowed for reduced drag that came in

9 Figure 2.1: 1938 Mercedes Benz W125 Record Car. Before there was a deep understanding of aerodynamics, manufacturers started exploring streamlined designs to improve the top speed of their cars. Retrieved from [31]. handy when bigger engines could not be manufactured. The ﬁrst known use of wings on a race car also dates back to the late 1920’s [32] when some experiments were done to improve stability at high speeds but widespread use of wings on race cars would be ignored for the next thirty-ﬁve years.

2.1.1 Mastering the Concepts and the New Standards

The ﬁrst documented and well succeed use of a wing on a race car dates back to 1956 when a Swiss engineer called Michel May put a wing on his Porsche 550 Spyder [33], his Porsche shown in Figure 2.2 and compared to a regular 550 Spyder. He was so successful that his private effort was faster than the cars supported by Porsche themselves so, Porsche convinced the organization to ban the wing on the pretence that it blocked the vision of the drivers that were following the car and so rear wings were once again forgotten.

(a) Michel May’s Porsche 550 Spyder in the 2018 Goodwood (b) Porsche 550 Spyder. Retrieved from [35]. Festival of Speed. Retrieved from [34].

Figure 2.2: See the difference between Michel May’s Porsche and the standard car. The wing meant a difference of four seconds on the qualifying time.

One of the ﬁrst big adopters of aerodynamic devices, and quite possibly the most inﬂuential and innovative developer, was Jim Hall of Chaparral Cars [36]. Chaparral was a small Canadian-American Challenge Cup (Can-Am) race car manufacturer based in Texas owned by Jim Hall and Hap Sharp.

10 Chaparral existed only during seven brief years but it was enough to change the use of aerodynamics on race cars forever. First campaigned through the 1963 Can-Am Season, the Chaparral 2 was having handling problems due to the front wheels of the car being prone to lifting of the ground and with this, achieving subpar results. In order to overcome this difficulty, the car was upgraded to the Chaparral 2B that added two front mounted wings (dive planes) and this change immediately improved driving accuracy and the driver’s confidence. The first big innovation though came with the 2C on the form of an adjustable rear wing show on its two both states in Figure 2.3. The manual transmission on the 2B was changed to an automatic on the 2C that left the left foot of the driver free during races. A third pedal was added to control the rear wing the was flat during straights to reduce drag and tipped up during corners to improve downforce.

(a) Chaparral 2C racing at Nassau, 1965. (b) Chaparral 2C in pits at Nassau, 1965.

Figure 2.3: Jim Hall driving the Chaparral 2C at Nassau, 1965 with the wing on the straight position (a) and on the ﬂat position (b). Also visible are the dive planes mounted ahead of the front wheels. These dive planes load the front wheels when the car is moving to prevent understeer. Retrieved from [37].

After the success of the 2C, the concept was taken to the extreme with the Chaparral 2E and 2F. They both had hydraulic adjustable high rear wings mounted straight on the rear uprights. On their seven years active, Chaparral pioneered the use of spoilers, rear wings and later, ground effect with the famous Chaparral 2J also known as the fan car. With the success of Chaparral use of wings on their cars, the news eventually reached Formula 1 (F1) teams that started to experiment in order to gain an advantage over the adversaries. McLaren was the ﬁrst to test a winged car in 1966 but due to a lack of funding, progress on this area was put on hold. In 1967 Lotus started testing with improvised rear wings made from helicopter rotor blades after Jim Clark raced an Indy car that possessed small wings and was amazed with the grip and stability generated by that car. For the 1968 season Lotus introduced the improved Lotus 49, the ﬁrst F1 car to have a rear mounted wing. Since understanding of aerodynamics was pretty rudimentary, the wing on the Lotus was mounted directly on the rear uprights since there is where downforce is better applied, directly on the rear wheels. Although campaigned with great success, Graham Hill won the 1968 World Championship with the Lotus 49, due to numerous accidents regarding a complete failure of the struts holding the rear wing, high wings as shown in Figure 2.4, mounted on the uprights were eventually banned and from there on, they had to be mounted on the bodywork. The following years led to wild experimenting with aerodynamic devices. Since CFD and wind tunnel

11 Figure 2.4: High winged F1 cars in the 1969 Spanish Grand Prix. Retrieved from [38]. testing was non existing back in the 1960’s and 1970’s, the only way teams had to evaluate the performance of aerodynamic devices was through testing and this led to some curious solutions to appear throughout the years. The aerodynamic era freedom culminated with the last ground effect cars in 1982.

2.1.2 Aero Package of a LMP Prototype

With the development of CFD studies and the use of wind tunnels, both displayed in Figure 2.5, in 2018 the knowledge of vehicles aerodynamics is vast and breakthroughs are mainly reserved for small areas usually found through loopholes on regulations. This knowledge means that the use of aerodynamic devices on race cars is now heavily regulated through the rulebooks that control motorsport.

(a) Porsche testing the 911 RSR on a wind tunnel before its (b) Vortices created by the aero package of the 2015 Chevrolet release in 2017. Retrieved from [39]. Indy Car can be visualized using CFD. Retrieved from [40].

Figure 2.5: Contemporary study of aerodynamics on racing cars.

The three devices responsible for generating downforce on an LMP car, highlighted in Figure 2.6, are: the front splitter, the rear diffuser and the rear wing. Of these three, the most important one is the front splitter. Responsible for an average of 50% of the car’s downforce, considering a perfect 50-50

12 aerodynamic setup, the splitter is the ﬁrst part of the car to face the air and so it dictates the airﬂow around the prototype.

Figure 2.6: Highlighted are the splitter in green, diffuser in blue and rear wing in red.

Next, the rear diffuser, responsible for 30% of the car’s downforce. The rear diffuser is a device that sits on the bottom rear of the car that uses Bernoulli’s principle to produce downforce. The air traveling between the car and the road surface is expanded on tunnels on the diffuser to create a low pressure zone at its entrance therefore generating downforce. Finally, there is the rear wing. Responsible for roughly 20% of the total downforce of a LMP prototype, the wing generates downforce using an airfoil proﬁle and it is attached directly to the gearbox of the car through two pillars, on an LMP3 car.

2.2 The Old ADESS-03 Wing

As mentioned before the rear wing of a LMP3 prototype is a very important part on the overall performance of the racing car and as such, it needs to withstand everything that is expected to happen during a race such as the aerodynamic loads generated and fatigue felt through bumps on the surface track. The rear wing then, needs to be designed as a structural part. The LMP3 regulations state that the rear wing is made up of three types of elements: the wing itself, the vertical supports, pillars, and the endplates [10]. The wing must be obtained by the extrusion on the Y direction of a proﬁle capable of generating downforce and it must ﬁt inside a volume of 300 mm horizontally, 150 mm vertically and 1600 mm transversally, as illustrated in Figure 2.7.

Figure 2.7: The wing “be framed by a volume measuring 300 mm horizontally × 150 mm vertically × 1600 mm transversally”. “The rear wing proﬁle is free but must be obtained by extrusions from Y of the constant section throughout the length of the rear wing” [10].

13 For this thesis, the only part that will be updated is the wing itself, not the pillars nor the endplates since both of these items ﬁt the regulations as intended. With this in mind, the rear wing must also reﬂect the idea behind a LMP3 prototype so, it must be cheap to manufacture and reliable so it can be used on the biggest number of races possible without the need to be replaced. The current design of the rear wing on the ADESS-03 prototype, shown in exploded view in Fig- ure 2.8, is made of four main parts: a top skin, a lower skin, a structural rib and a middle insert assembly to support the wing to the pillars. Apart from the parts mentioned above, there are also two aluminium inserts, one on each end, to attach the endplates to the wing.

Figure 2.8: The current design of the ADESS-03 wing with the centre aluminium insert assembly and the split rib.

Although the current design seemed good at ﬁrst, after some time the wings started to break during racing. The structural rib inside the wing is split in two halves, one on each side of the aluminium insert assembly on the middle. During assembly, the rib is bonded to the insert assembly and then to both top and lower skins which in turn, are then bonded to each other. The way the insert assembly was designed creates a point on the top skin, shown in Figure 2.9, where the load is concentrated, instead of being evenly distributed by the whole width of the wing, and so every wing started splitting from this point.

Figure 2.9: On this detail it is possible to see the inside of the wing where the rib meets the aluminium insert assembly. The rear of the aluminium insert assembly is exerting pressure on the top skin alone.

Apart from the ﬂawed design of the insert assembly, the rib split in half, shown in Figure 2.10, also proved to be a wrong choice since it did not allow the load to be distributed from one point of the wing to the other. Since the rib was cut before the insert, the only material left to hold the load is the middle part of the top skin that has two holes so the insert can ﬁt through, this provides the perfect place for a complete failure to occur.

14 Figure 2.10: Before bonding the top skin, ﬁrst there is the need to assemble both halves of the rib and the aluminium insert assembly.

2.3 Planning for Design, Development and Manufacture

After analysing the causes of failure of the previous wing and before starting the development process of the new wing, the work methodology was defined. On the design phase of the wing, updating the model using CATIA, standard considerations regarding component design were taken into account [41]. The new wing had to be structurally sound and, unlike the previous model, not feature any design choice that would compromise its efficiency. An important part of the design of a new structural component is FEA [42] [43]. FEA analysis allows the understating of the physical limitations of a new component without the need to actually manufacture and test it until it fails. Despite being very important, FEA analysis is also very demanding requiring a lot of preparation to do correctly and needing accurate data so the studies can be performed as close to real life working situations as possible. In order to establish goals for the optimization process, the new wing with the standard layup was submitted to a static stress analysis to understand its mechanical limitations. On this analysis, the loads to which the wing is submitted were simplified due to a lack of data, this simplification is demonstrated in Chapter 3. Despite being simplifications, these loads are a good approximation of the loads exerted on the real wing [44]. After the static analysis and with optimization goals defined, a structural optimization analysis [45] was performed using HyperWorks. The solver used, Optistruct, uses free size optimization to perform this kind of calculations. This optimization process has three stages and can be used to increase the structural performance of many components, all the way from Formula 1 parts [46] to aircraft wings [47]. The steps followed for the optimization process are readily available from various sources [48] and can be applied not only to composite structures, but to other kinds of structural parts [49]. During the optimization process is important to take later manufacturability into account so, before the optimization process is ended, ply cleanup is necessary [45]. Although information regarding ply cleanup is scarce, it was found that it can be done manually [27] or using functionalities within HyperWorks. Since the results were not satisfactory, a bespoke solution was developed using MATLAB, further described in Chapter 4.

15 With the results from the structural optimization ready, the tools needed to manufacture the wing were developed taking into account the restrictions related to working with composite materials [50]. With the tools ready, a simple calculation cost [51] was performed to understand how expensive, compared to the stantard layup, the optimized layup would be. With the optimized results not complying with the core of the LMP3 category, a new solution was devised to sit between the standard layup and the optimized layup. The whole development process can be described by the ﬂuxogram shown in Figure 2.11.

Figure 2.11: Development process ﬂuxogram.

16 Chapter 3

The New ADESS-03 Wing

In this chapter the new wing for both the ADESS-03 and the Pininfarina H2 Speed 2018 is designed. A static analysis is performed on the standard layup to understand its limitations.

3.1 Modeling the New Wing

The CAD software used for this thesis was Dassault Systemes` CATIA V5 since it is the CAD software package used at ADESS. Before the design of the new wing started there was a special consideration to take into account: a new car was being developed at that exact same time and this car was based on the ADESS-03 LMP3. The main difference regarding the wing is that instead of two pillars, the Pininfarina H2 Speed 2018 only has one central pillar, as shown in Figure 3.1, so the attachment points for the wings of both cars must be made in a way that both can be manufactured from the same mould.

Figure 3.1: Pininfarina H2 Speed 2018 at the 2018 Geneva Motor Show. On the ﬁgure is visible the central attachment of the wing to the central pillar, hidden inside the ﬁn. Retrieved from [52].

The first thing decided was to keep the rear wing profile so to not upset the dynamic balance of the car. This profile is a standard National Advisory Committee for Aeronautics (NACA) profile capable of

17 generating 400 kg of downforce at a speed of 280 km/h [53]. After deﬁning the proﬁle, the next thing was the rib design. One certainty was that the rib would need to follow the whole width of the wing to prevent weak zones damage on the structural integrity of the new part. The need to be able to hold the wing a single or double pillar was also taken into account. The middle section of the new rib has three indentations, shown in Figure 3.2, so the mould can be manufactured just one time and the same rib can be used for the wing of both the ADESS-03 and the H2 Speed with no need for further changes.

Figure 3.2: New rib and lower skin design. Visible on the ﬁgure are the three indentations that allow for both a single pillar or two pillars.

Speaking of indentations, two different conﬁgurations, illustrated in Figure 3.3, are planned for the top skin: one with two supports for the ADESS-03 and one with one for the H2 Speed. The cavities for the two support methods were designed to have the exact same size so the ﬁnal top skin could be changed by swapping the location of an add-on on the mould for the part.

Figure 3.3: On the left side, wing conﬁguration for the LMP3 prototype with two indentations for both rear pillars. On the right side, wing conﬁguration for the Pininfarina H2 Speed 2018 with one indentation for a single pillar.

Before finishing the design of the wing, three types of inserts, shown in Figure 3.4, were developed to be bonded inside the whole wing assembly. These inserts have standard thicknesses that are readily available from regular aluminium suppliers so that they can be waterjet cut from the original aluminium plate with no need of further machining. The first type is a profile like aluminium insert to close each end of the wing and allow the endplates to be attached. The second and third one are a bigger and smaller variation of the same insert, these ones are intended to go between the rib and the lower skin and their goal is to screw an M6 screw on each to hold the wing supports to the wing itself. While defining the dimensions for each element one important thing to take into account is bonding

18 Figure 3.4: On the left, aluminium inserts that fit between the rib and the lower skin and on the right, inserts to close the wing profile and allow the attachment of the endplates. areas and bonding gaps. A bonding area on both the top and lower skin, displayed in Figure 3.5, was designed protruding from the wing leading edge to allow a perfect bond between both halves of the profile. Areas like the one mentioned previously were also left on the rib to ensure a correct adhesion to the lower skin.

Figure 3.5: Side proﬁle of the wing before bonding the closing aluminium inserts. Here it is possible to see the aluminium inserts between the rib and the lower skin and in detail, the bonding areas for both the top and lower skin.

About bonding gaps, the theoretical gap suggested is 0.1 mm [54] for the best mechanical properties but, to account with manufacturing defects, at ADESS the usual gap left for bonding is 0.5 mm. This gap needs to be taken into account when dimensioning each part of a bonded assembly. For the moment, the dimensions chosen were those that allowed a proper bonding when the layup in use is the standard layup for the parts of the ADESS-03. After the optimization process is over and when the final theoretical thickness is obtainable, this dimensions should be updated to take into account the new thickness of each composite part and allow for correct bonding straight out of the mould with no need for corrections that would imply sanding down composite parts to allow a correct fit. Finally, the last parts designed were the support inserts that attach the wing to the pillars, shown in Figure 3.6 and Figure 3.7. These inserts are machined from a solid block of aluminium and they need to take into account the adjustability of the wing. In order to extract the best times out of each circuit, the aerodynamic load must be adapted to fit both high speed circuits and low speed circuits. High speed circuits require lower amounts of downforce to be able to achieve a higher top speed on straights while low speed circuits require higher amounts of downforce to help with cornering and braking distances. The wing on the ADESS-03 LMP3 has seven positions ranging from 10o to 4o with the zero being

19 Figure 3.6: New wing ready to be attached to the endplates and the pillars.

Figure 3.7: Detail of assembly – the M6 bolts hold the support insert against the body of the wing and screw directly to the aluminium inserts below the rib.

