The Preliminary Design of an Aircraft Wing Structure to Meet Aggressive Torque Box Strain Energy and Mass Targets

Stephen WanjihiaA dissertation submitted in partial fulfilment of the requirements for the degree of Bachelor of Engineering

March 2014School of Engineering and DesignBrunel UniversityLondon, United Kingdom

ATTENTION!IF YOU SEE _ KNOW THAT THERE IS A HIDDEN REFFERENCE THERE. PLEASE CHANGE TO SHOW MARKUP TO SEE IT.Topology Optimization of a Wing Box Rib

Abstract

This dissertation provides a methodology for generating the preliminary design of an aircraft wing box rib to meet aggressive strain energy and mass targets.Initially research is conducted to investigate the potential benefits and real world applications of topology optimisation; this has the double objective of giving the study a focus while providing initial aircraft wing geometry that a CAD model is built from. Furthermore research is also conducted to investigate the flight missions that the aircraft / type is typically exposed to and in doing so a greater understanding of the maximum wing loading and more importantly the conditions that the aircraft is in during which is achieved.Putting the two together, an aerodynamic study is conducted on the wing CAD model with the boundary conditions that the aircraft experiences when producing maximum wing loading. Therefore the objective of the aerodynamic study is to extract the surface pressures that act on the wing during the critical flight case.With great care the loads along with the CAD model are then transferred from the aerodynamic environment to the structural environment for structural analysis and optimisation. The structural analysis is conducted beforehand using the aerodynamic loads to gain an initial understanding of the stress distribution and displacement within structure. The structural analysis not only provides a better understanding of the structure to be optimised but also acts as a validation tool for the optimised structure. The factor of safety that the pre-optimised structure achieves can be compared to that of the post optimised structure, thus structurally validating the final optimised design.

to my family for their constant love and support and my loving girlfriend for her patience over the years

ACKNOWLEDGEMENTSI would like to thank my supervisor Dr. Narcis M. Ursache for his guidance on the project and also Dr. Jan Wissink for his insightful advice and guidance.

TABLE OF CONTENTS1.Introduction91.1.Context91.2.Background101.2.1.Size Optimisation101.2.2.Shape Optimisation101.2.3.Structural Optimisation111.2.4.Topography111.2.5.Topometry111.2.6.Topology111.3.Purpose111.4.Dissertation Outline112.Literature Review122.1.Approach132.2.Algorithms142.3.Objectives142.4.Domain152.5.Conclusion163.Methodology173.1.Introduction174.Geometry Design184.1.Aircraft Specification184.2.Wing Structure184.2.1.Wing Design194.2.2.Specification204.3.Mission214.3.1.Flight Case225.Aerodynamic Analysis235.1.Introduction235.2.Problem Study255.3.Flow Classification265.3.1.Subsonic vs. Supersonic & Incompressible vs. Compressible265.3.2.Laminar vs. Turbulent275.4.Boundary Conditions275.4.1.Geometry275.4.2.Grid285.4.3.Flow Solver Boundary Conditions285.5.Results295.6.Discussion316.Baseline Analysis336.1.Model Setup and Considerations336.1.1.Approach336.1.2.Geometry336.1.3.Material Property346.1.4.Mesh Creation346.1.5.Loads and Boundary Conditions356.1.6.Hypothesis366.1.7.Results366.1.8.Discussion387.Topology Optimisation397.1.FE Model Setup and Considerations397.2.Approach397.3.Geometry397.4.Material Property and Element property407.5.Loads and Boundary Conditions407.6.Meshing407.7.Analysis Setup407.8.Results417.9.Discussion417.9.1.Project Overview427.9.2.Results Overview437.9.3.Future Work447.9.4.Recommendations448.Conclusion46No table of contents entries found.

LIST OF TABLESTable 1 Wing geometrical specification23Table 2 Cessna Citation Mustang wing spar material properties24Table 3 Cessna Citation Mustang wing spar material properties24Table 4 Take-off flight case conditions25Table 6 Chord-Wise Coefficient of Pressure Distribution (Airfoils 1, 2 & 3), 10 degrees angle of attack32Table 7 Chord-wise Static Pressure Distribution (Airfoils 1, 2 & 3), 10 degrees angle of attack33

LIST OF FIGURESFigure 1Types of structural optimisation, size (top), shape (middle) and topology optimisation (bottom), Courtesy of ((Martin P Bendsoe & Sigmund, 2003))13Figure 2 Topology Optimisation, types of approach, macrostructure (top) and microstructure (bottom), Courtesy of ((G I N Rozvany et al., 1995))16Figure 5 NACA 23014 geometrical points23Figure 6 Critical conditions for a wing box structure (Courtesy of (Michael Chun-yung Niu, n.d.))25Figure 7 C-Mesh geometry around NACA 2301428Figure 9 Flow regime classifications (Courtesy of Dr Mark Jabbal)30Figure 11 Contours of Static Pressure for 10 degrees angle of attack k-omega model (airfoil 1)33Figure 13 Isometric View of Airfoils1, 2 & 3 and front, mid and rear spars geometry in Patran 201237Figure 14 Loads applied to Finite Element Model Patran39Figure 15 Applied load displacement plot (patran)40Figure 16 Finite Element Model Von-Mises Stress40Figure 17 Baseline Design of CCM Wing Ribs44

Contents Abstract Give the reader a brief outline of the dissertation Contents, Table of figures and List of Tables List of Symbols/Nomenclature Introduction Brief introduction to the report, i.e. analysis and studies conducted. Finally, in brief, discussing the aims of the report.Comment by me10stw: MAE 154B Context Justifying topology optimisation Background Brief yet detailed chronological account of optimisation, leading to structural optimisation and finally topology optimisation. Types of optimisation A brief discussion of the different types of optimisation, concentrating on the key differences.Comment by me10stw: See m5 General optimisation Theory, Algorithms and ApplicationsComment by me10stw: See m5Also An intro to Structural Opt Topology optimisation algorithms Multidisciplinary Topology Optimisation Project Description A description of the project (as stated in the project brief) and a breakdown of the major challenges of the project.Comment by me10stw: MAE 154B Delimitations of dissertation A description of the set project boundaries to ensure focus is kept within the study topic i.e. topology optimisation. Methodology Introduction Wing Structure Description of wing structural components Aircraft Selection Justification of aircraft selection through comparative study Airfoil Design Guiding the reader through the design process of the airfoil Geometry Introduction Highlighting the importance of the work conducted herein before providing a brief description of the simulation conducted Description of Software - Aerodynamic Analysis Introduction Highlighting the importance of the work conducted herein before providing a brief description of the simulation conducted Description of Tools - Ansys Workbench Fluid Flow (Fluent) Inputs and Constraints Pre-Analysis boundary conditions Procedure Geometry, Mesh, Physics Setup Results and Discussion Numerical Results, Verification & Validation Conclusion and Recommendations Finite Element Analysis Linear Static Analysis Geometry Properties Boundary Conditions & Loads Meshing Analysis Results Topology Optimisation Model Preparation Meshing Set-up Results Discussion Conclusion