6o regarding the proﬁle neutral line [53]. The wing adjustment is obtained by choosing the correct slot combination between the holes on the pillar and the holes on the wing insert, shown in Figure 3.8. The details for each conﬁguration can be found on the technical data of the ADESS-03 LMP3 Prototype.

Figure 3.8: On this illustration retrieved from the Aero guide for the ADESS-03 prototype it is possible to see all he possible wing adjustments and the correct slots. Retrieved from [53].

As mentioned before, the aerodynamic setup of the car will not change so, in order to keep the design as simple as possible the holes from the original insert assembly where projected to the new attachment inserts. This way, the pillars can stay the same and each team that orders the new replacement wing can simply rely on the old technical documentation to choose the downforce settings for each circuit.

20 3.2 FEA Analysis of the Standard Layup Wing

As mentioned, one of the most important things to do an accurate FEA analysis is data and unfor- tunately, the data currently available for the ADESS-03 is scarce. In order to do an analysis to the rear wing, ﬁrst the kind of loads dealt with must be known. According to the ADESS-03 technical manual, with the maximum downforce conﬁguration, at the top speed of 280 km/h, the ADESS-03 LMP3 Proto- type is capable of producing 2000 kg of downforce. Since that, as previously mentioned, approximately 20% of this downforce is generated by the rear wing, it is safe to assume that the rear wing at 280 km/h is generating 400 kg of downforce. Before start setting up the analysis is important to note one thing – the car is not always moving at top speed and, when moving at top speed, the stiffness of the wing is less important. Because no movable aerodynamic devices are allowed, like Drag Reduction Systems (DRS) in F1 shown in action in Figure 3.9, [55], at top speed the rear wing is just generating drag and slowing the car down.

Figure 3.9: Nico Rosberg at the 2016 Chinese Gran Prix taking full advantage of the DRS zone. See the gap on the rear wing. Retrieved from [56].

The wing stiffness is most important when the car is needing the most downforce to achieve the best performance so, wing stiffness is most important at fast corners. In slower corners the car is not moving fast enough to generate significant downforce so all the grip available is mechanical grip. On the opposite side we have fast sections of the circuit like straights. Here, no downforce is needed and for every kilogram of pressure exerted on the car, the car is losing top speed. Meanwhile in high speed corners, mechanical grip alone may not be enough to keep the car from sliding and as a result of sliding, losing cornering speed. To prevent sliding, the traction between the tyres and the track surface must be increased and this is done with the downforce generated by aerodynamic devices. To properly evaluate the current performance of the wing, the next step is to find out the load the wing is generating in high speed corners. Since there is no data available regarding the reference number of the NACA profile that is the main body of the wing nor the load generated in high speed cornering, the only option is to use what is available and that is data resulting from a test day at Autodromo´ do Estoril [57]. From this data it is possible to see that, when in the Parabolica Ayrton Senna corner, the ADESS-03

21 is moving at approximately 160 km/h as shown in Figure 3.10.

Figure 3.10: Parabolica Ayrton Senna is corner number 13 and the last corner before the main straight. It is possible to see the speed the AD03 is carrying throught the corner after 3250 m on the graph. Retrieved from [57].

With this information and the certainty that at 280 km/h, the rear wing is generating 400 kg of downforce, the downforce equation [58] can be used to calculate the load at 160 km/h,

1 D = × W × H × F × ρ × v 2, (3.1) 2 where D is the downforce, W is the wingspan, H is the chord, F is the lift coefﬁcient, ρ is the air density and v is the car’s speed, their results shown in Table 3.1.

Before finding the load generated at 160 km/h, first the value for the lift coefficient of the wing must be extrapolated from the information available. Since at 280 km/h the wing is generating 400 kg of downforce, using air density at 25oC the lift coefficient can be computed using equation 3.1.

The values needed to correctly find the lift coefficient value are presented in Table 3.1. After solving equation 3.1 in order to F, it is found that F = 2,25. With the value for the lift coefficient, equation 3.1 can be used again to find the load at 160 km/h, D = 1277,44 N.

After solving the equation, the values for both the average load case and the maximum load case are now available to proceed with the building of the FEA model.

22 Table 3.1: Wing parameters for downforce calculation. Name Value Wingspan [mm] 1600 Chord [mm] 300 Air Density (at 25oC) [kg/m3] 1,18 Average Speed [km/h] 160 Maximum Speed [km/h] 280

3.2.1 Building the FEA Model – Before Meshing

One important thing to do before meshing the CAD model of the wing is removing all the features of the wing that are unnecessary for the study and will only complicate the meshing process and increase calculation times. Features like holes and edge fillets can be removed to simplify the whole process. To do this most meshing software includes built in packages that allow this operation to be performed without the need to go back to CAD modelling again. Since the original CAD file was available, defeaturing of the wing model was done using CATIA. Apart from the holes and fillets, the aluminium inserts inside the wing were also removed from the analysis geometry. Since they are not part of the design space and despite providing some additional rigidity to the assembled part, their influence will not be accounted for the dimensioning of the composite layers of the wing. The final result of the simplified wing can be seen in Figure 3.11.

Figure 3.11: Original rib geometry vs defeatured model. Note the absence of ﬁllets or holes.

3.2.2 Meshing and Analysis

For this thesis, the software used for meshing, analysis and optimization is the HyperWorks Sofware Package since this was the software used in ADESS-AG. Included on this package are, among others, HyperMesh, Optistruct and HyperView. HyperMesh is the pre-processor used to edit the initial CAD geometry, meshing the model and set up all the analysis made for this thesis be they simple stress analysis or optimization calculations. Optistruct is one of the solvers available through the HyperMesh interface. It is capable of performing linear and non-linear analysis with static or dynamic loads. It can be used to analyse and optimize various aspects of a structure like its stiffness, strength, durability and vibration and also conduct thermal analysis among others.

23 After the calculations are ready, HyperView is used to see the results from the analysis.

Meshing the Model

The ﬁrst thing to do after importing the CAD model of the wing is to create the mesh of the model. For this the user must head to the “2D” panel in HyperMesh and select “automesh”. On this menu, shown in Figure 3.12, options like element type and element size can be selected.

Figure 3.12: On the automesh menu the user can input the requirements for the mesh design like the type of elements, element size and meshing strategy.

Since composite structures usually have areas much larger than their thickness, two of their dimensions are much bigger than the third, 2D elements will be used to mesh the model. 2D elements, also known as shell elements, are used to represent structures where one of the dimensions of our object of study is much smaller than the other two. Before choosing the element size for the model, a convergence study must be performed first to find the appropriate element size. For the next steps an element size of two will be used until the convergence analysis is finished. After performing the “2D automesh” meshing process, the user can check the mesh quality and perform local adjustments to improve the mesh quality. Within the “automesh” panel, the user can adjust the node density on each edge of the model so the elements on a face are as regular as possible. This functionality is shown in Figure 3.13.

Figure 3.13: Local edge reﬁnement being performed on one of the bonding areas of the rib to ensure the best possible mesh.

After completing the “automesh process”, the user should head to the “quality index” panel, shown in Figure 3.14, to evaluate the overall quality of the mesh and try to correct the elements that do not comply with the standard element quality criteria. Doing this will ensure the best results for the analysis performed.

24 Figure 3.14: No elements of the mesh built for this study fail any criteria of the standard quality control parameters for elements of element size two.

Element Preparation

After meshing the whole model and before going to material creation, there are two important steps to consider: one is the element normal orientation and the second is the material orientation. Before proceeding, the user must first guarantee that all the element normals are pointed on the right direction so that the plies are layed up on the correct order and finally, the element orientation must be consistent through the whole model. The normal orientation corresponding to this model is shown in Figure 3.15(a). Element orientation is especially important on composites since the fibre properties are only appli- cable on the direction the fibre is pointed. The analysis results will immediately raise suspicion if the elements do not have the correct orientation. The elements of this model aligned on the 0o direction are shown in Figure 3.15(b).

(a) The normal for the three elements of the wing pointing to (b) All the elements directions are aligned with the X axis as inside the body. This means that when laying up the wing, the shown. This means that if using 90o UD, the ﬁbre direction will mould surface will be the outer surface ensuring a perfect ﬁnish. be perpendicular to this axis.

Figure 3.15: Element normal and direction review.

With the mesh now completed, it is time to create the materials used on the model. For the standard layup the fabrics used are Standard Modulus 600 gsm Plain Weave carbon fibre fabrics (SM), see Figure 3.16 for the woven pattern. For the analyses performed on this thesis, the carbon fibre properties shown in Table 3.2 are carbon fibre properties readily available from suppliers and they were the ones used but, in order to get the most accurate results, one should create testing specimens and perform destructive tests in order to get the exact mechanical properties of the batch of carbon fibre used to

25 manufacture a certain part. Not every batch is the same and slight changes within the manufacture method of carbon ﬁbre fabrics may impact the performance of the ﬁnal part.

Table 3.2: Mechanical properties of Standard Modulus Plain Weave carbon ﬁbre fabric. Property Symbol Value

o Young’s Modulus 0 [MPa] E1 70000 o Young’s Modulus 90 [MPa] E2 70000

In-plane Shear Modulus [MPa] G12 5000

Major Poisson’s Ratio ν12 0.10 o Ult. Tensile Strength 0 [MPa] Xt 600 o Ult. Comp. Strength 0 [MPa] Xc 570 o Ult. Tensile Strength 90 [MPa] Yt 600 o Ult. Comp. Strength 90 [MPa] Yc 570 Ult. In-plane Shear Strenght [MPa] S 90 Density [g/cm3] ρ 1,6

Figure 3.16: Plain weave is one of the most common weaves found on woven fabrics. One ﬁlament of carbon goes above one ﬁlament and under the next and so on. Plain weave allows for equal mechanical properties along the 0o direction and the 90o direction.

HyperMesh does not ask for units while modelling so the user must input the values for each variable according to unit consistency [59]. The units used on this model are: grams, millimetres, and megapascal. Heading to the “create material” menu on HyperMesh, MAT8 is selected as a card image since this is the card used to represent orthotropic materials like composites. With the material now created it is time to create the carbon plies. While modelling composites on Hypermesh, the user has two options for approaching the modelling process: zone-based modelling or ply based modelling. For zone based modelling, shown in Figure 3.17(a), one property is created for each zone of the model. For example, if in one zone of the model there are two plies of 0o/90o plain weave and on another zone the same two plies but between them there is one ply of +45o/-45o, two properties must

26 be deﬁned on the separate zones of the material, one with the two plies and the second one with the three plies. With this method the plies are not connected across zones, each zone is its separate entity, and updating the model is laborious and requires updating each property separately. With ply based modelling, shown in Figure 3.17(b), the user deﬁnes laminates that are made of plies. Each ply is created according to its shape by selecting the desired elements. The plies are then assembled inside the laminate and the laminate property is then applied to the respective elements accordingly. This approach is faster to model and easier to update and, since this is the case, this will be the approach used for this model.

(a) Zone based modelling. (b) Ply based modelling.

Figure 3.17: Differences between a model modelled with zone based modelling compared to one modelled with ply based modelling. Retrieved from [60].

The standard layup deﬁned for the rear wing is shown in Table 3.3.

Table 3.3: Layup sequence for the standard wing laminates. Thickness Laminate Ply Name Material [mm] Orientation TOP FABRIC 0 SM 0,66 0o Top Skin TOP FABRIC 45 SM 0,66 45o LOWER FABRIC 0 SM 0,66 0o Lower Skin LOWER FABRIC 45 SM 0,66 45o RIB FABRIC 0 SM 0,66 0o RIB FABRIC 45 SM 0,66 45o Rib RIB FABRIC 45 2 SM 0,66 45o RIB FABRIC 0 2 SM 0,66 0o

Each ply is created by selecting the appropriate elements. After all the plies are created, the laminates must then be assembled for each of the wing components. On the “laminates” menu, shown in Figure 3.18, “Stack” is chosen for “card image” and “Smear” for the “laminate option” option. With the laminates created is now time to create the loads and constraints. All the six degrees of

27 freedom are constrained on the attachment area by selecting the respective surfaces. Two load cases must be considered: maximum load and average load. Applying the pressure created by the air moving around the wing profile exclusively on the top skin of the wing is a simplification of the real pressure distribution. In order to get the proper load distribution, a CDF analysis of the wing profile is needed to get the approximate load distribution, described in Figure 3.19. After the analysis is completed, the user can import the results to HyperMesh and map the pressure to the existing mesh elements. Since there is no CFD data available for the rear wing of the ADESS-03, for simplification, a constant pressure distribution on the top surface of the wing was considered for all the analysis.

Figure 3.18: Editing the top skin laminate it is possible to evaluate the laminate plies, their thickness, material and orientation. The laminate properties are also chosen here [61].

Figure 3.19: As can be seen, the pressure distribution is not constant along the surface of a airfoil. Retrieved from [62].

With the data calculated previously, it is possible to ﬁnd the pressure distributed on the surface of the wing capable of generating the desired loads. Using CATIA to measure the corresponding surface area, shown in Figure 3.20, the value obtained is 469000 mm2. With the previously known load values, the pressure for each of the loading cases is shown in Table 3.4.

28 Table 3.4: Pressure loading values. Maximum Pressure [N/mm2] Average Pressure [N/mm2] 0,01 0,0033

The values presented in Table 3.4 are calculated using the force computed previously, multiplied by a safety factor of 20%. This is the pressure value that is going to be used through the rest of this thesis. After creating the pressure loads by selecting the respective surfaces, the loads are mapped on the elements that correspond to each surface by using the option “loads on bc”. After all the loads and constraints are mapped, as seen in Figure 3.20, the two existing load cases area created: Maximum Pressure and Average Pressure, both of them having the same constraints but each one with its pressure value.

Figure 3.20: Selected surfaces for pressure mapping and mapped load.

Before ﬁnishing the model and proceeding with the analysis, connectors must be created between each of the elements of the wing. Once again, HyperMesh offers plenty of options regarding connectors – single point connectors like bolts and rivets, edge connectors like welds and area connectors like adhesives, which is this wing’s case. For the bonding of the wing, the bonding agent used is 3M’s Scotch-Weld 9323 B/A. In order to simplify the modelling and calculation process, the adhesive on the wing is assumed as perfectly rigid and incapable of suffering any major stresses that may cause failure. On the “connectors” menu within HyperMesh, “area connector” is chosen for modelling the adhesive. Rigid RBE2 elements are created that connect the elements between both bonding areas as seen in Figure 3.21. With the connectors ready it is now possible to proceed to the stress analysis. After asking Hy- perMesh to output displacement, composite failure and composite stress, everything is ready for the standard layup analysis. Before the analysis, the total mass of the wing is measured for a value of 4100 g.

3.2.3 Convergence Study

As previously mentioned, before settling on an element size, a convergence analysis must be performed. After setting up a model that allows to quickly change the element size without creating everything from zero, mainly a model before mapping the loads to the respective elements, multiple analyses were done with different element sizes. After all the analyses were ﬁnished, a plot was created that

29 Figure 3.21: Green RBE2 elements created on bonding areas that connect each component of the wing. relates the number of elements on the model with a local maximum stress.The plot and the values obtained through the convergence analysis are displayed in Figure 3.22.

500 Number of Local Stress

450 Elements [MPa] 28897 261,2 400 61944 313,8 246332 426 350

Local Stress [MPa] 380069 452,1 500180 454,6 300 677433 452,5 1519182 455,6 250 0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 Number of elements

Figure 3.22: Results of the convergence analysis.

From a direct observation of the resulting plot, it can be seen that after around 380000 elements, or element size 2, the stress results are very similar only increasing the computation time so element size 2 will be used for all the calculations.

Hardware Used for Calculations

All the calculations in this thesis were made using the hardware shown in Table 3.5.

Table 3.5: Computer hardware for calculations CPU AMD Ryzen 2700X; 3,7 GHz; 8 Cores; 16 Threads RAM 32 GB DDR4; 3200 MHz GPU Radeon RX 550; 2 GB HARD DRIVE Samsung 970 EVO; 3400 Mb/s Read; 2300 Mb/s Write

30 3.3 Standard Layup Analysis Results

After a total time of 540 seconds the results are out for the standard layup static analysis and they are presented in Table 3.6. Although a signiﬁcant displacement of 7,47 mm, plotted in Figure 3.23(a), is achieved for the maximum pressure load case, the wing is well within the allowed stress with the failure criteria [63] being close to 0, plotted in Figure 3.23(c), everywhere on the wing apart from a local high of 0,64, plotted in Figure 3.23(c) and (d), probably due to the geometry of the zone.

Table 3.6: Mechanical behaviour of the standard layup. Mass [g] Maximum Displacement [mm] Average Displacement [mm] 4131,07 7,47 2,47

(a) Maximum pressure displacement plot. (b) Average pressure displacement plot.

Figure 3.23: Results from the standard layup static analysis.

After seeing the results from this first analysis it is possible to establish real goals for the optimization process. The main goal is to get the stiffest structure possible for the least possible mass. To achieve this goal, not only the Standard Modulus Plain Weave carbon fibre fabric used for the standard layup will be used but also, High Modulus Unidirectional carbon fibre fabric (HM). With unidirectional fabrics it is possible to increase the rigidity of the whole wing on a certain direction without the need of adding more material to reinforce unnecessary directions.

31 32 Chapter 4

Optimization Process

After the analysis of the standard layup, the next step is the optimization study. Before starting the optimization process, first it is better to understand how Optistruct handles optimization studies. In order to better understand optimization one must first became familiar with its most fundamental concepts [64]: design space, design variables, objective function and design constraints. Design space is the area of the object that is being subjected to the optimization study. On this case, the design space is the whole wing. If the aluminium inserts were included on the FEA model, the skins and the rib of the wing would still be design space but the aluminium inserts, since they were already defined, they would be non-design space because they would not be subjected to the optimization study. Design variables are the parameters that can change during the optimization process. On this model, the design variables will be the thickness of each element on each ply. The objective function is the aim of the optimization study. If there was no objective function, the optimization study would not know when to stop. Finally, there are the design constraints. These constraints are user input regulations that dictate the direction that the optimization study must take and place they certain bounds on the optimization analysis. For example, if the goal was to minimize the mass of an object, its rigidity can be constrained so that this way, the optimization algorithm will not turn the initial object into a small dot in space - the minimum possible mass. In short, the optimization process iterates the values of the design variables inside the design space so that the result of the objective function is maximum or minimum. The result of the objective function must fall between the bounds imposed by the design constraints. The maximum (or minimum) value of the objective function inside the conditions required by the design constraints corresponds to the optimized values of the design variables.

4.1 Optistruct Optimization

Optistruct handles composite optimization in three different stages show in Figure 4.1 . The three optimization stages are described in-depth in the following chapters.

33 Figure 4.1: Optistruct’s composite optimization process. Adapted from [25].

4.1.1 Free Size Optimization

Free size optimization [24] is the first step of the optimization process used by Optistruct. To begin the free size optimization, the user must first define the available material and material orientations for each area through “super plies”. A super ply is a composite ply that is much thicker than the final ply that will eventually be used on the manufacturing process. Free size optimization begins by subtracting material to each super ply until the ideal thickness of each element is found. The result is a laminate with variable thickness throughout its area that may not translate to a manufacturable laminate later on. To solve this problem, Optistruct outputs the free size result in the form of four (default value) plies per each original super ply. This number of plies has the best balance between the thickness of each element and the contour of the final ply [61]. An example of how free size outputs the plies is shown in Table 4.1. The first of the four plies has the shape of the original super ply while the other three now have different shapes according to the distribution of the element thicknesses for that material/direction combination.

Table 4.1: Example of plies created after the free size analysis. See that there are four plies created for each original superply. Original Ply Free Size Plies 101100 101200 TOP FABRIC 0 101300 101400 102100 102200 TOP UD 0 102300 102400

Overall, the free size optimization process can be represented mathematically [25] as shown in Equation 4.1.

34 Minimize f (x)

U Subject to gj (x)–gj ≤ 0, j = 1, . . . , M (4.1)

L U xik ≤ x ik ≤ xik , i = 1, . . . , Np k = 1, . . . , NE

U ”Where f (x) is the objective function, gj (x) and gj represent the j − th constraint response and its upper bound, respectively. M is the total number of constraints, NE the number of elements and Np the number of super plies; x ik is the thickness of the i − th super ply of the k − th element”, as seen in [25].

Before proceeding to the next step of the optimization process, one must note that any change to the shape of each ply should be made at this point. These changes are usually to make the shape of the ply easier to manufacture.

4.1.2 Size Optimization

After the free size optimization, there are four times more plies than the ones that existed on the original model before the free size optimization. The next step is to provide Optistruct with the thicknesses with which the plies can be made of.

After importing the file resulting from the free size optimization, each ply is now a design variable. During the size optimization, Optistruct will iterate the thickness of each ply between a lower bound, usually 0, and an upper bound defined by the user that is usually a multiple of the Manufacturable Thickness (TMANUF) of each ply. For example, if the default value for the upper bound is 0,0123 mm, the upper bound defined by the user will be 0,44 mm for a TMANUF of 0,22 mm. This means that each ply will have a thickness of 0,22 mm up to a maximum of two plies generated from the original 0,023 mm ply.

Using the supplied data, Optistruct will try to ﬁnd the best balance between which plies are kept and which plies are no longer needed.

4.1.3 Shufﬂe Optimization

The final stage of Optistruct optimization is shuffling, or stacking, optimization. After the size optimization there is a finite number of plies each with a manufacturable thickness. On this last step, manufacture constraints are defined like cover plies and the maximum number of consecutive plies with the same orientation that is allowed.

After the shuffle optimization the optimization process is over and hopefully, the final model complies with the objective defined on the beginning of the process and respects the constraints applied.

35 4.2 Wing Optimization

4.2.1 Free Size Optimization

Before beginning the optimization process, a small change was made to the FEA model to simplify the work process on the following steps. Beginning with the CAD model, the three components of the wing were split in half to allow for symmetry mesh mapping on HyperMesh. After importing the updated CAD file to HyperMesh, a new mesh was built on half of the model. Spe- cial care was taken to ensure that there were no CTRIA3 elements on the mesh and that the whole mesh was made of CQUAD4 elements that respected the default quality parameters defined by HyperMesh. After having half the mesh ready, the other half was meshed and mapped to the remaining surfaces using the “periodic mesh” functionality. This tool allows the elements created by symmetry to be associated to the symmetric surfaces and this is a huge help when applying loads and defining area constraints. It is also very useful when constraining the free size results in order to get perfectly symmetric plies. Before proceeding with the analysis, all the elements and nodes on the model were renumbered. After having the meshed model ready, the first thing to do is to create the HM material. The properties to input on the new material are shown in Table 4.2.

Table 4.2: Mechanical properties of high modulus unidirectional carbon ﬁbre fabric. Property Symbol Value

o Young’s Modulus 0 [MPa] E1 175000 o Young’s Modulus 90 [MPa] E2 8000

In-plane Shear Modulus [MPa] G12 5000

Major Poisson’s Ratio ν12 0.30 o Ult. Tensile Strength 0 [MPa] Xt 1000 o Ult. Comp. Strength 0 [MPa] Xc 850 o Ult. Tensile Strength 90 [MPa] Yt 40 o Ult. Comp. Strength 90 [MPa] Yc 200 Ult. In-plane Shear Strenght [MPa] S 60 Density [g/cm3] ρ 1,6

With the new material ready, the next step is creating the super plies. Each of the three elements of the wing must have a laminate that has two cover plies: one ply of SM material at 0o/90o on the mould surface and another ply of SM material at -45/o+45o on the inner surface. The goal of these plies is to enclose the whole laminate inside them in order to achieve a better ﬁnish and component durability. For this reason, each of the wing elements has two super plies of SM material, one at 0o and the other at 45o. The rest of the super plies laminate can be checked in Table 4.3. Direction 79.5o for the angled superplies was chosen because it is the angle of the biggest diagonal of the wing, as shown in Figure 4.2, and it is cheaper to manufacture, as shown ahead in Figure 5.10. An analysis was made to compare the results of both directions and the wing with the 79,5o direction reinforcement was signiﬁcantly lighter and stiffer than the one with 45o. Results are shown in Table 4.4. After creating the super plies and respective laminates, the next step is to create the design variables.

36 Table 4.3: Layup sequence for the super ply wing laminates. Thickness Laminate Ply Name Material [mm] Orientation TOP FABRIC 0 SM 2 0o TOP UD 0 HM 2 0o TOP UD 90 HM 2 90o Top Skin TOP UD 79.5 HM 2 79,5o TOP UD -79.5 HM 2 -79,5o TOP FABRIC 45 SM 2 45o LOWER FABRIC 0 SM 2 0o LOWER UD 0 HM 2 0o LOWER UD 90 HM 2 90o Lower Skin LOWER UD 79.5 HM 2 79,5o LOWER UD -79.5 HM 2 -79,5o LOWER FABRIC 45 SM 2 45o RIB FABRIC 0 SM 2 0o RIB UD 0 HM 2 0o RIB UD 90 HM 2 90o Rib RIB UD 79.5 HM 2 79,5o RIB UD -79.5 HM 2 -79,5o RIB FABRIC 45 SM 2 45o

Table 4.4: Comparison between free size results with UD reinforcements at 45o and 79,5o. Maximum Average Number of Plies Orientation Mass [g] Displacement [mm] Displacement [mm] Created 45o 5393,97 1,53 0,51 72 79,5o 5322,08 1,27 0,42 72 Difference -1,3% -17,0% -17,0%

37 Figure 4.2: Wing angle from corner to corner.

One design variable was created for each existing laminate so, one for the top skin, one for the lower skin and one for the rib. Inside the ”design variables” menu, two restrictions were applied to each laminate: 1 – All the plies must be symmetrical regarding the middle plane of the car. This is one of the reasons why having a perfectly symmetric mesh is ideal. 2 – The ply balance between the -79.5o and 79.5o orientations must be the same. This means that the shape and thickness of each ply created from the original super ply is the same. The ﬁrst ply created from the 79.5o super ply has the same thickness and shape as the ply ﬁrst created from the -79.5o and so on. Regarding optimization constraints, the mass was constrained to a maximum of 4000 g. After the free size analysis, the total mass of the wing should be below 4 kg if the design is feasible. As for the objective function, the objective is the maximum possible stiffness for the smallest mass. With this in mind, the objective function is minimizing the weighted compliance of the wing, 0,85 weight for the average load and 0,15 for the maximum load.

Free Size Results

In Table 4.5 is shown the result of the free size analysis to the laminate of the top skin. The first number of the Ply Name column value corresponds to the ID of the laminate. In this case, the top skin laminate is ID 1 so each ply begins with 1. The second and third numbers refer to the original superply. When looking closely, it is possible to notice that every ply that has a 1 on its third number is made of SM material and also has a 0o orientation. There was only one superply that had this combination and it was the original 0o SM superly called ”TOP FABRIC 0”. Another look at the table reveals that there are only four entries on the table with the number 1 on its third number: plies number 101100, 101200, 101300 and 101400. This confirms what was said previously about Optistruct free size optimization creating four plies per each original superply. After importing the results from the free size analysis it was noted that, although constrained, when measured, the mass of the model was 6600 g which is 65% more than the mass constraint of 4000 g. Despite this, the solver displays that all the constraints were met and the design is feasible. Also, the mass on the output file is 4000 g, as shown in Figure 4.3. This problem was later identified to be due to the way the optimization works. As mentioned previously, free size optimization finds the best thickness for each element and creates a laminate with continuous thickness variation. When exporting the results, since the results cannot be

38 Table 4.5: Plies created for the top skin laminate after the free size optimization. For the complete results please refer to Appendix A. Ply Name Material Thickness [mm] Orientation 101100 SM 0,06 0o 102100 HM 0,05 0o 103100 HM 0,13 90o 104100 HM 0,15 79,5o 105100 HM 0,15 -79,5o 106100 SM 0,14 45o 101200 SM 0,07 0o 102200 HM 0,09 0o 103200 HM 0,22 90o 104200 HM 0,22 79,5o 105200 HM 0,22 -79,5o 106200 SM 0,20 45o 101300 SM 0,15 0o 102300 HM 0,24 0o 103300 HM 0,85 90o 104300 HM 0,84 79,5o 105300 HM 0,84 -79,5o 106300 SM 0,49 45o 101400 SM 1,73 0o 102400 HM 1,62 0o 103400 HM 0,79 90o 104400 HM 0,79 79,5o 105400 HM 0,79 -79,5o 106400 SM 1,17 45o

39 Figure 4.3: Despite 65% bigger that the maximum constraint when imported, the mass on the Output ﬁle still displays 4000 g after 14 iterations with a feasible design achieved. continuous, Optristruct will try to ﬁnd the best balance and so transforms the thickness of the laminate into plies, four plies for each super ply. During this discretization process an increase in mass is expected but one that is not so big. After contacting Altair, one of the probable causes is due to the fact that the whole wing is design space. Despite this setback, this problem was later solved on the next stages of optimization. After the free size optimization, Table 4.6 was calculated to understand the differences between the free size layup and the standard layup. As can be observed after the free size optimization, the model is now 60% heavier than the standard layup but now presents a displacement 86% smaller.

Table 4.6: Mechanical behaviour and mass comparison between the standard layup and the free size layup. Maximum Average Layup Mass [g] Displacement [mm] Displacement [mm] Standard 4131,07 7,47 2,47 Free Size 6589,42 1,07 0,35 Difference 59,5% -85,6% -85,6%

4.2.2 Ply Shape Edit

The result obtained from the free size optimization is a purely theoretical result. This result is the answer to the question: “how much material of this orientation in needed, and where is it needed?” and it has no regards to the manufacturability of the actual plies. Because of this, if the shape of the plies is not edited before the size optimization, in the end the result may present pleasing results with a low mass and high rigidity but it might not be manufacturable [25] . As mentioned previously, size optimization changes the thickness of the plies to manufacturable values and shufﬂe optimization changes the order of the plies on the laminate. If the user wants to improve the manufacturability of the plies of the laminate, it must be done in this moment. There are usually two approaches to this problem: 1 – Use the built in functionalities of HyperMesh.

40 2 – Adjust the ply shapes manually. After the free size optimization, one can use OSSMOOTH within HyperMesh to perform a simple ply clean up. The user deﬁnes the number of iterations and an area ratio – this area ratio will remove from each ply all the small patches whose area is smaller than the ratio allowed by the user. Manually adjusting the shape of the plies seemed like a lengthy and laborious process, due to the number of plies and the number of elements on the model, so the ﬁrst approach used was obviously OSSMOOTH.

OSSMOOTH

Trial runs were performed with OSSMOOTH and a previous model to ﬁnd the ideal area ratio and iterations parameters. After each run, the total mass and number of plies were measured to see if there were any consid- erable differences and if the results converged after a number of iterations of area ratio. One important thing to notice is the huge time involved on each OSSMOOTH run. For the free size model, the total time of one run of OSSMOOTH was about 24h. Despite this, more than one instance of OSSMOOTH can be run at one time so the whole iteration process was faster than expected. In Table 4.7 are the results obtained from the OSSMOOTH convergence analysis.