1. To the women of my life:2. 3. Abstract4. 5. Contents, Table of figures and List of Tables6. List of Symbols/Nomenclature7. 8. 9. IntroductionComment by me10stw: MAE 154BWithin this chapter a context for the study is provided, thereafter a brief background of optimisation in general is given before the various types of structural optimisation are identified and covered. Thereafter the purpose of the study is defined before an outline of the report is specified.9.1. ContextFuel costs for the past 23 years have suffered from a constant inflation (Department of Energy and Climate Change 2012) and for a flight company today this accounts to a significant proportion of approximately a third of overall operating fees. As a result, flight companies are making a conscious effort to cut costs from elsewhere in the business; By simply removing an olive from the salad container of each first class passenger, American Airlines are said to have saved up to $500,000 per year (Robinson G & Stern 1997).While Airline business search for margins through budgeting, OEMs are pursuing their margins through efficient designs and less material waste.In an interview Dr. Matthew Gilbert of Sheffield University stated, Over a thirty year lifetime of an aircraft, carrying one kilogram is equivalent to $100,000 of aviation fuel. The importance of reducing aircraft weight can be witnessed in thethrough cases such as of Airbus collaboration with Altair Engineering where the company is reported to have made weight savings of up to 1000kg per A380 (Krog et al. 2004). According to Dr. Matthew Gilberts estimates, that equates to commercial savings of approximately $3.3million each year. Furthermore, the aerospace industry is under immense pressure to reduce emissions, both nationally and internationally, from governments and aviation authorities through key policies such as Flightpath 2050(Parliament 2012), ACARE 2020 (Quentin & Co-chairman 2007).These examples of cost saving were chosen to give the reader an better insight into the pressure, effects and results of minimising expenditure within the aerospace industry. Other methods of achieving methods of achieving this are are through incorporating solutions such as flight model optimisation, incorporating drag reduction devices or structural optimisation.

9.2. The ACARE 2020 vision for commercial transport aircraft targets a 50% reduction per passenger kilometre in fuel consumption and CO2 emissions, with a 20-25% reduction to be achieved through airframe improvements. This step change in performance is dependent on the successful integration of Multi-Disciplinary Design Capabilities (MDDC) at the preliminary design stage.9.3. The ACARE 2020 vision for business transport air ship focuses on a half decrease for every traveler kilometer in fuel utilization and Co2 discharges, with a 20-25% lessening to be accomplished through airframe enhancements. This step change in execution is reliant on the fruitful joining of Multi-Disciplinary Design Capabilities (MDDC) at the preparatory outline stage.9.4. The ACARE 2020 vision for business transport flying machine focuses on a half lessening for every traveler kilometer in fuel utilization and Co2 discharges, with a 20-25% diminishment to be attained through airframe upgrades. This step change in execution is reliant on the effective mix of Multi-Disciplinary Outline Abilities (MDDC) at the preparatory configuration stage.9.5. 9.6. 9.7. "Saving even a few pounds of a vehicle's weight ... could mean that they would also go faster and consume less fuel. Reducing weight involves reducing materials, which, in turn, means reducing cost as well."9.8. Henry Ford, 1923.9.9. HYPERLINK "https://www.vrand.com/companyProfile.html" https://www.vrand.com/companyProfile.html9.10. 9.11. 9.12. 9.13.

9.14. BackgroundIt is important initially to become cognizant of the topic optimisation before applying it to a specific particular purpose. In the book Elements of Structural Optimization (Haftka, 1992), Haftka makes a notable comment regarding the origin of optimization, Optimization is concerned with achieving the best outcome of a given operation while satisfying certain restrictions. Human beings, guided and influenced by their natural surroundings, almost instinctively perform all functions in a manner that economizes energy or minimizes discomfort and pain. The motivation is to exploit the available limited resources in a manner that maximizes output or profit. The early inventions of the lever or the pulley mechanisms are clear manifestations of mans desire to maximize mechanical efficiency. I believe this to be both an accurate description of the term optimisation as well as a factual portrayal into its origins. Haftka goes on to describe an optimal design by quoting Wilde, i.e. the best feasible design according to a preselected quantitative measure of effectiveness (Wilde, 1978).It is with this understanding that we can now go on to define structural optimisation as a method that uses constraints such as density or mass to obtain the greatest performance for a structure. Structural optimisation is made up of three sections; i) Size ii) Shape and iii) Topology/Layout Optimisation.

Figure 1Types of structural optimisation, size (top), shape (middle) and topology optimisation (bottom), Courtesy of ((Bendsoe & Sigmund 2003))9.14.1. Size OptimisationSize optimisation manipulates parameters of a structure such as plate thickness, beam cross section size, etc. to find the optimal design.9.14.2. Usually associated with structures such as bridges, space frames, features such as the thickness of a plate or the cross sectional size of a beam structure, size optimisation modifies these dimensions to achieve an optimal design.9.14.3. Shape OptimisationWithin shape optimisation, the boundary of the domain is manipulated to achieve an optimal structure.