Table 4.7: OSSMOOTH effects on the free size model after multiple analysis with varying area ratios and iterations. Number of Number of Area Ratio Mass [g] Mass Reduction [%] Iterations Plies Created NA NA 50 3451,52 NA 100 0,0125 48 3430,85 -0,6 300 0,0125 48 3430,85 -0,6 100 0,025 47 3436,53 -0,4 300 0,025 47 3436,53 -0,4 100 0,05 36 3389,85 -1,8 300 0,05 36 3389,85 -1,8 100 0,075 35 3403,43 -1,4 300 0,075 35 3403,43 -1,4 100 0,0875 29 3251,41 -5,8 300 0,0875 29 3251,41 -5,8 100 0,1 29 3296,00 -4,5 300 0,1 29 3296,00 -4,5 100 0,2 29 3296,00 -4,5 300 0,2 29 3296,00 -4,5 100 0,4 29 3296,00 -4,5 300 0,4 29 3296,00 -4,5

From Table 4.7 it is possible to see that the mass gains are negligible through most of the OSS- MOOTH runs and that the number of plies stagnates if an area ratio bigger than 0,0875 is used. Also, the difference in the number of iterations only changes the smoothness of the contour of the exported

41 plies, not the shape of the plies on the FEA model itself. This can be seen in Figure 4.4.

Figure 4.4: 10000 iterations vs 100 iterations with an area ratio of 0,075. Although the surfaces created are different, yellow contour, the shape of the ply within the FEA model is still the same.

Not updating the shape of the plies within the model itself was the main problem found with OSS- MOOTH. Not only OSSMOOTH takes too long to run but also it does not change the shape of the plies signiﬁcantly on the FEA model, as can be seen in Figure 4.4. It is a good tool to export the ﬁnal ply results to CAD so they can be cut but, for the rest of this thesis, it is not good enough. Since the results from OSSMOOTH were not as expected, the next thing to try was editing the shape of the plies manually. As expected, this process takes a long amount of time and a lot of attention to correctly select the elements since HyperMesh does not automatically select the symmetrical opposite element to the one that is highlighted so, there is the need to do both sides manually. This option was discarded and a third one was devised.

4.2.3 MATLAB Bespoke Cleanup

Since the results of OSSMOOTH were below expectations and manually editing the shape of the plies was not feasible for more than one or two plies, a MATLAB solution was thought of and implemented. For each analysis, HyperMesh outputs a .fem ﬁle with all the data from the FEA model so it can be called by the Optistruct solver. This data can be written to a number of well know formats like Abaqus, Ansys, LsDyna, RADIOSS among others. Each of these data formats has its own speciﬁcations and they can be hard to interpret and use on bespoke solutions like this one, fortunately, one can choose to export the bulk data using “free format export”. Using HyperWorks help, it is possible to understand how the bulk data is written so special solutions like this one can be developed. The structure of the bulk data is perfectly explained in HyperWorks help and is shown in Figure 4.5.

After exporting the .fem file, a strategy for cleaning up the plies was devised. The user will need to input in how many “sections”, as described in Figure 4.6, he wants to divide the wing. After that, MATLAB will compare the elements on each section of the wing before and after the optimization and decide whether to simplify the elements, remove them completely or fill up the whole section as it was before the optimization run. In order for the MATLAB algorithm to work, first the bulk data file must be imported and after that, sorted and organized so the code can do its work easily.

42 Figure 4.5: Picture from HyperWorks Help explaining how the bulk data on the .fem ﬁle is separated. Retrieved from [61].

Figure 4.6: Ply 102200 as seen in by MATLAB. In this case, the user decided to use a square size of 60 so, the longer edge of the wing was divided in 60 elements of the same size.

The important sections of the bulk data are: the sets section, identified as $HMSET on the bulk data file, the nodes section, identified as GRID on the bulk data file, and finally, the elements section, identified as CQUAD4 on the bulk data file. Each set indicates the shape of each ply. Before the sets section begins on the bulk data file, there is one entry for each ply on the model with the respective thickness, material and corresponding set. For each set there is an ID number and a list containing all the elements that are part of that set. Nodes are self-explanatory and they are the corners of each element. On the GRID section there is the node ID followed by its X, Y and Z coordinates. Finally, on the elements section there is the element type, on this case CQUAD4, followed by its ID number and after, the nodes on each corner separated by commas. Previously, while setting up the FEA model, two important steps were taken to ensure that the MAT- LAB implementation was as easy as possible. The first step was to guarantee that there were no CTRIA3 elements on the model. Not only does this contribute to the overall quality of the mesh but also simpli- fies the import and sorting process of the bulk data file. One less coordinate on some random elements could break the whole algorithm if not planned carefully.

43 Second step was to renumber all the elements on the model. Once again this makes coding easier because HyperMesh will number the elements starting from the first component. This means that it will start numbering the elements from 1 beginning on the top skin, after that is finished it will number the elements on the lower skin and finally the rib. The final result is that from 381114 elements, the first 133150 elements are part of the top skin. 133151 to 272412 are part of the lower skin and finally, from 272413 to the end they are part of the rib. See Figure 4.7 for the bulk data section where this is highlighted.

Figure 4.7: Element numbering as seen on the bulk data for the free size analysis.

Before settling on a section size, once again, various analyses were conducted to study the inﬂuence of the section size for ply clean up on the ﬁnal model. Each size was subjected to the MATLAB algorithm, imported to HyperMesh and then subjected to a static analysis. Each one of these models was then scored against the model resulting from the free size analysis. The results from this analysis are shown in Table 4.8.

Table 4.8: Scoring system for the MATLAB square size value. Square Mass Maximum Average Mass Max. Displ. Av. Displ. Total Size [g] Displacement Displacement Score Score Score Score 20 5390,10 1,85 0,61 1,22 0,58 0,58 0,90 30 5569,19 1,58 0,52 1,18 0,68 0,68 0,93 40 5708,00 1,46 0,48 1,15 0,74 0,74 0,95 50 5857,73 1,29 0,42 1,12 0,83 0,83 0,98 60 5914,54 1,15 0,38 1,11 0,93 0,93 1,02 70 5976,96 1,14 0,38 1,10 0,94 0,94 1,02 80 6018,42 1,06 0,35 1,09 1,01 1,01 1,05 100 6134,65 0,98 0,32 1,07 1,09 1,09 1,08 120 6241,13 0,98 0,32 1,06 1,10 1,12 1,08

Reference 6589,42 1,07 0,35 1 1 1 1

From the results shown in Table 4.8, it was chosen to use a section size of 60. This size presents the best score between the value immediately above and below, apart from size 100. The ﬁnal decision between size 60 and size 100 went to size 60 because the plies resulting from the 100 cleaning process were too close to the original plies resulting from the free size analysis.

44 The results from the MATLAB clean up are easily visible before the algorithm is finished through a module implemented on the code. This module displays the shape of each ply before the cleanup, after the cleanup and finally, the original uncleaned ply on top of the cleaned ply plotted in different colours so it is easier to see the differences. The MATLAB results are shown below in Figure 4.8 as they are outputed through the cleanup process in MATLAB, in Figure 4.9 after importing to HyperMesh and in Figure 4.10 on the whole laminate final aspect.

Figure 4.8: For the plies 101200, 213200 and 311300, compare the results before (blue) and after (red). Please refer to Appendix A for bigger ﬁgures.

Figure 4.9: Ply 101200 on the HyperMesh model, before and after cleaning.

Figure 4.10: Difference between the top skin laminate before and after cleaning.

As can be seen from Figures 4.9 and 4.10, the difference in the overall ply outline is notable. Small patches disappeared and the ﬁnal result seems much more manageable. Although not perfect, this MATLAB algorithm was developed as a proof of concept and further reﬁning parameters can be inputted to improve the results even further. The total time for a MATLAB cleanup is around 20 minutes, as shown in Figure 4.11, which corresponds on a huge gain compared to either OSSMOOTH or manual cleanup. Compared to OSSMOOTH, the MATLAB algorithm is 72x faster and comparing to manual cleanup, the gain is simply not measur- able. If the user decides to go for the manual cleanup process, he must be entirely focused on this job

45 while with either OSSMOOTH or the MATLAB algorithm, he is free to work on something else. Also, cleaning up a complex ply took more than 4 hours, since the model after free sizing has more than 70 plies, it is easy to understand the gains either in time or in simple user workload.

Figure 4.11: Time to execute the Matlab code for ply cleanup.

4.2.4 Cleaned Plies vs Free Size Plies

Before deciding to go ahead with the MATLAB model, the effectiveness of the cleanup had to be measured. It was necessary to understand what was lost during the cleanup process and to better understand this, a static analysis was performed to compare the new cleaned free size model to the previous free size model. The results of this analysis are compared to the free size model results in Table 4.9.

Table 4.9: Mechanical behaviour and mass comparison between the free size layup and the cleaned free size layup. Maximum Average Layup Mass [g] Displacement [mm] Displacement [mm] Free size 6589,42 1,07 0,35 Free size MATLAB 5914,54 1,15 0,38 Difference -10,2% 7,5% 8,6%

As can be seen in Table 4.9, after cleaning up the plies the model is now 10% lighter which is a good perk to have and will help reduce the weight deﬁcit imposed by the inner workings of the free size analysis. Although the displacement is 8% bigger, looking at the results it is possible to see that 8% corresponds to just 0,03 mm when submitted to Average Pressure so this change is practically negligible. A similar process was done to compare this new model to the standard layup and the results are displayed in Table 4.10. As can be seen from Table 4.10 the results are in line with what was obtained on the previous comparison between the free size layup and the standard layup. The displacement values are practically

46 Table 4.10: Mechanical behaviour and mass comparison between the standard layup and the cleaned free size layup. Maximum Average Layup Mass [g] Displacement [mm] Displacement [mm] Standard 4131,07 7,47 2,47 Free size MATLAB 5914,54 1,15 0,38 Difference 43,2% -84,5% -84,5% the same while this new model gains some margin on the standard layup by having a smaller mass.

4.2.5 Size Optimization

Before proceeding with the size analysis there are two mandatory actions to take – the ﬁrst one is to change the output card from FSTOSZ (free size to size) to SZTOSH (size to shufﬂe) so the solver knows that it needs to perform a size analysis; the second one is to update the upper boundaries of the design variables, now one for each ply, and their TMANUF. The TMANUF chosen for every ply of this model is 0,22 mm. After editing the upper boundaries of the design variables, they now look like what is presented in Table 4.11.

Table 4.11: Sample of some plies with their upper boundaries edited. The second column is the value attributed to them after the free size analysis and the third column is the same upper boundary but after being edited by the user. Upper Boundary Edited Upper Ply Name After Free Size [mm] Boundary [mm] 101100 0,0693 0,44 101200 0,0828 0,44 101300 0,1769 0,44 101400 2,0710 2,42 102100 0,0578 0,44 102200 0,1133 0,44 102300 0,2890 0,66 102400 1,9400 2,42 103100 0,1593 0,44 103200 0,2696 0,66 103300 1,0252 1,32 103400 0,9458 1,32 104100 0,1847 0,44 104200 0,2588 0,66 104300 1,0082 1,32 104400 0,9484 1,32

As previously mentioned, after importing the free size model it was evident that the total mass of the wing was higher than the constraint deﬁned. It was also mentioned that this problem would be solved later on the development of this thesis.

47 For all the three steps of the optimization process, the user must define the objective function and the constraints and these can change through the course of optimization. The constraints and objective function for the free size analysis may or may not be the same as the ones used on the size analysis and later on the shuffle analysis. Since the shape of the plies is already defined after the free size analysis and the size analysis goal is to find a suitable manufacturable thickness for every ply on the model, it is expected that after the end of the size analysis the model will comply with the weight constraints. For the size analysis, the objective function was left the same, minimize the model compliance, while the constraints were updated: the mass constraint for the size analysis was increased to 4500 g.

Results

After the size analysis there are now 110 plies on the model. Although after the free size analysis there were 72 plies, 18 original super plies each split in four after the free size analysis, after the size analysis the model has 52% more plies than it had after the size analysis. This is due to the fact that during the size analysis the thickness of the plies must reach a value that is a multiple of the manufacturable thickness, for this model TMANUF is 0,22 mm. With this in mind, the plies with the lowest thickness after the free size analysis will disappear since they can not get close to the value of TMANUF while the plies with bigger thickness will be split accordingly. For example, one ply that after the free size analysis had a thickness of 2 mm, can spawn up to 9 plies after the size analysis. In Table 4.12 it is possible to see the evolution of the lower skin laminate plies through the size analysis. After looking at Table 4.12 it is possible to see that after the free size analysis, the thickest ply was ply 213400 since after the size analysis this ply spawned 4 plies. Following ply 312400 are plies 216400 and 217400 both of which spawned 3 plies each. Curious to see that the number of plies created by plies 216100, 216200, 216300 and 216400 are the same as the plies created by plies 217100, 217200, 217300 and 217400. This is due to the balance constraint applied to the plies with directions of both 79.5o and -79.5o that will persist through the whole optimization process. Also from the table it is possible to see plies that did not create any ply meaning that their corresponding area on their specific orientation is not influential on the final result. Keeping the trend of comparing the optimization stage to the standard layup, see Table 4.13. After the size optimization, the model is now just 5.6% heavier than the standard layup, a huge change on the previous result obtained after the free size optimization. As expected, since the solver is now working with discrete ply thickness the final result between the output file and the imported model is more accurate. With the discretization of the plies some rigidity is lost with the displacement now being 76.5% lower compared to the previous 84.5%.

4.2.6 Shufﬂe Optimization

Up until shufﬂe analysis, Optistruct ignores the order of the plies on the laminate due to the “smear” option previously chosen on the set up of the free size analysis. Since the shufﬂing optimization focus on the order of the plies on the laminate, after importing the results from the size analysis the user can

48 Table 4.12: Lower skin laminate after size optimization. For the complete results please refer to Ap- pendix A.

Ply Name Plies Created After Size Ply Name Plies Created After Size 213100 213101 216100 NA 213200 NA 216200 216201 213300 NA 216301 213401 216300 216302 213402 216401 213400 213403 216400 216402 213404 216403 214100 214101 217100 NA 214200 NA 217200 217201 214300 NA 214400 214401 217301 217300 215100 215101 217302 215200 215201 217401 215301 217400 217402 215300 215302 217403 215400 215401 218100 218101 218200 NA 218300 218301 218401 218400 218402

Table 4.13: Mechanical behaviour and mass comparison between the standard layup and the size layup. Maximum Average Layup Mass [g] Displacement [mm] Displacement [mm] Standard 4131,07 7,47 2,47 Size 4362,40 1,750 0,58 Difference 5,6% -76,5% -76,5%

49 check that on each of the three laminates, the “laminate option” has changed from “smear” to “total”. This change will make Optistruct account for the changes on the element rigidity due to the stacking order of the plies on the laminate. One thing that can also be observed is that while after the free size analysis the plies were the design variables, for the shuffle optimization the laminates are once again the design variables and there are just three: one for the top skin laminate, one for the lower skin laminate and the last one for the rib laminate. Before beginning, the user must define manufacturing constraints for each of the design variables. These manufacturing constraints consist on a maximum number of consecutive plies, the number and orientation of cover plies and one more option related to the use of core material. On this model, there will only be one constraint, the number of consecutive plies on each direction must be limited to two maximum plies. Cover plies are intended for the final manufacture of the wing, as mentioned earlier but, since they are defined by their orientation on the constraint menu and due to the fact that on the model there is both SM material and HM material both with orientation 0o, for the shuffle optimization it was chosen to leave this option unchecked.

Results

In Table 4.15 are the results of the shuffle optimization for the lower skin laminate. As can be seen from the left side of Table 4.15, the laminate is almost ready for manufacture. All the plies have a manufacturable thickness, due to the size analyis, and after the shuffle analysis, the resulting laminate now respects all the manufacturing constraints. One notable fact is the number of fabric plies spread throughout the middle of the laminate. The goal for all the laminates is to have as close to just two cover plies made from SM material as possible. The result of the shuffle analysis proves the need for a manual edit before the part is ready to manufacture. To understand how the mechanical properties of the model have evolved, once again a comparison was needed with the standard model. The results are shown in Table 4.14.

Table 4.14: Mechanical behaviour and mass comparison between the standard layup and the shufﬂe layup. Maximum Average Layup Mass [g] Displacement [mm] Displacement [mm] Standard 4131,01 7,47 2,47 Shufﬂe 4362,40 2,08 0,69 Difference 5,6% -72,2% -72,2%

After the shufﬂe optimization, the mass of the model did not change compared to the size optimization since the plies are the same. The displacement however became a little worse due to the manufacturing constraints. Despite being a little worse, the difference in displacement with the average load is just 0,1 mm compared to the size analysis which is, once again, almost negligible. For the complete results of the shufﬂe optimization please refer to Appendix A.

50 4.2.7 Manual Laminate Edit

Before the laminates are ready for manufacture, the plies must be edited. After analysing each SM material ply individually, some of them were deleted due to their reduced size as seen in Figure 4.12 with the final result shown in Figure 4.13. The deleted plies are seen in Table 4.15. On the left side is the original layup after the shuffle analysis. On this side, in bold and italic are the plies that were deleted, note that all of the deleted plies were SM material with orientation 0o and all of them had the same shape, illustrated once again in Figure 4.12. One of the plies with orientation 0o was edited to cover the whole laminate area and this ply will be the face mould ply. One 45o ply was also edited to cover the whole area of the laminate and this one will be the closing ply of the laminate and will face the inside of the wing. This plies are highlighted in italic in the left side of the table. This process was conducted for all three of the laminates and the final layup of the lower skin laminate can be seen on the right side of Table 4.15.

Table 4.15: Lower skin laminate before and after the manual edit. For the complete results please refer to Appendix A.

Ply Name Material Orientation Ply Name Material Orientation 218101 SM 45o 213101 SM 0o 213101 SM 0o 215101 HM 90o 215101 HM 90o 216201 HM 79,5o 216201 HM 79,5o 217201 HM -79,5o 217201 HM -79,5 214101 HM 0o 214101 HM 0o 215201 HM 90o 215201 HM 90o 218301 SM 45o 218301 SM 45o 216301 HM 79,5o 216301 HM 79,5o 216302 HM 79,5o 216302 HM 79,5o 215301 HM 90o 213401 SM 0o 217301 HM -79,5o 215301 HM 90o 217302 HM -79,5o 217301 HM -79,5o 218401 SM 45o 217302 HM -79,5o 215302 HM 90o 218401 SM 45o 216401 HM 79,5o 213402 SM 0o 216402 HM 79,5o 215302 HM 90o 215401 HM 90o 216401 HM 79,5o 218402 SM 45o 216402 HM 79,5o 216403 HM 79,5o 213403 SM 0o 217401 HM -79,5o 215401 HM 90o 217402 HM -79,5o 218402 SM 45o 217403 HM -79,5o 216403 HM 79,5o 214401 HM 0o 217401 HM -79,5o 218101 SM 45o 213404 SM 0o 217402 HM -79,5o 217403 HM -79,5o 214401 HM 0o

51 Figure 4.12: Ply 213402 deleted during the laminate editing. As seen in Table 4.15 before, all the plies deleted with the 0o orientation had the same shape.

(a) Top skin laminate without cover ply. (b) Top skin laminate with cover ply.

Figure 4.13: The new top skin laminate .

4.3 Analysis of the Optimization Results

After editing the manual editing of the plies, the layup is ready and it is time for its ﬁnal evaluations. A static analysis was conducted to see the results. These results are displayed in Table 4.16 along with the results from the standard layup for comparison. Regarding total mass, an increase in 12% can be observed. The standard layup is around 4100 g while the optimized layup is 4639,4 g. However, although there are some losses on the weight area, the

52 Table 4.16: Mechanical behaviour and mass comparison between the standard layup and the edited layup. Maximum Average Layup Mass [g] Displacement [mm] Displacement [mm] Standard 4131,07 7,47 2,47 Shufﬂe Edited 4639,40 2,04 0,67 Difference 12,3% -72,7% -72,7% gains regarding the rigidity of the wing are notable.

As can be seen in Table 4.16, under maximum load the displacement was reduced from almost 7,5 mm to just 2 mm. Also, under average load the maximum displacement is just 0,67 mm which can barely be noticed by just looking at the wing. An incorrect curing process may cause more warpage on the ﬁnal wing than the displacement during load. One curious thing to see is the movement of the maximum displacement areas. As can be seen in Figure 4.14, while in the standard layup the maximum displacement was along the whole border of the wing, now it has shifted to a small zone on the rear part of the wing close to the gurney ﬂap guaranteeing more stability for the endplates.

Figure 4.14: Shifting of the maximum displacement zones.

Regarding composite failure, the load concentration zones around the pillar supports have disappeared and now the maximum failure criteria is just 0,314 compared to the previous 0,64. This means the composite structure is even less prone to failure.

Figure 4.15: Composite failure criteria plot with the ﬁnal layup.

53 With the optimization process done, it is time to start planning the manufacturing process.

54 Chapter 5

Manufacturing Planning and Analysis

As mentioned before on the design stage of the wing, the first thing to do after the optimization process is to update the CAD geometry of the wing to reflect the changes on the laminate thickness. Using OSSMOOTH within HyperMesh it is possible to export the new ply geometry to an .stp file. It is possible to choose to do it with just one iteration to export the ply geometry as it is or, more iterations to simplify the ply shape as can be seen in Figure 5.1.

(a) Ply 101200 exported using 1 iteration. (b) Ply 101200 exported using 300 iteration.

Figure 5.1: Difference between ply 101200 after exporting to .stp using OSSMOOTH with either 1 iteration or 300 iterations.

As can be seen from Figure 5.1, the ply exported with 300 iterations has a general smoother outline compared to the ply exported with just one iteration. This is because with just one iteration, OSSMOOTH will not try to simplify the ply shapes and will just create the geometry as the ply is on the moment. When exporting the ply geometry to use on the real model for manufacture, it is advised to run OSSMOOTH with a big number of iterations to remove the hard corners that exist on the model resulting from the ply clean-up process. Hard corners make each ply harder to cut and create stress concentration zones on the ﬁnal laminate.

The .stp file HyperMesh exports contains just the surfaces of the plies with no thickness so, within the CAD environment, thickness should be added to all the plies based on the final thickness obtained on the final optimized model so the inserts dimensions, bonding gaps and other dimensions that depend on the laminate thickness can be updated according to the theoretical final laminate thickness.

55 5.1 The Wing Assembly Process

After updating the CAD model of the wing it is time to produce the adequate guides to properly manufacture the part. As can be read on Chapter 3 of this thesis, the wing is made of three composite components, top and lower skin and rib, and some smaller, aluminium components. The assembly process is fairly simple since after bonding the wing there is only the need to attach the endplates and the pillar supports on their respective places. The most time consuming process of the wing build process though, after the manufacture of each individual component, is the bonding process of the wing itself that is described In Figure 5.2. This ﬁgure illustrates the bonding assembly process as shown in the Plybook for the Pininfarina H2 Speed 2018 Rear Wing.

Figure 5.2: Wing bonding instructions as shown on the Pininfarina H2 Speed 2018 Rear Wing Ply- book [65].

After bonding the wing and before moving on to the next process the final bonded part must be cleaned of excess bonding agent that may spill during the process. This process is important specially along the leading edge of the wing since not only this is the joining edge between the top and lower skins, it is also the part of the wing that also comes in contact first with the air moving around. If not finished properly, defects on the leading edge may affect the air flow around the wing profile and reduce the overall performance. With the main wing body bonded and properly finished, what is left to do is just opening the holes on the inserts to attach both the pillar supports and the endplates and after that, tapping them according to specification. With the drilling and tapping done, the endplates and pillar attachments can be tightly secured to the main body of the wing and the final part is ready to be put on the car.

56 5.2 Mould Design

No composite part can be produced without a mould. A composite material is made of two components: the matrix and the reinforcement. On this case, the composite material used is carbon fibre pre-impregnated fabrics so, the matrix is an epoxy resin solution and the reinforcements are carbon fibre filaments, woven in case of the plain weave fabric or unidirectional in case of the HM fibre. In any case, pre-impregnated fibres need to be laid down on a mould and later cured until the epoxy matrix turns from liquid to solid and the part is ready. Designing a good mould is as important as designing the part itself and various considerations need to be taken into account when designing the part to guarantee the best possible result. Although fairly flexible, composite parts manufacturing has its limits and the designer can end up with a part impossible to produce if these limitations are not taken into account. A good mould will not only provide the best final part but also must help the laminator do its job properly by making the laminating process as easy as it can be. Good access to tighter areas of the part to guarantee that the laminator’s hands fit and good margins after the trimline to ensure the part fits perfectly after trimming and also to provide mould support to attach curing consumables provide simple solutions that improve the quality of the lamination process and of course, of the final part. Since every moulded part needs to be de-moulded, considering draft angles and leverage zones to open closed moulds makes the de-moulding process easier and directly, preventing the part from being damaged during the process. Since the wing has three composite components, one mould per component is needed and as such, three moulds need to be designed.

5.2.1 Top Skin Mould

The top skin mould is the most complex of the three moulds designed. Since the wing needs to be easily adapted to both the ADESS-03 LMP3 and the Pininfarina H2 Speed 2018, the mould needs to reﬂect this ability. A solution to this problem was to use add-ons that go on the mould as seen in Figure 5.3. According to whether a wing for the ADESS-03 LMP3 or the Pininfarina H2 Speed 2018 is being manufactured, these add-ons just need to be swapped to manufacture one top skin or the other. For the ADESS-03 wing, two add-ons are used to create the two cavities for both pillar supports. If the top skin is intended for the H2 Speed though, one add-on is used on the middle to create the single cavity for the single pillar support of the H2 Speed wing. To attach the add-ons securely in place, the bottom of the add-ons is both drilled and tapped. The mould main body also needs to be perforated to allow screws to pass so they can attach to the bottom of the add-ons as illustrated in Figure 5.4. The holes on the main body of the mould are blind so not to difﬁcult the passage of the screws and they are countersunk, as can be seen in Figure 5.4, so the head of the screws is aligned with the bottom surface of the mould. This way it is possible to easily work with the mould on the top of a table without the mould moving around too much. In order to create the bonding area on the top skin, another part needs to be added to the mould

57 Figure 5.3: Top skin mould with add-ons for the ADESS-03 top skin manufacture.

Figure 5.4: Add-ons attachment to the main body of the mould. assembly. This new part is once again attached to the main body of the mould using screws and can be made from a simple plate of the same material used on the rest of the mould. See in Figure 5.5 the exploded view of the top skin mould with all the ﬁve separate components that make up the whole top skin mould assembly.

Before the mould is finished, a trim line must be added. Either by scratching the surface of the mould with the appropriate tool or by using an adhesive film to limit the contour of the final part, the trim line is essential for the final finish of the component. While laminating, prepreg fabrics are tacky to the touch due to the resin in them. They must be kept inside a freezer while they are stored to prevent the resin from completely curing and so rendering the fabrics useless. While laminating at ambient temperature, the fabrics will continuously get tackier as the resin on them starts to heat up and loosen from the carbon filaments.

After laminating and when on the oven, the fabrics will heat up and the resin will became liquid before curing. Since the trimline is an engraving or an embossing on the mould surface, this line will appear on the final part as a slender groove on its surface. After de-moulding, the trimmer equipped with an appropriate cutting tool will remove the excess material from the carbon part cutting the part by the trimline engraved on its surface. Perfect trimlines ensure the best fitting of the final part.

58 Figure 5.5: Top skin mould with add-ons and bonding area plate removed.

In Figure 5.6 the ﬁnal Top Skin Mould can be seen with the respective trimline in pink.

Figure 5.6: Top Skin mould completely assembled to begin the manufacture of the component. Notice the trim line in pink.

5.2.2 Lower Skin Mould

The Lower Skin mould follows the same principles as the Top Skin mould with the exception of the add-ons to produce the cavities. For the wings for the ADESS-03 and the Pininfarina H2 Speed, all the components are the same except for the top skin so, the mould used to produce the lower skin for the ADESS-03 wing is the same mould used to produce the lower skin used on the H2 Speed wing. What keeps this mould from being just a single part is the plate needed to, once again, create the bonding area on the leading edge of the wing. A duplicate of the plate used on the top skin mould can be used for the lower skin mould. In Figure 5.7 is shown the Lower Skin Mould with the respective trimline in pink.

59 Figure 5.7: Lower Skin mould with trim line in pink.

5.2.3 Rib Mould

Finally, despite looking like the most complex part of the three, the rib mould is actually the easiest of the three to design since there are no special precautions to take while manufacturing the part. Despite being easier to design, this mould is probably the most expensive one due to the complexity of the ﬁnal part. Regarding design constraints, all the limitations regarding the wing adaptation from the ADESS-03 LMP3 to the Pininfarina H2 Speed 2018 were accounted for during the design phase of the rib to ensure a simpler overall process. As with the lower skin, the rib used on both wings is the same so the same mould can be used for both wings. Shown in Figure 5.8 is the rib mould with the respective trimline in pink.

5.3 Special Considerations and Manufacturing Procedure

Before sending the moulds to be machined there is one special precaution to take. Depending on the material used to machine the moulds, usually moulds are machined from steel, aluminium or tooling block, depending on the number of parts that are intended to be produced during the mould’s lifetime, the final geometry of the mould before adding holes for threads and other features that require geo- metrical precision, should be shrunk depending on the thermal expasion coefficient of the material from which the moulds are manufactured. As mentioned earlier, all these parts are made from prepreg fibres that need to be cured in an oven. When inside the oven, temperatures can go as high as 120oC and as such, the material will expand changing the final dimensions of the part. On a smaller part this change in dimension may not be noticeable but as the part grows in size, so does the change in dimensions. In order to ensure proper consolidation between the plies, the part must also be subjected to vacuum and in order to do so, special preparations must be made as illustrated in Figure 5.9.

60 Figure 5.8: The rib mould with the trim line in pink.

Figure 5.9: If a visual cut is done by the plane in blue on the ﬁrst image during the curing process, the second image can be seen.

As can be seen in Figure 5.9, in light blue there is the mould itself and on top of it, are the carbon layers in black. Following the carbon plies is a layer of peel ply, in yellow, a plastic film that prevents the resin from escaping from the fibres and going to the next layer - the breather, in green. The breather is a fabric like material that is usually used on other vacuum bagging methods to absorb the excess resin. When working with prepreg fibres though, since the ratio between fibre and resin is already perfect, the goal of the breather is to help evenly distribute the vacuum pressure throughout the part. Finally, there is the vacuum film, in red, that encloses all the layers and keeps them tight against the mould surface.

61 While bagging the mould, this bag will be perforated to allow vacuum intakes to be connected. There are various techniques of vacuum bagging available but these moulds were designed with the envelope technique in mind. With the envelope method, the whole mould is placed inside the bag, the vacuum film is arranged so it forms a bag around the mould as seen in Figure 5.9 and then vacuum is applied. Although this method implies a bigger use of vacuum film, it is significantly faster for bigger parts like these and if properly applied, the bag is reusable for the next batch of parts. To finish the manufacture procedure, there is one more step that needs to be taken into account. While laminating a big number of plies the laminator cannot be certainly sure that the plies are in place. While the first ply may have a good adhesion to the mould and the second as well, as the lamination procedure continues the laminate will continue to get progressively thicker and the latter plies may not be properly laid down. To prevent this from happening, a debulk needs to be performed given an interval of plies. A debulk consists on a simple technique of putting the whole part under vacuum for a certain amount of time so the plies can be pressed down against each other. After the debulk is done the laminator can continue to build the laminate against the surface of the mould. Although simple, debulks represent a huge time fraction on the whole laminating process due to the bagging involved and the time spent while the part is resting under vacuum.