9.14.4. Shape optimisation allows changes to be made to the border of the geometry.9.14.5. Structural OptimisationStructural optimisation from (Christensen & Klarbring 2009) is described as the subject of making an assemblage of material sustain the loads in the best way. Structural optimisation can then be further divided into three sections i.e. topography, topometry, topology. The focus of this report will be on topology optimisation.9.14.6. Give a brief description on how structural optimisation separates itself from size and shape optimisation9.14.7. Topography9.14.8. TopographySimilar to topology optimisation, within topography the best arrangement of beads within a material is sought by varying the element offset from the mid-plane component.Define9.14.9. 9.14.10. Topometry9.14.11. TopometrySimilar to topology, topometry optimisation seeks the ideal material layout within a structure by varying the element wise thickness.Define9.14.12. TopologyFor topology optimisation, the material layout of the structure is manipulated by varying the element density between 0(void) and 1(material) in an effort to achieve an ideal material layout for a given load and objective.FULLY DEFINE!

9.15. PurposeThe purpose of this report is to provide a working methodology for the design of a rib to withstand locally applied compressive rib loads. Starting from a baseline and using the concepts of topology optimisation, the design would cater for both the global wing bending/twist loads and the locally applied rib compression loads. The global finite element model should be loaded by a combination of critical flight loads. Minimum weight formulation and constrain the total elastic energy in each load case to be lower than that of a baseline design, leading to a more efficient design.9.16. Dissertation OutlineThis next chapter of this report reviews the available topology optimisation literature through investigation of each step of the optimisation operation. In doing so the vastness of the topic that is topology optimisation is realised. A conclusion to the literature review is provided before the methodology section. The methodology is logically explained with the focus of each section being the discussion of achieved results. The sections of the methodology include; CAD (geometry design), CFD (aerodynamic study), FEA and Topology optimisation. Thereafter the results, discussion and conclusion, are provided.

10. Literature ReviewThe following section provides a brief outline of the literature regarding topology optimisation. It does not intend to provide an in depth critique of the vast field that is topology optimisation, for that the reader is referred to text such as (Bendsoe & Sigmund 2003), (Rozvany 2001) or (Eschenauer & Olhoff 2001).Using the optimality criteria (OC) method, Australian engineer MichellMic, A. G. M. LVIII . The Limits of Economy of material in Frame-structures. 8, 175177 (1904) was able to determine the least weight arrangement of truss structures. In doing so entered his name into the history books as being one of the first to develop a new way of identifying structurally optimal forms. Thereafter within , Rozvany has further developed and extended Michells work to beam systems. Within (Rozvany et al. 1995) Rozvany GIN, Bendsoe MP, Kirsch U (1995) Layout optimization of structures. Appl Mech Rev ASME 48:41119it is seen that Michells early work in structures lacked practicality, however, using his basic principles, Prager and Rozvany were able to define the optimal layout theory. Although its application today is mostly seen within the specific subject of exact analytical solutions of benchmark problems, optimal layout theory has had profound ramifications on the fields of both continuum structures and numerical methods. See (T. Lewiski, G. I. N. Rozvany, T. Sok 2013) for current work by Rozvany extending analytical solutions of Michells trusses.From a review of the literature (Rozvany 2000) it is seen that topology optimisation of structures and composite continua is divided into two topics i.e. Layout Optimisation (LO) also referred to in the literature as low volume fraction and Generalised Shape Optimisation (GSO) also known as variable topology shape optimisation. LO deals with skeletal structures and has its principles founded on those of Michells work and, therefore, is not a new field of structural mechanics by any means, Ref, (Rozvany 2001). GSO, on the other hand, deals with both the shape and topology of the internal of a structure of a continuum concurrently.Sometimes referred to as the godfather of topology optimisation, Martin Bendsoe contributed significantly to the technique of homogenisation. Within (T. Lewiski, G. I. N. Rozvany, T. Sok 2013) we see that he contributed to the development of the initial precise analytical solutions for the stiffness tensor of homogenized optimal microstructures. Furthermore via text such as (Bendsoe & Kikuchi 1988), (Ma et al. 1993) it can be seen that he pioneered research in the exploration of the homogenisation method. Having said that, within his book (Bendsoe & Sigmund 2003), Bendsoe mentions that his work in homogenisation can be seen as a natural continuation of the solid plate optimisation studies performed by Cheng and Olhoff 1981. In parallel to his research of the homogenisation method, Bendsoe also originally suggested the SIMP approach.From the text it can be seen that topology optimisation is quite literally a century old problem that has been vastly explored and broken down into numerous branches differing in methods or applications. That being said, the following section aims to better explain the topic of topology optimisation by roughly exploring the various branches it is divided into.According to research conducted, initially it is necessary specify all the functional and performance requirements of the structure to be optimised. Generating accurate information at this stage will result in the deeper understanding of the structure. In doing so, the correct problem formulation can be created which is necessary to select the ideal optimisation method, resulting in the efficient material layout for a set of constraints given an objective function(s).

10.1. Rozvany GIN (1972a) Grillages of maximum strength and maximum stiffness. Inlet J Mech sci 14:1217-1210.2. ApproachDetailed within (Eschenauer & Olhoff 2001) we can see that as initial division, topology optimisation consists of two rough classes, i.e. Microstructure approach or material and Macrostructure approach or geometrical, see fig below.

Figure 2 Topology Optimisation, types of approach, macrostructure (top) and microstructure (bottom), Courtesy of ((Rozvany et al. 1995))

As in fig above, the microstructure approach works by spreading a mesh throughout the domain and attaching a stiffness-density relation to the property of the element, the structure can then be optimised given a predefined loading, constraint and criteria. Using the density as a design variable i.e. 0 Void and 1 Solid, an optimum material distribution is achieved. The geometric approach works by attaching a variable geometry to the material locations thus achieving an optimal design.10.3. AlgorithmsAlthough analytical methods are significantly important as they provide early approximate predictions to problems as well as validation of solutions, their capabilities tend to become limited as the geometries and loading conditions of actual structures become more and more complex to formulate. This along with the ever growing research in numerical methods and high speed computing during the latter half of the last century became the main drivers for the reliance that structural analysis today has on numerical methods, specifically FEM.

That being said, in order to conduct topology optimisation on a given structure via the aid of a numerical solver, depending on the objective(s) of the optimisation, an optimisation must be selected. These are complex algorithms that are specifically written to result in the improvement of the selected objective function. In order to better explain this, first the various branches and segments of topology optimisation are discussed including a brief look at the algorithms and the differences within the formulas that compose them.