5.4 Costs of Manufacture

The costs of the whole manufacturing process can be split in two categories: material costs and worker related costs. The material costs cover the cost of the carbon itself and of the aluminium used on the inserts. As for the worker related costs, they count the total time spent on laminating the plies, the time spent debulking the laminates, the unmoulding time, the trimming time and the bonding time. For the aluminium inserts these costs would be the machine usage and the time spent on cutting the aluminium plate. Since the aluminium inserts are a constant, their cost will not be accounted for on these next calculations. Relying on the data from HyperMesh, the area of each ply was calculated to understand how many square meters of carbon are needed on the manufacture of the wing, these values can be seen in Table 5.1. Since not all the plies are made of the same material, in order to get the total cost of each component of the wing, the retailing prices for both SM [66] material and HM [67] material were found. These costs are readily available by a simple internet search. With the cost of SM at 26 e/m2 and HM at 63 e/m2, the cost of each component can be calculated and the results for the top skin laminate are presented in Table 5.1. Despite giving a good approximation, this method to calculate the price of each ply is not 100% accurate. Since all the plies are cut from a single roll, there is going to be some waste every time a ply is cut and this waste depends on the orientations of the ply. Figure 5.10 exempliﬁes this problem. As can be seen from Figure 5.10, the ply with the orientation of 79.5o has a bigger waste area than the ply with an orientation of 90o. Although they seem like they have no waste at all, since it is not

62 Table 5.1: Example of laminate material cost from ply area with top skin laminate. For the complete results please refer to Appendix B. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 101100 SM 529140,88 0 0,00 101200 SM 345637,66 0 0,00 101300 SM 151215,92 1 3,93 101400 SM 16339,39 3 1,27 102100 HM 529140,88 0 0,00 102200 HM 277138,28 1 17,46 102300 HM 138938,18 1 8,75 102400 HM 29008,70 2 3,66 103100 HM 529140,88 1 33,34 103200 HM 305580,85 0 0,00 103300 HM 84100,19 6 31,79 103400 HM 33996,58 6 12,85 104100 HM 529140,88 0 0,00 104200 HM 317806,44 1 20,02 104300 HM 91005,22 2 11,47 104400 HM 34726,11 6 13,13 105100 HM 529140,88 0 0,00 105200 HM 317806,44 1 20,02 105300 HM 91005,22 2 11,47 105400 HM 34726,11 6 13,13 106100 SM 529140,88 1 13,76 106200 SM 331761,07 1 8,63 106300 SM 172284,32 1 4,48 106400 SM 50433,42 3 3,93 45 233,08 Number of Plies Total Cost

63 Figure 5.10: Inﬂuence of cutting directions on waste area. possible with the roll presented on the image to cut a ply of 0o next to a ply of 90o, the area around the ply of 90o must be maximized by cutting, for example, more plies with an orientation of 90o. Despite having a smaller waste area, the smalls areas that are on each side of the ply with an orientation of 0o will probably be waste as well if a ply that is capable of ﬁtting on that small space is not found.

When asking for a quotation for a part like this, all the plies outlines are supplied and then in-house, the manufacturer will assemble all the plies with their respective orientation on proper software. After assembling all the plies on a big sheet of “carbon”, it is possible to know how many linear meters of carbon are needed to manufacture a certain part. These linear meters already account with the wasted material. With the price for the material of every single component, next the cost associated with the workers must be calculated. The values used for the manufacture work are described in Table 5.2.

64 Table 5.2: Table with assumptions made regarding work cost and manufacturing time. Variable Value Time Spent per Ply [minutes] 12 Time for Debulk [minutes] 40 Time for Trimming [minutes] 60 Time for Unmoulding [minutes] 10 Time for Assembly [minutes] 60 Debulk Interval [plies] 4 Worker Cost per Hour [e] 40

With the values from Table 5.1 and from Table 5.2, it is possible to estimate the total cost of the optimized model. The results are displayed in Table 5.3 and Table 5.4. With everything taken into account, the final value for the cost of the optimized rear wing is 2463,35e. Since there is no other value to compare it to, the same process was done to find the cost of the standard layup. The results of the cost evaluation of the standard layup are found in Table 5.6 and Table 5.7. To have a better idea of the difference between the material and work related costs, Table 5.7 presents values for both the standard and optimized layup as well as the difference between them in percentage. The increased number of plies reflects itself not only on the material cost but also on the total time cost. The material cost is simple to understand: there is no HM fibres used on the standard layup while this type of fabric is the foundation of the whole optimization process and with the HM fibers used on this part costing almost 2,5 times more than SM fibres, an increase in price is obviously expected. The main difference appears in the time cost mainly to the time spent on debulks. Both of the models need to be trimmed and bonded but the time spent laying up the plies is increased on the optimized model and, while there are no debulks on the standard layup, the optimized model needs more than 5 debulks per component. These calculations do not reflect the reality perfectly since more than one mould can be laminated at the same time and the same thought process goes for the debulks. Despite all its flaws, this calculation method is enough to demonstrate that the optimized model is simply too expensive to be manufactured to the light of the philosophty behind a LMP3 prototype. If the LMP3 category was not cost bound like Formula 1 and the hybrid LMP1’s, probably this solution would be feasible but since this is not the case, another solution must be found.

5.5 Devising a Simpliﬁed Layup

Since the final result of the optimization is simply too expensive to be manufactured, another solution must be devised. The first thing that comes to mind is obviously simplifying the optimized layup by reducing the number of plies. Increasing the TMANUF of each ply may seem like a good solution but having different rolls of carbon fibre with difference thicknesses may end up being more expensive on the long run. Also, prices vary with how common is the use of a certain carbon thickness, stocks availability and more factors so, accounting for the total price of the new wing would be impossible.

65 Table 5.3: Cost of the manufacture of each of the individual laminates for the optimized layup. Laminating Time [hours] Laminating Cost [e] 9 360,00 Total Debulking Number of Debulks Preparation Time [hours] Debulking Cost [e] 11 7,26 290,40 Top Skin Laminate Trimming Cost [e] Unmoulding Cost [e] Assembly Cost [e] 40,00 6,67 40,00

Total Worker Cost [e] 737,07

Laminating Time [hours] Laminating Cost [e] 5,4 216,00 Total Debulking Number of Debulks Preparation Time [hours] Debulking Cost [e] 6 3,96 158,40 Lower Skin Laminate Trimming Cost [e] Unmoulding Cost [e] Assembly Cost [e] 40,00 6,67 40,00

Total Worker Cost [e] 461,07

Laminating Time [hours] Laminating Cost [e] 7,4 296,00 Total Debulking Number of Debulks Preparation Time [hours] Debulking Cost [e] 9 5,94 237,60 Rib Laminate Trimming Cost [e] Unmoulding Cost [e] Assembly Cost [e] 40,00 6,67 40,00

Total Worker Cost [e] 620,27

Table 5.4: Optimized layup total cost. Total Worker Cost [e] 1818,4 Total Material Cost [e] 644,95 Total Part Cost [e] 2463,35

66 Table 5.5: Cost of the manufacture of each of the individual laminates for the standard layup. Laminating Time [hours] Laminating Cost [e] 0,4 16,00 Total Debulking Number of Debulks Preparation Time [hours] Debulking Cost [e] 0 0 0,00 Top Skin Laminate Trimming Cost [e] Unmoulding Cost [e] Assembly Cost [e] 40,00 6,67 40,00

Total Worker Cost [e] 102,67

Laminating Time [hours] Laminating Cost [e] 0,4 16,00 Total Debulking Number of Debulks Preparation Time [hours] Debulking Cost [e] 0 0 0,00 Lower Skin Laminate Trimming Cost [e] Unmoulding Cost [e] Assembly Cost [e] 40,00 6,67 40,00

Total Worker Cost [e] 102,67

Laminating Time [hours] Laminating Cost [e] 0,8 32,00 Total Debulking Number of Debulks Preparation Time [hours] Debulking Cost [e] 0 0 0,00 Rib Laminate Trimming Cost [e] Unmoulding Cost [e] Assembly Cost [e] 40,00 6,67 40,00

Total Worker Cost [e] 118,67

Table 5.6: Standard layup total cost. Total Worker Cost [e] 324 Total Material Cost [e] 101,71 Total Part Cost [e] 425,71

67 Table 5.7: Comparison between total cost of standard layup and optimized layup. Layup Total Material Cost [e] Total Worker Cost [e] Total Part Cost [e] Standard 101,71 324,00 425,71 Optimized 644,95 1818,40 2463,35 Difference 534% 461% 479%

5.5.1 Simpliﬁed Layup Study and Optimization

A safer approach is to create a simplified layup that prioritizes on each laminate the dominant direction obtained through the previous optimization process. The goal with this new approach is to have a new simplified layup for the wing that in the end is made up from two woven fabric cover plies and inside reinforced by a single direction of HM plies or, two directions if the dominant direction needs to balanced. For this simplified laminate, the optimization process will be repeated in full to obtain the best possible result. This new layup will hopefully be the perfect balance between the standard layup that is cheap to produce and the optimized layup that has great mechanical behaviour. Before deciding the dominating directions for each laminate, first the optimization results from the previous effort must be analysed. Looking at Table 5.8 it is possible to see how many reinforcement HM plies exist on each of the laminates and the respective dominant direction.

Table 5.8: Occurence of each direction of reinforcement on each of the laminates. Number of Plies on Occurrence Laminate Direction Occurrences the Laminate Percentage 90o 13 30% o Top Skin 79,5 943 21% 0o 4 9% 90o 5 21% o Lower Skin 79,5 6 24 25% 0o 2 8% 90o 4 11% o Rib 79,5 9 35 26% 0o 6 17%

From the information in Table 5.8, the dominant direction on each of the laminates is clear apart from the Lower Skin where the number of plies on both 79,5o and 90o are very similar. Althought the 79,5o direction ends up having a bigger percentage of the total laminate thickness, for the new simpliﬁed layup it was decided to used the 90o direction to match with the Top Skin laminate. This way both the Top and Lower Skin laminate are matching with just 90o HM reinforcements while the Rib laminate keeps the 79,5o HM reinforcement.

Using the existing mesh from the previous optimization process, a new model to conduct a new opti-

68 mization analysis was prepared. The superplies chosen for this new analysis are displayed in Table 5.9.

Table 5.9: Superplies used for the optimization process of the new simpliﬁed layup. Thickness Laminate Ply Name Material [mm] Orientation TOP FABRIC 0 SM 0,66 0o o Top Skin TOP UD 90 HM 2 90 TOP FABRIC 45 SM 0,66 45o LOWER FABRIC 0 SM 0,66 0o o Lower Skin LOWER UD 90 HM 2 90 LOWER FABRIC 45 SM 0,66 45o RIB FABRIC 0 SM 0,66 0o RIB UD 79.5 HM 2 79,5o Rib RIB UD -79.5 HM 2 -79,5o RIB FABRIC 45 SM 0,66 45o

To prevent Optistruct from creating too much fabric plies, the thickness for the superplies used on the free size optimization was reduced from the 2 mm used until now to 0,66 mm that corresponds to a single layer of 600 gsm plain weave carbon fibre fabric. The optimization process described on Chapter 4 was once again used for this new simplified laminate. After finishing the manual editing of the plies after the final shuffle optimization, the final layup obtained is shown in Table 5.10. As can be seen in Table 5.10, the new laminates are much simpler than the laminates resulting from the previous optimization process. Although manufacturing constraints were once again applied on the shuffle analysis to prevent consecutive stacking of plies of the same direction, since the number of plies is reduced now and with only one reinforcement direction available on both the Top and Lower Skin laminates, the end result is exactly what was expected: a solid HM reinforcement core wrapped with plain weave woven plies on each end. With a reduced number of plies the manufacturing cost for this new simplified layup is expected to be much lower than the layup obtained with the previous optimization. It is also expected that it will perform slightly worse but to be able to quantify the loss in mechanical performance a static analysis was performed. The results are displayed in Table 5.11. As expected, the displacement results are slightly worse with the simplified layup displacement under average pressure being now slightly above 1 mm. The unexpected surprise though was the final mass of the model just above 3300 g. With the standard layup weighting around 4100 g, this difference on the total mass allows one of the main objectives of creating a laminate that outperforms the standard layup in every aspect, objective that was not achieved with the previous optimized layup, to be crossed of the list now. In order to better compare results, Table 5.12 shows both the percentage difference and real difference between the new simplified layup and the previous optimized layup masses and displacements. When looking at the results in Table 5.12 one may be deceived to think that a percentage difference of 67% on both displacements is a great loss but, looking at the real difference between their values it

69 Table 5.10: Final laminates obtained for the new simpliﬁed layup. For the complete optimization results please refer to Appendix C. Laminate Ply Name Material Thickness [mm] Orientation 101301 SM 0,66 0o 103101 HM 0,22 90o 103201 HM 0,22 90o 103202 HM 0,22 90o 103203 HM 0,22 90o 103301 HM 0,22 90o o Top Skin 103302 HM 0,22 90 103303 HM 0,22 90o 103304 HM 0,22 90o 103305 HM 0,22 90o 103306 HM 0,22 90o 103401 HM 0,22 90o 106401 SM 0,66 45o 218401 1 SM 0,22 0o 215101 HM 0,22 90o 215201 HM 0,22 90o 215202 HM 0,22 90o 215203 HM 0,22 90o 215301 HM 0,22 90o Lower Skin 215302 HM 0,22 90o 215303 HM 0,22 90o 215304 HM 0,22 90o 215305 HM 0,22 90o 215401 HM 0,22 90o 218401 SM 0,66 45o 307401 SM 0,66 0o 310201 HM 0,22 79,5o 311201 HM 0,22 -79,5o 310301 HM 0,22 79,5o Rib 311301 HM 0,22 -79,5o 310401 HM 0,22 79,5o 311401 HM 0,22 -79,5o 312101 SM 0,66 45o

Table 5.11: Results from the static analysis of the new simpliﬁed layup. Mass [g] Maximum Displacement [mm] Average Displacement [mm] 3303,89 3,41 1,13

70 Table 5.12: Mechanical behaviour differences of the new simplified layup compared to the previous optimized layup. Mass Maximum Displacement Average Displacement Difference Difference Difference Difference -29% 67% 67% Difference [g] and [mm] -1335,51 1,37 0,45 is possible to see just how much these new layups do not flex under load. While the previous optimized layup had a maximum displacement under average load of just 0,67 mm, the new simplified layup is 67% worse since it flexes until a maximum displacement of 1,13 mm. The real displacement change is close to just half a millimeter, and with a total wingspan of almost 1,6 m, half a millimeter is negligible. On the other hand, saving more than 1,3 kg on just one component is drastic and an amazing trade-off for the lost in mechanical performance. To understand how the new simplified layup stands against the standard layup, Table 5.13 shows the difference in performance between the two.

Table 5.13: Mechanical behaviour differences of the new simpliﬁed layup compared to the standard layup. Mass Maximum Displacement Average Displacement Difference -20% -54% -54%

As mentioned before, the new simplified layup manages not only to be lighter than the previous optimized layup but also lighter than the standard layup. Despite being lighter, the new simplified layup also presents much better mechanical performance with a displacement 54% lower compared to the standard layup. With these new results both objectives of making a stronger component that was also lighter than the original model have been achieved. Before proceeding with the cost analysis and comparison of the new layup, first the structural integrity of the new part was confirmed. Once again, with the results from the static analysis performed earlier, the failure criteria and displacement plot are present below in Figure 5.11.

(a) Failure criterion plot. (b) Average displacement plot.

Figure 5.11: Results from the static analysis of the new simpliﬁed layup.