10.4. 10.5. 10.6. ObjectivesWithin topology optimisation, the implication of the objective function embodies the efficiency of the design with reference to an initial target design goal. Common examples of objective functions are; maximum strain, natural frequency, weight etc. Topology optimisation can be further divided, depending on the number of objectives functions being considered, into either problems that consider a single objective (Single Objective Analysis) or an average of multiple objectives, i.e. Multi-Disciplinary Optimisation (MDO). Single Objective Analysis (SOA) is a straightforward case and rarely appears in text however MDO is a field that still offers some novelty. The reader is referred to (ROELAND DE BREUKER 2013) for an in depth look at MDO in the field of aero structures.The multi or even scalar objective analysis can be mathematically represented as;

With the difference between the two being the number of objective function(s) to fulfil, within the formula this would be represented by the term fn.

10.7. 10.8. 10.9. Typical objective functions include;10.10. Strain energy density10.11. Mises Equivalent Stress10.12. Mean Compliance and Maximum Displacement (for stiffness design)10.13. Maximum strain (for formability study of sheet metals)10.14. 10.15. DomainDepending on the intended domain to be optimised, topology optimisation can be classified into either; continuum or discrete structures.

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The continuum structures approach considers the domain to be made up of a continuous blend of both material and void elements. Thus by altering the density of each element between the two, a final optimal design to predefined criteria is obtained under loading.Sometimes referred to as the ground structure approach, the discrete structures approach works by converting the structural domain (the design space) into an array of nodal positions and linking all connections using truss members. Once the structure is loaded the members that are under-loaded are eliminated by varying the density to zero from the domain leaving an efficient structure for a given loading condition.

and a glimpse into the algorithmsthereafter a discussion

in order to conduct optimisation on a given structure via a numerical method such as finite element, the numerical solver

an optimisation method would have to be selected method would still need to be combined with an algorithm.

developed into an alternative method for.helped numerical methods of topology optimisation reach its current stage of practicability.

The recent progress made in fields of structural optimisation, by scientist such as Bendsoe9, Xie 10, has caused the surge in research efforts back to the fundamentals of structural mechanics which in effect have helped numerical methods of topology optimisation reach its current stage of practicability.

Although analytical methods served as useful and powerful tools for structural optimization in the early days, they could not handle most optimization problems of real structures as it was impossible to formulate and represent those complex geometries of structures as well as complex loading and boundary conditions. Fortunately enough, in the late 50s and early 60s the booming numerical search techniques and high speed electronic computers made numerical methods ideal alternatives for structural analysis and optimization. Particularly the finite element method, which will be reviewed in Section 2.3, became dominant.

and maximising / minimising of the objective function yielding and efficient design.

, a minimum compliance topology optimisation of a wing box rib for a given set of constraints, MOA would consider say the averaged minimum compliance topology optimisation of a wing box ribSingle Objective

Multi-Disciplinary Optimisation

10.16. ConclusionBased on the findings of the reviewed literature, the importance of topology optimisation can clearly be seen in its versatility. It is seen from the literature review that there are numerous variations to the setup of the topology optimisation problem. As a result of the continued research efforts in the topic, the boundary of topology optimisation is continually being broadened. This is no surprise as initial principles of structural optimisation were introduced a century ago. With applications ranging from biomechanical to aerospace and beyond, the versatility of topology optimisation makes it a powerful tool that can be used within any structurally application. Based on the research conducted, an understanding of the problem classification has been achieved which will assist the author generate a problem formulation for the topology optimisation of a wing box rib. This will be elaborated on further in subsequent chapters.

11. General optimisation theory and applicationsComment by me10stw: See m5Also An intro to Structural Opt12. An explanation of the of the structural optimisation process.13. Arrive at conclusion that structural optimization is to determine design variables within a design space in a precise and logical fashion so that the objective function(s) will be minimised (maximised).14. 15. Given Structure / Specifications / Design Space16. 2.1 Finite Element Discretization17. The general concept of topology optimization is to determine optimal placement of a given material in space. In other words, the goal is to determine which points x should be filled with material and which points should be voids. The design parameter x is continuous in space. However, to consider the true continuous problem is not very practical and it is convenient to discretize the problem using the finite element method, both in terms of the geometry and in terms of the design parameter. When applying finite element discretization on the design domain, we can think of the geometrical representation as pixels of black and white representing solid and void areas where the discretized design vector (rho symbol) turns pixels on or off. Given a design domain (sigma symbol) of finite elements, we thus seek to find an optimal subset (sigma symbol)mat of elements that should be filled with material, i.e. the elements e (capital epsilon symbol) (sigma symbol)mat for which _e should be 1.18.

19. Problem Formulation20. Once the structural domain, also known as the design space, has been created and converted to an array of 21. Immediately after the definition of the type of structure required and the establishment of specifications, the optimization problem needs to be formulated. This includes the definition of the design variables, the variation of constraints, the adoption of the objective function, and thus the standard formulation of the optimization problem.22. There are three classes of problem formulations. The first class of structural optimization is sizing problems. These consist of 23. Design Variables24. Design variables are not preassigned quantities of a structural system and will vary with the optimization algorithm. According to Kirsch [41], they may represent the mechanical or physical properties of the material, the topology of the structure, the geometry or configuration of the structure, the cross-sectional dimensions or the member sizes.25. 26. Objective function27. 28. 29. 2.5.1 Objective Functions30. Volume31. The volume objective, measured in [m3], is linearly dependent on (rho symbol):32. 33. and has the following derivative with respect to the design parameters _e:34. 35. where is the base volume of each element.36. Compliance37. The compliance is a way to describe the stiffness of a structure with respect to a specific load case: the stiffer the structure is, the lower the compliance is. It is a scalar measure and is here formulated as:38. 39. where is the element sti_ness matrix in local coordinate system with unit Young's modulus (E = 1 [-]). The derivative of the compliance is:40. 41. 42. The element displacement in local coordinate system,, is found solving the global displacements where is the global load vector, and then transforming the relevant partition of u into local coordinates. The stiffness matrix is found as43. 44. 45. 46. 47. 48. 49. 50. 2.2.2.4 Formulations for evaluating the objective function51. Formulations for evaluating the objective function aim to minimize, maximize, or minimize the maximum of a speci_ed design response. The latter is not as intuitive as the two _rst, and is elaborated below for clari_cation. The _minimizing the maximum_-formulation is often referred to as the Min-Max-formulation, or the Bound formulation. It is so far the most widely implemented formulation in commercial software aimed at handling multiple load cases. The formulation was proposed as a less time consuming alternative to creating Pareto frontiers and automatically selecting the appropriate optimum [20, 21]. The formulation inserts an objective _ which acts as a new objective, simultaneously acting as an upper bound on all other objectives, treating the original objectives as constraints. The problem can be expressed as: 52. 53. 54. 55. 56. 57. Figure 2.12 demonstrates the di_erence in optimal designs when using the MinMax-formulation instead of merely minimizing the strain energy.58. 59. Constraints and Standard formulation60. 61. Optimisation Methods62. 2.2.2.1 SIMP-model63. The Solid Isotropic Microstructure with Penalization (SIMP)-model, also known as the penalized, proportional stiness model, is a gradient-based model [17] expressed in mathematical terms as presented in equation 2.5. The method is widely used, and one out of two possible algorithms for use with Abaqus ATOM.64. Gradient (local) optimisation approach :65. 66. 67. The algorithm interpolates between extreme values as shown in equation 2.4. Choosing the value p > 1 makes intermediate densities unfavourable because the Stiffness Volume ratio will decrease. Values of p exceeding 3 is assumed to perform well for both 2D and 3D-structures, as discussed in [7].68. The workflow of the SIMP-algorithm can be seen in figure 2.7, following the description in [17].69. SIMP usually starts with a uniform distribution of densities in the elements of the design domain and a volume fraction equal to the one specified. The first step in the iterative analysis is solving the equilibrium equations, followed by a sensitivity analysis calculating the derivatives of the design variables (ref. the element densities). Simulation settings provide the possibility to limit the magnitude of the density updates. To ensure numerical stability, filtering techniques are applied before the densities are updated using the minimum compliance criteria, followed by a new finite element analysis. This procedure is repeated until convergence has been reached, as described in figure 2.7. Further discussion on numerical stability is discussed below.70. 2.2.2.2 RAMP-model71. As the second out of two possible interpolation algorithms in Abaqus ATOM, the Rational Approximations of Material Properties (RAMP)-model is briefly presented to enlighten the use or possible misuse of the algorithm. The RAMP method as first presented in [18], was formulated to solve the problem of design dependent loads, like pressure loads from wind, water, snow, etc. As element density is updated, the initial surface properties of the design are no longer valid, and loads are no longer unambiguous. As an alternative approach to the initial formulation, a mixed displacement-pressure formulation can be used, defining the void phase to be an incompressible hydrostatic fluid transferring pressure loads without further parameterization of the surface [19], as shown in figure 2.9.72. Figure 2.10 is included to show the possible error of choosing the RAMP- model when performing topology optimization without the use of pressure loads. If not specified, the solver will use the default algorithm, normally the SIMP algorithm.73. 74. 75.

76.

77. 78. Explain the structural optimisation process79. 80. 81. One can roughly separate topology optimization into two approaches; the Material- or Microapproach vs. the Geometrical or Macro-approach, whereas the last approach is the most used in commercial software today [7]. The inherent differences between the two approaches will be clarified at a later stage in the thesis. Theory also separates between gradient-based and non-gradient-based algorithms, whereas the difference will be explained later. Keep in mind that combinations of both approaches and algorithms exist. Topology optimization can roughly be divided into treatment of two different types of domains; continuum and discrete structures. Discrete structures often refer to larger constructions like bridges, cranes and other truss structures, while continuum structures often refer to smaller, single piece parts and components. As already mentioned in section 1.3, continuum structures are of main interest in this thesis.82. When performing optimization, one must also distinguish between the number of objectives. If there is one objective, or the objective consists of a weighted average of objectives, the process is referred to as a Single Objective Analysis (SOA). If there is more than one objective, the process is said to be a Multi- Disciplinary Optimization (MDO) or a Multi- Objective Analysis (MOA).83. Project Description / Mission84. The aim of this project is to design a wing box rib to withstand locally applied compressive rib loads. Starting from a baseline and using the concepts of topology optimisation to minimise volume and elastic compliance in each load case to be lower that of a baseline design, consequently generating a more efficient design.85. The design would cater for both the global wing bending/twist loads and the locally applied rib compression loads.86. The global finite element model should be loaded by a combination of critical flight loads.87. Stochastic (global) optimisation method :

88. Methodology88.1. IntroductionThis report provides an accurate approach to the design of a wing box rib via the concepts of topology optimisation with the objective of minimising volume and compliance. The methodology will therefore provide a general description of the steps taken by the author, from initial aircraft selection through to final linear static analysis, to validate the optimisation results, see [X results]. In doing this report aims to provide a standardised approach to the efficient design of structural wing components, specifically a wing box rib.The methodology is simplified into four key sections that portray the critical phases that the project can be simplified into; CADGeometry Design Consideration of aircraft for optimisation study Exploration of wing structure Wing airfoil optimisation Airfoil exploration and generation of idealised wing structure on Aerodynamic StudyCFD Linear Static AnalysisSet up of model geometry Creating an accurate mesh for simulation Set up of simulation boundary Conditions, reference values and monitors Numerical results and validation FEA Importing model geometry Assign material properties to the geometry Create mesh Assign element properties Assign loads and boundary conditions Set up of linear static analysis Results Topology optimisation Importing model geometry Assign material properties to the geometry Create mesh Assign element properties Assign loads and boundary conditions Set up of optimisation Results and validation

88.2. Description of Software

89. Geometry Design89.1. as well as this in most cases it is also used to store fuelAs a result of the lift produced the wing experiences aerodynamic loading that can be summarised into three major forces; Bending, Shear, Torsion That being said the optimisation problem is idealised as a 2D airfoil to simplify the solution