As can be seen from Figure 5.11(a), the failure criteria hit a maximum value of 0,65, far away from

71 the structural limit value of 1 so, according to this plot, this new laminate option is viable from a structural point of view. One interesting thing to note is the change on the displacement plot presented in Figure 5.11(b) compared to the previous optimized layup. While with the standard layup the displacement is almost constant trough the whole width of the tip of the wing, after the first optimization process was over it was possible to see that the highest displacement area shifted to the back end of the wing, although still staying on the tip. With this new simplified layup thought, the highest displacement area shifted yet again, moving away from the gurney flap but concentrating on a specific area of the Top Skin laminate. After checking the HyperMesh model it is easy to understand, this specific area doesn’t have any kind of reinforcement and the only plies available to distribute the load are the cover plies. This is not worrying though since the real wing will have an aluminium insert on each end and this deformation will not be so noticeable. With the mechanical benefits of this new layup approved, it is time to move forward to the cost analysis to see if the final cost is acceptable or, if like with the previous optimized layup, deviates from the regulations goal to make a cheap thrilling racing car.

5.5.2 Simpliﬁed Layup Cost Study

To ensure that the new simpliﬁed layup is indeed cheaper to produce than the previous optimized layup, the same cost analysis performed previously was conducted here with exactly the same parameters. The results illustrated in Table 5.14 compare the costs of manufacturing a new wing with this new simpliﬁed layup versus the same wing manufactured with the previously optimized layup. For the complete results please refer to Appendix D.

Table 5.14: Cost difference between simpliﬁed layup and optimized layup Layup Total Material Cost [e] Total Worker Cost [e] Total Part Cost [e] Optimized 644,95 1.818,40 2.463,35 Simpliﬁed 437,80 682,40 1.120,20 Difference -32% -62% -55%

As expected, Table 5.14 shows that the new simplified layup is indeed much cheaper than the previously optimized layup. Although the difference on the material cost is smaller than expected, the difference in worker cost makes up for it. The total material cost is higher than expected probably due to the fact that this new simplied layup uses mainly HM fabrics that are almost three times more expensive than the regular woven counterparts. Also, due to having less directions available for the optimzation means that the new plies are usually larger than the plies on the previous optimization. Established that the new simplified layup is cheaper than the previously optimized layup, it is time to compare it to the standard layup. Once again, the same process applies and the results are shown in Table 5.15. Once again, as expected, the simplified layup is considerably more expensive than the standard

72 Table 5.15: Cost difference between simplified layup and standard layup. Layup Total Material Cost [e] Total Worker Cost [e] Total Part Cost [e] Standard 101,71 324,00 425,7 Simplified 437,80 682,40 1.120,20 Difference 330% 111% 163% layup. The material cost is what makes of most of the difference of 163% on the final price due to the use of HM fibres. Expecting an optimized layup to be cheaper than the standard layup is not reasonable so deciding if the new optimized layup will proceed to production based solely on its final price is not a good approach. This new simplified layup is 20% lighter and 54% stiffer than standard so apart from the additional rigidity, it brings along increased performance. An increase in cost of 163% for a completely different part that has suffered a thorough optimization process to not only deliver the most perfomance but also, do it at the lowest possible price seems like a good trade off. The final price may eventually be reduced by decreasing the frequency of the debulk operations, reducing worker time and as such, reducing the total cost of the part. Despite sounding simple, this solution by have its trade offs as the final result may come with an expected loss in quality. As expected from this layup on the beginning of this chapter, this solution presents a good balance between the cheaper standard layup and the more expensive, more performing optimized layup of Chapter 4.

Final Part and Moulds

Shown in Figure 5.13 are the ﬁnal moulds used to manufacture the new wings for both the ADESS-03 and the Pininfarina H2 Speed 2018. Also, seen in Figure 5.12 is one wing for the Pininfarina H2 Speed 2018. This wing weighted a total of 3727 g, with the carbon components weighting a total of 3407 g, the aluminium inserts 220 g and ﬁnally, 100 g of structural adhesive.

Figure 5.12: Final H2 Speed wing

73 Figure 5.13: Final wing moulds.

74 Chapter 6

Conclusions

6.1 Achievements

The main objective of this thesis was to design a new wing that mainly, would not break under use. Using the opportunity created, an optimization study was also developed to try and extract every drop of mechanical performance allowed by the geometry of the wing. Difficulties during the optimization process led to the creation of bespoke tools that provided significant quality of life improvements to the design process. In the end of the first optimization study, a working model was obtained, slightly heavier but stiffer than the previous model. This new laminate model coupled with the new design would be a perfect endpoint but fortunately, is was not. After planning the whole manufacturing process, a cost study was performed to find how much more expensive the new wing with the new laminate would be to manufacture. The conclusion was unfavourable for the first optimization study since the new wing, despite being an overall better part, was much more expensive meaning that it would never get out of the drawing board. Using the results from the first optimization study and a little ingenuity, a feasible design was reached that represents the perfect balance between the mechanical strength of the first optimized model and the cheaper standard laminate. The new design is 20% lighter and 54% stiffer. Despite being 163% more expensive, this value compared with the original 479% difference for the optimized layup seems about right for the increase in performance this new part provides. In the end of this thesis, it is safe to say that the end result is not only pleasant to look at, but it is also a feasible design and a design that, if needed, can be sent when needed for manufacture.

75 6.2 Future Work

This study was developed as part of a complete update for the ADESS-03 bodywork. Although the time spent developing this study made it impossible for the first wings manufactured with the updated design to feature the new updated layup, the next ones manufactured will surely count with improved performance in a lighter package. As this thesis is being written, a complete CFD study of the ADESS-03 is being prepared and with it, comes valuable data to be used to improve the performance of the car. This study took a long time but it laid important foundations that will reduce the time spent applying this exact same process to any other part of the car. On a design perspective, exploring CATIA Composites workbench would be beneficial for future work. The compatibility between CATIA and HyperMesh, although not perfect is perfectly usable and using the Composites workbench would improve the time managing future updates to the bodywork and most of all, simplify the process of providing instructions to perform a correct layup of the final part. There are, for example, tools that can help flatten the shape of the plies for automated cutting and tools to make the plybook making process much faster. Finally, regarding HyperWorks, one interesting suggestion would be to explore its HyperStudy package since HyperStudy allows for multiple objective optimization which in turn can help to return improved optimization results. It does come with a steeper learning curve though.

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81 82 Appendix A

Optimized Layup - Optimization Evolution

A.1 Plies Created After Free Size Optimization

Table A.1: Top skin laminate plies after free size optimization Ply Name Material Thickness [mm] Orientation 101100 SM 0,06 0o 102100 HM 0,05 0o 103100 HM 0,13 90o 104100 HM 0,15 79,5o 105100 HM 0,15 -79,5o 106100 SM 0,14 45o 101200 SM 0,07 0o 102200 HM 0,09 0o 103200 HM 0,22 90o 104200 HM 0,22 79,5o 105200 HM 0,22 -79,5o 106200 SM 0,20 45o 101300 SM 0,15 0o 102300 HM 0,24 0o 103300 HM 0,85 90o 104300 HM 0,84 79,5o 105300 HM 0,84 -79,5o 106300 SM 0,49 45o 101400 SM 1,73 0o 102400 HM 1,62 0o 103400 HM 0,79 90o 104400 HM 0,79 79,5o 105400 HM 0,79 -79,5o 106400 SM 1,17 45o

83 Table A.2: Lower skin laminate plies after free size optimization Ply Name Material Thickness [mm] Orientation 213100 SM 0,05 0o 214100 HM 0,03 0o 215100 HM 0,18 90o 216100 HM 0,17 79,5o 217100 HM 0,17 -79,5o 218100 SM 0,07 45o 213200 SM 0,07 0o 214200 HM 0,06 0o 215200 HM 0,43 90o 216200 HM 0,39 79,5o 217200 HM 0,39 -79,5o 218200 SM 0,15 45o 213300 SM 0,15 0o 214300 HM 0,14 0o 215300 HM 1,11 90o 216300 HM 1,10 79,5o 217300 HM 1,10 -79,5o 218300 SM 0,32 45o 213400 SM 1,73 0o 214400 HM 1,77 0o 215400 HM 0,27 90o 216400 HM 0,33 79,5o 217400 HM 0,33 -79,5o 218400 SM 1,46 45o

84 Table A.3: Rib laminate plies after free size optimization Ply Name Material Thickness [mm] Orientation 307100 SM 0,04 0o 308100 HM 0,05 0o 309100 HM 0,11 90o 310100 HM 0,12 79,5o 311100 HM 0,12 -79,5o 312100 SM 0,13 45o 307200 SM 0,05 0o 308200 HM 0,07 0o 309200 HM 0,11 90o 310200 HM 0,08 79,5o 311200 HM 0,08 -79,5o 312200 SM 0,24 45o 307300 SM 0,06 0o 308300 HM 0,14 0o 309300 HM 0,28 90o 310300 HM 0,18 79,5o 311300 HM 0,18 -79,5o 312300 SM 0,70 45o 307400 SM 1,85 0o 308400 HM 1,74 0o 309400 HM 1,51 90o 310400 HM 1,62 79,5o 311400 HM 1,62 -79,5o 312400 SM 0,92 45o

85 A.2 MATLAB Cleaned Plies Comparison - HyperMesh

A.2.1 Ply 101200

Figure A.1: Ply 101200 before MATLAB cleanup.

Figure A.2: Ply 101200 after MATLAB cleanup.

86 A.2.2 Ply 213200

Figure A.3: Ply 213200 before MATLAB cleanup.

Figure A.4: Ply 213200 after MATLAB cleanup.

87 A.2.3 Ply 311300

Figure A.5: Ply 311300 before MATLAB cleanup.

Figure A.6: Ply 311300 after MATLAB cleanup.

88 A.3 MATLAB Cleaned Plies Comparison - MATLAB

A.3.1 Ply 101200

Figure A.7: Ply 101200 before MATLAB cleanup.

Figure A.8: Ply 101200 after MATLAB cleanup.

89 Figure A.9: Ply 101200 comparison before and after MATLAB cleanup.

90 A.3.2 Ply 213200

Figure A.10: Ply 213200 before MATLAB cleanup.

Figure A.11: Ply 213200 after MATLAB cleanup.

91 Figure A.12: Ply 213200 comparison before and after MATLAB cleanup.

92 A.3.3 Ply 311300

Figure A.13: Ply 311300 before MATLAB cleanup.

Figure A.14: Ply 311300 after MATLAB cleanup.

93 Figure A.15: Ply 311300 comparison before and after MATLAB cleanup.

94 A.4 Comparison - Cleaned Plies vs Free Size Plies

Table A.4: Comparison between top skin plies before and after cleaning. Area before MATLAB Area after MATLAB Ply Name [mm2] [mm2] Difference 101100 529146,36 529140,88 0% 102100 529146,36 529140,88 0% 103100 529146,36 529140,88 0% 104100 529146,36 529140,88 0% 105100 529146,36 529140,88 0% 106100 529146,36 529140,88 0% 101200 337727,35 345637,66 2% 102200 293808,87 277138,28 -6% 103200 311887,03 305580,85 -2% 104200 317531,78 317806,44 0% 105200 317531,78 317806,44 0% 106200 331928,38 331761,07 0% 101300 167184,74 151215,92 -10% 102300 148430,60 138938,18 -6% 103300 110767,94 84100,19 -24% 104300 108603,93 91005,22 -16% 105300 108603,93 91005,22 -16% 106300 156264,51 172284,32 10% 101400 29332,07 16339,39 -44% 102400 37589,38 29008,70 -23% 103400 51581,68 33996,58 -34% 104400 50586,44 34726,11 -31% 105400 50586,44 34726,11 -31% 106400 57712,50 50433,42 -13%

95 Table A.5: Comparison between lower skin plies before and after cleaning. Area before MATLAB Area after MATLAB Ply Name [mm2] [mm2] Difference 213100 555785,81 555785,32 0% 214100 555785,81 555785,32 0% 215100 555785,81 555785,32 0% 216100 555785,81 555785,32 0% 217100 555785,81 555785,32 0% 218100 555785,81 555785,32 0% 213200 334932,84 325735,65 -3% 214200 295199,51 295518,81 0% 215200 333948,70 316325,22 -5% 216200 324893,03 296411,67 -9% 217200 324893,03 296411,67 -9% 218200 345183,54 348805,06 1% 213300 183531,13 185656,50 1% 214300 163481,22 157318,04 -4% 215300 155791,72 137581,85 -12% 216300 147003,90 127655,47 -13% 217300 147003,90 127655,47 -13% 218300 180329,87 178425,07 -1% 213400 30381,05 21994,84 -28% 214400 43201,39 36156,16 -16% 215400 110248,29 96161,70 -13% 216400 98198,93 83888,53 -15% 217400 98198,93 83888,53 -15% 218400 80561,69 69315,83 -14%

96 Table A.6: Comparison between rib plies before and after cleaning. Area before MATLAB Area after MATLAB Ply Name [mm2] [mm2] Difference 307100 435531,33 435530,98 0% 308100 435531,33 435530,98 0% 309100 435531,33 435530,98 0% 310100 435531,33 435530,98 0% 311100 435531,33 435530,98 0% 312100 435531,33 435530,98 0% 307200 286831,92 292878,82 2% 308200 262618,09 246783,11 -6% 309200 297797,82 279450,46 -6% 310200 319347,81 310053,27 -3% 311200 319347,81 310053,27 -3% 312200 270201,22 275860,12 2% 307300 201090,18 199679,70 -1% 308300 145484,25 130528,57 -10% 309300 119284,23 100466,49 -16% 310300 129776,38 91214,21 -30% 311300 129776,38 91214,21 -30% 312300 114052,79 115509,57 1% 307400 24511,02 13216,04 -46% 308400 33624,28 26934,61 -20% 309400 28753,27 16244,15 -44% 310400 12379,65 7899,59 -36% 311400 12379,65 7899,59 -36% 312400 51987,25 56176,24 8%

97 A.5 Plies Created After Size Optimization

Table A.7: Top skin laminate plies after size optimization.

Ply Name Plies Created After Size Ply Name Plies Created After Size 101100 NA 104100 NA 101200 NA 104200 104201 101300 101301 104301 101401 104300 104302 101402 101400 104401 101403 104402 102100 NA 104403 102200 102201 104400 104404 102300 102301 104405 104406 102401 102400 102402 105100 NA 105200 105201 103100 103101 103200 NA 105301 105300 105302 103301 103302 105401 103303 105402 103300 103304 105403 103305 105400 105404 103306 105405 105406 103401 103402 106100 106101 103403 106200 106201 103400 103404 106300 106301 103405 106401 103406 106400 106402 106403

98 Table A.8: Lower skin laminate plies after size optimization.

99 Table A.9: Rib laminate plies after size optimization.

Ply Name Plies Created After Size Ply Name Plies Created After Size 307100 NA 310401 307200 NA 310402 307300 NA 310403 310404 307401 310400 310405 307400 307402 310406 307403 310407 308100 308101 310408 308200 NA 311100 311101 308300 NA 311200 NA 308401 311300 NA 308402 311401 308400 308403 311402 308404 311403 308405 311404 309100 309101 311400 311405 309200 NA 311406 309300 309301 311407 309401 311408 309400 309402 312100 312101 310100 310101 312200 NA 310200 NA 312300 312301 310300 NA 312401 312402 312400 312403 312404

100 A.6 Plies Created After Shufﬂe Optimization

Table A.10: Top skin laminate plies after shufﬂe optimization.