89.2. Aircraft SpecificationAs aircraft traffic becomes greater so too does the demand for the reduction in aircraft noise caused by the engine and airframe. As stated via Breguet Range Equation the [X introduction] the fuel consumption of an aircraft is inversely proportional to the weight of the vehicle. In other words the higher the aircraft weight, the more engine power required which means more fuel burn and in effect more engine noise.Ref [(Review 2009)X-Caa.co.uk/docs/33/200903.pdf] states that already operating in the US, Very Light Jets (VLJs) will likely expand to the UK and Europe. EUROCONTROL predict the number of VLJs operating in European airspace per day will rise by 300 aircraft each year in the period 2008-2015. Proven relatively more efficient, it would seem that VLJs are destined to become the more popular mode of air transport.As stated in section 1.3[X Project description], the goal of this project is to design a wing box rib to withstand locally applied compressive rib loads. Within reason this infers that, considering the optimised wing box rib provides stiffness and weight values lower than that of the original design, the choice in aircraft type is irrelevant. That being said, given the recent efforts in topology optimisation of passenger jet structural components, see (MSC 2007)_ the aircraft type selected for an optimisation study is the Very Light Jet (VLJ).It is proposed that by applying the concepts of topology optimisation to the efficient design of the wing box rib of a VLJ, the final design achieved will result in not only less fuel burn, less emissions and better range but also less overall noise.Therefore the Cessna Citation Mustang (CCM) is selected as the subject of the wing box rib design study. The CCM wing utilises a NACA 23014 airfoil at the root and a NACA 23012 airfoil at the tip. Therefore the specific aircraft to be studied for the efficient design of its wing box rib is the Cessna 510 Mustang.Insert Pic here.89.3. Wing StructureThe wing of an aircraft has the main tasks of providing majority of the lift for the aircraft. In order to do this, characteristics such as span, taper ratio, airfoil camber etc. have to be manipulated to cope with the desired speeds, weight and aerodynamic loading of a given aircraft. Within (Niu 1999) it is mentioned that as result of the air pressures and inertia loadings the loads acting on a wing, design loads can essentially be broken down to shears, torsion and bending moments. Niu also states the central part of the wing bounded by the front and rear spars, takes the wing loads from the nose and rear sections and carries them to the fuselage, together with its own loads. This structural configuration is referring to the wing box. Also known as the torque box, its structural components consist of the spars, ribs and stringers. 89.3.1. based on the selected aircraft, 89.3.2. 89.3.3. the following sections provide details of the geometrical specification of the aircraft.89.3.4. Wing details Name the airfoil and specify the wing geometries as a whole89.3.5. Wing DesignThe objective of the study is to design a rib to withstand locally applied compressive rib loads, specifically a wing box rib. Within the paper (Krog et al. 2004), Lars Krog lists the functional requirements for a wing box rib as: Maintain the sectional shape of a wing box Function as panel breakers for skin/stringer compression panels Provide support for attachment of fuel systems Provide support for attachment of flap-tracks and pylons Function as physical fuel tank boundaries Distribute locally applied air pressure loads Support locally applied loads, like those from pylon attachment, Landing gear and flap tracksThis would suggest that the crucial structural requirement for a wing box rib would be to maintain stiffness both in compression and tension. Topology optimisation is a process that is conducted in the early stages of a design to help gain a better understanding of the precise structural layout that would result in a significant enhancement of a desired characteristic. Applied to the objective of designing rib, the precise material layout would result in significant improvements in the load carrying ability of the structure as well as massive weight savings.In this study topology optimisation is used as intended i.e. as a tool within the initial stages of a design to study the precise configuration of material within a wing box rib that would result in significant improvements in both the weight and stiffness of the structure. Therefore for optimisation, a general design is considered against specific loads from with detailed sizing being performed thereafter.To enable the study of the wing box rib of a CCM, the wing was idealised as a series of 2D airfoil sections. That being said to enable the study of a CCM wing (Cessna Citation Mustang), the NACA airfoil was idealised as an entire of the wing cross section.The root and tip airfoil geometry, sourced from UIUC Airfoil Coordinates Database, were modelled using commercially available CAD software Siemens NX before exporting geometry to both FEA and CFD software for analyses.A design of the selected aircraft initially is modelled on before exporting geometry to both FEA and CFD software for analyses. The following sections provide details of the structural configuration and geometrical specification of the aircraft.

AirfoilNACA 23014 - 23012

Wing Span, b/2 [m]5

Thickness to Chord Ratio0.12

Taper Ratio, 0.5

Planform Area, S [m2]5.625

Aspect Ratio, A17.7

Chord Length, croot [m]1.5

Chord Length, ctip [m]0.75

Figure 4 Cessna Citation Mustang Idealised Wing Bay

Table 1 Wing geometrical specification

The airfoil cross section was then partitioned and surfaced to idealise the internal structures of the wing i.e. spar and rib structure. See fig X

Figure 5 NACA 23014 geometrical points89.3.6. 89.3.7. / Justificationsas the complete internal structure of the wing with partitions being made to signify 89.3.8. Topology optimisation is a tool that is used in the early stages of a design to provide 89.3.9. powerful tool that is used in the early stages of a design to potentially reduce its structural weight and thus provide significant improvements elsewhere. 89.3.10. 89.3.11. SpecificationWithin (Niu 1999) it is stated a generic guideline is given to the location of the spars of a wing within the wing box structure. It is stated that in general the front spar is located at around 15% of the chord whereas the rear spar is located at between 55% - 60%. This information was modified for the current study due to the 3 spar wing configuration of the CCM. The end result was a front spar located at 15% of the chord, a middle spar located at 36% of the chord and a rear spar located at 75% of the chord. The thought process behind this was that as Niu stated, generally the front spar is located at around 15% of the chord, this was maintained. The rear spar was moved back from 55-60% to 75% of the chord, this was done in an effort to cope with the loads from the control surfaces. This leaves the mid spar to be placed at the maximum chord thickness location, i.e. 35% of the chord.Niu also states that wing rib locations are based on the locations of the aileron and flap hinges. Furthermore, rib spacing is influenced by panel size considerations. These specifications complicated the study without assisting to achieve its objective. To simplify the study, these specifications were not implemented.