Name Material Orientation Name Material Orientation 106101 SM 45o 103301 HM 90o 103101 HM 90o 106401 SM 45o 102201 HM 0o 101301 SM 0o 104201 HM 79,5o 103302 HM 90 105201 HM -79,5o 102301 HM 0o 104301 HM 79,5o 103303 HM 90o 104302 HM 79,5o 101401 SM 0o 105301 HM -79,5o 103304 HM 90o 106201 SM 45o 106402 SM 45o 105302 HM -79,5o 101402 SM 0o 104401 HM 79,5o 103305 HM 90o 104402 HM 79,5o 101403 SM 0o 104403 HM 79,5o 103306 HM 90 104404 HM 79,5o 102401 HM 0o 104405 HM 79,5o 103401 HM 90o 104406 HM 79,5o 106403 SM 45o 106301 SM 45o 102402 HM 0o 105401 HM -79,5o 103402 HM 90o 105402 HM -79,5o 103403 HM 90o 105403 HM -79,5o 103404 HM 90o 105404 HM -79,5o 103405 HM 90o 105405 HM -79,5o 103406 HM 90o 105406 HM -79,5o

101 Table A.11: Lower skin laminate plies after shufﬂe optimization Name Material Orientation 218101 SM 45o 213101 SM 0o 215101 HM 90o 216201 HM 79,5o 217201 HM -79,5o 214101 HM 0o 215201 HM 90o 218301 SM 45o 216301 HM 79,5o 216302 HM 79,5o 213401 SM 0o 215301 HM 90o 217301 HM -79,5o 217302 HM -79,5o 218401 SM 45o 213402 SM 0o 215302 HM 90o 216401 HM 79,5o 216402 HM 79,5o 213403 SM 0o 215401 HM 90o 218402 SM 45o 216403 HM 79,5o 217401 HM -79,5o 213404 SM 0o 217402 HM -79,5o 217403 HM -79,5o 214401 HM 0o

102 Table A.12: Rib laminate plies after shufﬂe optimization.

Name Material Orientation Name Material Orientation 312101 SM 45o 312402 SM 45o 308101 HM 0o 309401 HM 90o 307401 SM 0o 310407 HM 79,5o 309101 HM 90o 310408 HM 79,5o 310101 HM 79,5o 311401 HM -79,5o 311101 HM -79,5o 311402 HM -79,5o 310401 HM 79,5o 312403 SM 45o 312301 SM 45o 308403 HM 0o 310402 HM 79,5o 308404 HM 0o 307402 SM 0o 309402 HM 90o 307403 SM 0o 311403 HM -79,5o 309301 HM 90o 311404 HM -79,5o 310403 HM 79,5o 312404 SM 45o 312401 SM 45o 311405 HM -79,5o 310404 HM 79,5o 311406 HM -79,5o 310405 HM 79,5o 308405 HM 0o 310406 HM 79,5o 311407 HM -79,5o 308401 HM 0o 311408 HM -79,5o 308402 HM 0o

103 A.7 Laminates After Manual Editing

Table A.13: Top skin laminate plies after manual editing.

Name Material Orientation Name Material Orientation 101403 SM 0o 105405 HM -79,5o 103101 HM 90o 105406 HM -79,5o 102201 HM 0o 103301 HM 90o 104201 HM 79,5o 106401 SM 45o 105201 HM -79,5o 103302 HM 90o 104301 HM 79,5o 102301 HM 0o 104302 HM 79,5o 103303 HM 90o 105301 HM -79,5o 103304 HM 90o 106201 SM 45o 106402 SM 45o 105302 HM -79,5o 103305 HM 90o 104401 HM 79,5o 103306 HM 90o 104402 HM 79,5o 102401 HM 0o 104403 HM 79,5o 103401 HM 90o 104404 HM 79,5o 106403 SM 45o 104405 HM 79,5o 102402 HM 0o 104406 HM 79,5o 103402 HM 90o 106301 SM 45o 103403 HM 90o 105401 HM -79,5o 103404 HM 90o 105402 HM -79,5o 103405 HM 90o 105403 HM -79,5o 103406 HM 90o 105404 HM -79,5o 106101 SM 45o

104 Table A.14: Lower skin laminate plies after manual editing. Name Material Orientation 213101 SM 0o 215101 HM 90o 216201 HM 79,5o 217201 HM -79,5o 214101 HM 0o 215201 HM 90o 218301 SM 45o 216301 HM 79,5o 216302 HM 79,5o 215301 HM 90o 217301 HM -79,5o 217302 HM -79,5o 218401 SM 45o 215302 HM 90o 216401 HM 79,5o 216402 HM 79,5o 215401 HM 90o 218402 SM 45o 216403 HM 79,5o 217401 HM -79,5o 217402 HM -79,5o 217403 HM -79,5o 214401 HM 0o 218101 SM 45o

105 Table A.15: Rib laminate plies after manual editing.

Name Material Orientation Name Material Orientation 307401 SM 0o 310407 HM 79,5o 308101 HM 0o 310408 HM 79,5o 309101 HM 90o 311401 HM -79,5o 310101 HM 79,5o 311402 HM -79,5o 311101 HM -79,5o 312403 SM 45o 310401 HM 79,5o 308403 HM 0o 312301 SM 45o 308404 HM 0o 310402 HM 79,5o 309402 HM 90o 309301 HM 90o 311403 HM -79,5o 310403 HM 79,5o 311404 HM -79,5o 312401 SM 45o 312404 SM 45o 310404 HM 79,5o 311405 HM -79,5o 310405 HM 79,5o 311406 HM -79,5o 310406 HM 79,5o 308405 HM 0o 308401 HM 0o 311407 HM -79,5o 308402 HM 0o 311408 HM -79,5o 312402 SM 45o 312101 SM 45o 309401 HM 90o

106 Appendix B

Material Cost for Optimized Layup

Table B.1: Material cost for top skin laminate. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 101100 SM 529140,88 0 0,00 101200 SM 345637,66 0 0,00 101300 SM 151215,92 1 3,93 101400 SM 16339,39 3 1,27 102100 HM 529140,88 0 0,00 102200 HM 277138,28 1 17,46 102300 HM 138938,18 1 8,75 102400 HM 29008,70 2 3,66 103100 HM 529140,88 1 33,34 103200 HM 305580,85 0 0,00 103300 HM 84100,19 6 31,79 103400 HM 33996,58 6 12,85 104100 HM 529140,88 0 0,00 104200 HM 317806,44 1 20,02 104300 HM 91005,22 2 11,47 104400 HM 34726,11 6 13,13 105100 HM 529140,88 0 0,00 105200 HM 317806,44 1 20,02 105300 HM 91005,22 2 11,47 105400 HM 34726,11 6 13,13 106100 SM 529140,88 1 13,76 106200 SM 331761,07 1 8,63 106300 SM 172284,32 1 4,48 106400 SM 50433,42 3 3,93 45 233,08 Number of Plies Total Cost

107 Table B.2: Material cost for lower skin laminate. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 213100 SM 555785,32 1 14,5 213200 SM 325735,65 0 0,0 213300 SM 185656,50 0 0,0 213400 SM 21994,84 4 2,3 214100 HM 555785,32 1 35,0 214200 HM 295518,81 0 0,0 214300 HM 157318,04 0 0,0 214400 HM 36156,16 1 2,3 215100 HM 555785,32 1 35,0 215200 HM 316325,22 1 19,9 215300 HM 137581,85 2 17,3 215400 HM 96161,70 1 6,1 216100 HM 555785,32 0 0,0 216200 HM 296411,67 1 18,7 216300 HM 127655,47 2 16,1 216400 HM 83888,53 3 15,9 217100 HM 555785,32 0 0,0 217200 HM 296411,67 1 18,7 217300 HM 127655,47 1 8,0 217400 HM 83888,53 3 15,9 218100 SM 555785,32 1 14,5 218200 SM 348805,06 0 0,0 218300 SM 178425,07 1 4,6 218400 SM 69315,83 2 3,6 27 248,2 Number of Plies Total Cost

108 Table B.3: Material cost for rib laminate. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 307100 SM 555785,32 0 0,0 307200 SM 325735,65 0 0,0 307300 SM 185656,50 0 0,0 307400 SM 21994,84 3 8,9 308100 HM 555785,32 1 27,4 308200 HM 295518,81 0 0,0 308300 HM 157318,04 0 0,0 308400 HM 36156,16 5 8,5 309100 HM 555785,32 1 27,4 309200 HM 316325,22 0 0,0 309300 HM 137581,85 1 6,3 309400 HM 96161,70 2 2,0 310100 HM 555785,32 1 27,4 310200 HM 296411,67 0 0,0 310300 HM 127655,47 0 0,0 310400 HM 83888,53 8 4,0 311100 HM 555785,32 1 27,4 311200 HM 296411,67 0 0,0 311300 HM 127655,47 0 0,0 311400 HM 83888,53 8 4,0 312100 SM 555785,32 1 11,3 312200 SM 348805,06 0 0,0 312300 SM 178425,07 1 3,0 312400 SM 69315,83 4 5,8 37 163,6 Number of Plies Total Cost

109 Appendix C

Simpliﬁed Layup - Optimization Evolution

C.1 Plies Created After Free Size Optimization

Table C.1: Top skin laminate plies after free size optimization. Ply Name Material Thickness [mm] Orientation 101100 SM 0,14 0o 103100 HM 0,24 90o 106100 SM 0,13 45o 101200 SM 0,19 0o 103200 HM 0,52 90o 106200 SM 0,24 45o 101300 SM 0,22 0o 103300 HM 0,94 90o 106300 SM 0,24 45o 101400 SM 0,12 0o 103400 HM 0,30 90o 106400 SM 0,05 45o

110 Table C.2: Lower skin laminate plies after free size optimization. Ply Name Material Thickness [mm] Orientation 213100 SM 0,05 0o 215100 HM 0,25 90o 218100 SM 0,10 45o 213200 SM 0,20 0o 215200 HM 0,68 90o 218200 SM 0,21 45o 213300 SM 0,31 0o 215300 HM 0,91 90o 218300 SM 0,28 45o 213400 SM 0,09 0o 215400 HM 0,16 90o 218400 SM 0,08 45o

Table C.3: Rib laminate plies after free size optimization. Ply Name Material Thickness [mm] Orientation 307100 SM 0,04 0o 310100 HM 0,14 79,5o 311100 HM 0,14 -79,5o 312100 SM 0,06 45o 307200 SM 0,10 0o 310200 HM 0,40 79,5o 311200 HM 0,40 -79,5o 312200 SM 0,19 45o 307300 SM 0,24 0o 310300 HM 0,86 79,5o 311300 HM 0,86 -79,5o 312300 SM 0,31 45o 307400 SM 0,28 0o 310400 HM 0,60 79,5o 311400 HM 0,60 -79,5o 312400 SM 0,09 45o

111 C.2 Plies Created After Size Optimization

Table C.4: Top skin laminate plies after size optimization. Ply Name Plies Created After Size 101100 NA 101200 NA 101300 101301 101400 101401 103100 103101 103201 103200 103202 103203 103301 103302 103303 103300 103304 103305 103306 103400 103401 106100 NA 106200 NA 106300 NA 106400 106401

112 Table C.5: Lower skin laminate plies after size optimization. Ply Name Plies Created After Size 213100 NA 213200 NA 213300 NA 213400 NA 215100 215101 215201 215200 215202 215203 215301 215302 215300 215303 215304 215305 215400 215401 218100 NA 218200 NA 218300 NA 218400 218401

Table C.6: Rib laminate plies after size optimization. Ply Name Plies Created After Size 307100 NA 307200 NA 307300 NA 307400 307401 310100 NA 310200 310201 310300 310301 310400 310401 311100 NA 311200 311201 311300 311301 311400 311401 312100 312101 312200 NA 312300 NA 312400 NA

113 C.3 Plies Created After Shufﬂe Optimization

Table C.7: Top skin laminate plies after shufﬂe optimization. Ply Name Material Orientation 106401 SM 45o 103101 HM 90o 103201 HM 90o 103202 HM 90o 103203 HM 90o 103301 HM 90o 101301 SM 0o 103302 HM 90o 103303 HM 90o 103304 HM 90o 103305 HM 90o 103306 HM 90o 101401 SM 0o 103401 HM 90o

Table C.8: Lower skin laminate plies after shufﬂe optimization. Ply Name Material Orientation 218401 SM 45o 215101 HM 90o 215201 HM 90o 215202 HM 90o 215203 HM 90o 215301 HM 90o 215302 HM 90o 215303 HM 90o 215304 HM 90o 215305 HM 90o 215401 HM 90o

114 Table C.9: Rib laminate plies after shufﬂe optimization Ply Name Material Orientation 312101 SM 45o 307401 SM 0o 310201 HM 79,5o 311201 HM -79,5o 310301 HM 79,5o 311301 HM -79,5o 310401 HM 79,5o 311401 HM -79,5o

115 C.4 Laminates After Manual Editing

Table C.10: Top skin laminate plies after manual editing. Ply Name Material Orientation 101301 SM 0o 103101 HM 90o 103201 HM 90o 103202 HM 90o 103203 HM 90o 103301 HM 90o 103302 HM 90o 103303 HM 90o 103304 HM 90o 103305 HM 90o 103306 HM 90o 103401 HM 90o 106401 SM 45o

Table C.11: Lower skin laminate plies after manual editing. Ply Name Material Orientation 218401 1 SM 0o 215101 HM 90o 215201 HM 90o 215202 HM 90o 215203 HM 90o 215301 HM 90o 215302 HM 90o 215303 HM 90o 215304 HM 90o 215305 HM 90o 215401 HM 90o 218401 SM 45o

116 Table C.12: Rib laminate plies after manual editing. Ply Name Material Orientation 307401 SM 0o 310201 HM 79,5o 311201 HM -79,5o 310301 HM 79,5o 311301 HM -79,5o 310401 HM 79,5o 311401 HM -79,5o 312101 SM 45o

117 Appendix D

Material Cost for Simpliﬁed Layup

Table D.1: Material cost for top skin laminate. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 101100 SM 529140,879 0 0,00 101200 SM 389200,806 0 0,00 101300 SM 226367,115 1 5,89 101400 SM 107332,629 1 2,79 103100 HM 529140,879 1 33,34 103200 HM 328859,736 3 62,15 103300 HM 182826,825 6 69,11 103400 HM 115364,755 1 7,27 106100 SM 529140,879 1 13,76 106200 SM 375069,523 0 0,00 106300 SM 246799,853 0 0,00 106400 SM 167672,687 0 0,00 14 194,30 Number of Plies Total Cost

118 Table D.2: Material cost for lower skin laminate. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 213100 SM 555785,317 0 0,00 213200 SM 333890,298 0 0,00 213300 SM 211350,774 0 0,00 213400 SM 135259,838 0 0,00 215100 HM 555785,317 1 35,01 215200 HM 329770,367 3 62,33 215300 HM 224496,036 5 70,72 215400 HM 176023,135 1 11,09 218100 SM 555785,317 0 0,00 218200 SM 384964,884 0 0,00 218300 SM 225404,941 0 0,00 218400 SM 138797,631 1 3,61 11 182,76 Number of Plies Total Cost

Table D.3: Material cost for rib laminate. Number of 2 Ply Name Material Area [mm ] Ocurences Cost per Ply [e] 307100 SM 435530,977 0 0,00 307200 SM 228682,852 0 0,00 307300 SM 89830,516 0 0,00 307400 SM 26469,144 1 0,69 310100 HM 435530,977 0 0,00 310200 HM 206541,75 1 13,01 310300 HM 120852,534 1 7,61 310400 HM 59351,255 1 3,74 311100 HM 435530,977 0 0,00 311200 HM 206541,75 1 13,01 311300 HM 120852,534 1 7,61 311400 HM 59351,255 1 3,74 312100 SM 435530,977 1 11,32 312200 SM 248057,662 0 0,00 312300 SM 157566,044 0 0,00 312400 SM 106352,891 0 0,00 8 60,74 Number of Plies Total Cost

119 120