As the CCM wing design utilises 3 spars rather than the generic 2 spars, the advice from Niu is heeded but modified In general, the front spar is located at about 15% chord, the rear spar at 55 to 60%" (Page 251). I was going to simply assume that a three spar wing would have a comparable layout but with a mid spar located halfway between the front and rear.Materials

Wing StructureRibs

MaterialAluminium 7075-T651

Elastic Modulus (N/m2)7.169E+10

Poisson Ratio0.33

Shear Modulus (N/m2)2.69E+10

Density (kg/m3)2810k

The CCM Specification & Descriptions states that the wing structure is constructed of three monolithic spars, each machined from a single piece of aluminium alloy. As the material spec is not provided, typical aluminium alloy specs for the spar and ribs were selected instead.Wing StructureSpar

MaterialAluminium 2024-T4

Elastic Modulus (N/m2)7.31E+10

Poisson Ratio0.33

Shear Modulus (N/m2)2.8E+10

Density (kg/m3)2780

Table 2 Cessna Citation Mustang wing spar material propertiesTable 3 Cessna Citation Mustang wing spar material properties

The wing of the Cessna Citation Mustang utilises a NACA 23014 airfoil at the root and a NACA23012 airfoil at the tip.FurthermoreUsing Kirchoffs plate theory we can assume that the planar loads of a wing box are more significant than the lateral loads

Applying this to the wing of the Cessna Citation Mustang, this was initially idealised as airfoil s

design the wing ofSHOW A GENERAL WING INTERNAL STRUCTURE AND ALSO SHOW YOUR ARFOIL INTERNAL STRUCTURE, GIVING DIMENSIONS AND MATERIAL PROPERTIES

89.4. 89.5. 89.6. Mission ProfileThe objective of the study is to design a rib to withstand locally applied compressive rib loads; as justified above, the specific aircraft selected for this is the Cessna Citation Mustang. It is essential that the design cater for the global wing bending and twist loads as well as the locally applied rib compression loads. To do this a mission cases of a VLJ were studied and it was found that typical missions profiles of VLJs consists of; Engines start & warm up, Take-off Climb, Cruise, Descend, Loiter, Land. Of these cases the most critical flight case with regards to wing loading was found to be either take-off or landing. By designing the rib to withstand the loads from the critical case and an envelope is built that will ensure the safety of the structure under all other loads.Within (Peery 2011) states that one of four flight conditions will produce the highest stress in an airplane, i.e. positive high angle of attack (PHAA), positive low angle of attack (PLAA), negative high angle of attack (NHAA) and negative low angle of attack (NLAA). He summarises that one of these conditions will be critical for the design of almost every part of the airplane. Figure 6 Critical conditions for a wing box structure (Courtesy of (Niu n.d.))When analysing the current study and comparing it to Peerys findings we can see that, based on the typical flight mission of a typical VLJ, either the take-off or landing phases of the flight would have to be assessed to ensure the structurally efficient design of a wing box rib.Thus take-off phase can be selected as the critical flight case to be studied and the loads used as the foundation of the analysis conducted.89.6.1. Perhaps create this on excel89.6.2. 89.6.3. Flight Case

Rather than investigating

The typical mission profile of a very light jet consists of; Engines start & warm up, Take-off Climb, Cruise, Descend, Loiter, Land. to do this the applied loads that the ribs are designed to would have to be the most severe

The highest lift producing cases from these would translate to From these cases it is clear that critical flight cases from these with regards to wing loading would be either the take-off or landing case. This

Therefore in an effort to improve the efficiency of the aircraft through the topology optimisation of the wing box rib, the most critical flight case with regards to wing loading was The.

Angle of AttackVelocityAltitude

10o213mph i.e. 95m/sSea Level

The following parameters define the typical flight conditions of a CCM during take-off at sea-level; these were used in the simulations conducted.Table 4 Take-off flight case conditions

90. 91. 92. 93. 94. 95. 96. Figure 2.3 shows a sketch of the aerial refuelling mission profile of the KC-X. Firstly taxi on the run way and take off then ascent to cruise altitude 40,000 feet. The KC-X will refuel other aircraft at 40,000 feet then return fly back to the base. When approach the base, the KC-X will do loiter for one hour and then do descent and landing.97. 98. Figure 2.4 shows the sketch of both cargo transfer mission and medical evacuation mission. Taxi one the runway then take-off climb to 40,000 feet. One hour loiter before landing and then do descent and landing.99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. The objective of this project is to design a new military fuel transport aircraft for the United State Air Force. According to the request, the USAF aims to replace its current aerial refuelling fleet which consists of Boeing KC-135Rs. Better range and payload requirement is necessary for the new aircraft. Three different tasks competency is also required which are aerial refuelling, cargo transfer and medical evacuation. A typical mission for the new aircraft can take off from Guam carrying military personnel to South Korea, transfer military supplies from Guam to South Korea, or take off from Okinawa to prepare for an aerial refuelling mission near North Korean airspace.110. Mission Specification & Mission Profile111. As determined by the USAF, the mission requirement numbers are concerned:112. Passengers: 150 (125 Patients to 25 Medical Personnel; 5:1 ratio)113. Cargo: 18 x 464L Pallets (5,000 lbs/each)114. Crew: 3: Pilot, co-pilot, boom operator115. Fuel Capacity: 150,000 lbs116. Range: 1,500 nmi for aerial refuleing mission117. 1,800 nmi for cargo transfer and medical evacution missions118. Cruising Altitude: 40,000 ft119. Cruise Speed: 612.7mph (M=0.83)120. Figure 2.3 shows a sketch of the aerial refueling mission profile of the KC-X. Firstly taxi on the run way and take off then ascent to cruise altitude 40,000 feet. The KC-X will refuel other aircraft at 40,000 feet then return fly back to the base. When approach the base, the KC-X will do loiter for one hour and then do descent and landing.121. 122. Figure 2.4 shows the sketch of both cargo transfer mission and medical evacuation mission. Taxi one the runway then take-off climb to 40,000 feet. One hour loiter before landing and then do descent and landing.123. 124. Critical Mission Requirements125. The KC-X has two critical mission requirements. The first is large cargo capacity. The U.S. government is planning to move marine troop from Okinawa to Guam in 2014. Large cargo capacity could assist transport large quantities of supplies. The second is the reduction in noise during take-off and landing. Okinawa and Guam are both popular sightseeing place. Noise could affect local residents and vibrations could damage local landscape.126. Comparative Study127. This section will compare different refueling aircraft designs. Currently, there are four different refueling jet powered aircrafts service around the world. They are KC-135R, KC-767, KC-30 and KC-10. The KC-135R is the current fleet for the USAF. Figure 2.5 to figure 2.8 shows these four aircrafts. Table 2.1 express specifications of these four aircraft.128. 129. Wing Structure130.

131. Geometry 132. Airfoil Design133. 134.

135. For everything ask why? How? What? Relate and where? DONT WASTE TIME!!!!! ANSWER AS MUCH AS POSSIBLE AND MOVE ON!!!!! MOT WORD COUNT! CONTENT!!!! HAVE ALL THE QUESTIONS BEEN ANSWERED?? NO!!!!!REANSWER LATER136. BULLET POINT 137. Aerodynamic Analysis137.1. IntroductionThe necessity for speedier and more exact routines for the estimations of fluid flow around bodies and specifically regions of interest has been the primary driver behind the quick advancement of CFD (Computational Fluid Dynamics). In the past decade, within industries where fluid interaction plays a major role, the use of CFD packages has been the obvious decision. Within the subject of fluid dynamics, there are numerous business CFD bundles accessible for demonstrating flow in or around bodies. The PC recreations show characteristics and points of interest that are challenging, costly or difficult to measure or recreate tentatively.The CFD software used in this study uses Reynolds average Navier-Stokes equations. To define RANS we should iterate that fluctuations and unsteadiness are inherent to turbulent flows, i.e. the velocity fluctuations take place in all directions and have and infinite number of scales (degrees of freedom). RANS operates under the principle that any property can be expressed as the sum of its average, and fluctuation values, = +^' this is known as Reynolds decomposition. The outcome of implementing Reynolds decomposition in the Navier-Stokes equations is known as RANS and it yields a set of governing equations for average flow fields, thus the values for any property are constant over time.For the current study the Navier-Stokes equations can be expressed as;

Within which the inviscid flux vectors (G1, G2 and G3), are mathematically represented through the equation below within which u1, u2 and u3 represents the velocity, whereas represents the density and p represents the pressure of the fluid.(H. C et al. 2013)

For the viscous flux vectors (G1,V, G2,v, and G3,v) these are represented by the equation below within which, yy and zz represent the normal stresses.

Within (Dippold 2005) Vance Dippold conducted a study to investigate the performance of various turbulence models and wall functions within the WIND flow solver. Dippold made a comparison of the performance of Chiens K- against Mentors SST solvers in simulating incompressible flow on three differing geometries. Dippold reasoned that in the vicinity of neutral or favourable pressure gradients, both turbulence models performed adequately well however, Dippold stated that in the presence of adverse pressure gradients, the SST clearly produced more accurate results.Within Ref (S 2010), we see that Using CFD S. Sarada et al. attempted to acquire an approved philosophy to gauge the aerodynamic coefficient values for the aforementioned subsonic airfoil. Comparing 2D to 3D airfoils, the study made a notable conclusion that although for 3D simulations using K- yielded accurate results in the stalling region, the 2D results in the stalling region were unreliable. It is with this information that the Spalart-Allamaras model was selected to simulate the turbulence flow around the airfoil for the current study.By dividing or discretising the system up into small simple bodies or elements of a finite volume and given that each finite quantity can be converted to an algebraic equation, by reconnecting the bodies together through common nodal points, an approximate system of equations for the model can be obtained and solved numerically using the fundamentals of conservation of mass and momentum. Having said that the higher the quality of the mesh, the higher the accuracy of the results and as such, the following adaptions we utilised to add resolution.

(understand the problem and identify the key modelling objectives)(once the geometry is obtained, the discretization of the model to small elements and nodes is conducted)When Navier-Stokes equations are coupled together with the continuity equation and accurate proper boundary conditions, the effect is a complete series of comparisons that could be utilized to compute a flow. This phase of the overall study will use these models to study external 2D turbulent incompressible flow around an airfoil with the configuration shown below.

FluidAir

Density ()1.225 (kg/m3)

Viscosity ()1.7894 (kg/ms)

Velocity (U)95 (m/s)

H1150 (m)

R1150 (m)

l11.5 (m)

Table 5 CFD boundary conditions

Figure 7 C-Mesh geometry around NACA 23014

reasoned that both turbulence models were found to work well in the vicinity of an unbiased or favourable weight angle; however the X2 plainly performed better when an unfavourable weight slope was available.

The following chapters discusses the details of the problem being studied, geometry and mesh generating, solver setup and results.137.2. 137.3. 137.4. 137.5. 137.6. IntroductionProblem StudyWhy do CFD?Computational Fluid dynamics was essentially used to study the airflow around the airfoil at take-off case and predict the in-flight aerodynamic loads that the airfoil experiences. What aerodynamic loads?For the current case the loads acting on an airfoil can be summarised into three major components; Lift This is the component of the resultant aerodynamic load to acting perpendicular to the airflow around the airfoil Drag This is the component of the resultant aerodynamic load to acting parallel to the airflow around the airfoil Moment This is a rotational effect on the airfoil as a result of the net lift and drag loads. (This is measured about the aerodynamic centre, for all thin airfoil shapes this at quarter the quarter chord i.e. 25% of the chord distance from the leading edge)For a 2D wing section the coefficients of these forces can be surmised as;

How do you go about studying the airflow around the airfoil?To study the airflow we must first become cognizant of the type of flow regime that we are dealing with. We can do this my examining the conditions of the flight case being studied and making some assumptions based on those conditions.137.7. Flow ClassificationThe following parameters describe the case being studied;Flight Case: Take offAirfoil: NACA 23014(Mod)Angle of Attack: 10oVelocity: 213mphAltitude: Sea Level TALK ABOUT SIMPLIFICATION OF THE PROBLEM 3D TO 2DFluid flows can be classified in a variety of ways:Internal vs. external.Steady vs. unsteady.Single-phase vs. multiphase.Elliptic vs. parabolic vs. hyperbolic.Assumption 1&2137.7.1. Subsonic vs. Supersonic & Incompressible vs. CompressibleSince the flight case being studied in this case is of take-off at 213mph, i.e. 95.22m/s, at sea-level. Converting the speed to Mach using the equation 1, where V is the velocity of the aircraft and a is the local speed of sound, see equation 2, we obtain a Mach number of 0.28.

Using the density change as a function of Mach number table below we can see that for flow of Mach