Belly Landing of the LocalHawk UAV Low-Velocity Impact Simulation Using an Explicit Finite Element Solver Master’s thesis in Product Development HANS MAGNUS THORSEN Department of Product and Production Development Division of Product Development CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2013 Master’s thesis MASTER’S THESIS IN PRODUCT DEVELOPMENT Belly Landing of the LocalHawk UAV Low-Velocity Impact Simulation Using an Explicit Finite Element Solver HANS MAGNUS THORSEN Department of Product and Production Development Division of Product Development CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2013 Belly Landing of the LocalHawk UAV Low-Velocity Impact Simulation Using an Explicit Finite Element Solver HANS MAGNUS THORSEN c© HANS MAGNUS THORSEN, 2013 Department of Product and Production Development Division of Product Development Chalmers University of Technology SE-412 96 Gothenburg Sweden Telephone: +46 (0)31-772 1000 Cover: Gradual failure for ply #9 in a [90, 0, 90, 0, 90, 0, 90, 0, 90] stacking sequence with a descend velocity of 2.5 [m/s] and pitch angle of θ = 0 deg Chalmers Reproservice Gothenburg, Sweden 2013 Belly Landing of the LocalHawk UAV Low-Velocity Impact Simulation Using an Explicit Finite Element Solver Master’s thesis in Product Development HANS MAGNUS THORSEN Department of Product and Production Development Division of Product Development Chalmers University of Technology Abstract During the summer of 2012, a total of three UAV airframe concepts were developed in the LocalHawk summer student project at Kongsberg Defence Systems (KDS) in Kongsberg, Norway. All of the airframe concepts had belly landing as the preferred conceptual solution for landing the UAV. Out of those three concepts, the third was selected for further development, however, before the students of 2013 could start working on it, the feasibility of belly landing as a conceptual solution for that particular concept would have to be investigated. Four concepts for the skin and internal stiffening structure of the fuselage was developed using product development methodology. Out of those four, two were selected for detailed scrutiny. The Multiframe concept had in total nine inner frames, consisting of rigid foam, that supported the payload and batteries, and a composite skin built up by nine plies of an unbalanced woven fiberglass prepreg. Relying on a sandwich structure, five plies of the aforementioned composite material on each side of an 8 [mm] thick foam core, the Sandwich Skin concept’s structure had two larger frames supporting the payload and the batteries. An explicit Finite Element (FE) solver, Ansys AUTODYN, was applied to simulate the low-velocity impact between the 12.5 [kg] UAV’s fuselage and a rigid, smooth surface representing the ground. Several different stacking sequences were tested at a descend velocity of 2.5 [m/s] and pitch angle of 0 deg. From the stacking sequence tests, a preferred stacking sequence was selected based on its maximum stress and resistance to failure. Using this selected stacking sequence, both skin and internal stiffening structure concepts were tested at descend velocities of 1 [m/s] and 2.5 [m/s], with the pitch angle, θ, either set to 0 deg or 6 deg. For the third UAV airframe concept, all tested cases end in severe failure in every ply. Generally, the narrow bulge on the belly of the fuselage is forced inwards towards the payload, resulting in failure initiation on the inner skin surface. From this area, the material failure propagates through plies along the center-line of the belly. As the bulge continues to be forced inwards, tensional stresses on the outside of the skin, on either side of the now more-or-less flattened bulge, result in material failure. At θ = 6 deg, the bulge does not come into contact with the ground in the short duration of the analysis, however, the total weight and the narrow rear body of the UAV, i.e. little surface area in contact with the ground which results in an increased contact force, is enough to ensure material failure. These results dictate either a redesign of the UAV to include a landing gear, or a fresh start, designing a new UAV. An optional possibility is to scale down the UAV, and increase surface landing area, so that the UAV can utilize the advantages of the simplistic solution of landing on its belly. Regardless of the chosen path, a UAV weighing in total 12.5 [kg], with such a small surface area in contact with the ground during landing, is deemed unfit for belly landing. Keywords: Explicit, FEM, UAV, Belly Landing, Composite, Low-Velocity Impact i ii Preface This 30 ECTS thesis was submitted to the Department of Production and Product Development in partial fulfillment of the requirements for the degree of Master of Science (M.Sc.) in Mechanical Engineering, with a specialization in Product Development, at Chalmers University of Technology. Acknowledgements First of all I would like to state my sincere appreciation to my external supervisor at KDS, Heming Melvold Andersen, for his guidance, patience, and support, which without, I would not have been able to complete my thesis. Also deserving gratitude at KDS, is Per Olav Kristiansen for his helpful guidance throughout the project, as well as specific advice in uncertain matters. I would also like to thank EDR&Medeso for providing me with free training in Ansys Explicit STR, specifically Mikael Lauth for his very open, pedagogical, and straight-forward approach to teaching the course. He has also provided me with valuable, free, support after the completion of the course, even taking the time to go through my model to offer advice on improvement, for which I am extremely grateful. Gurit deserves recognition for them providing me with composite material data and specific advice for my case. And of course, I would like to thank my internal supervisor at Chalmers, associate professor Dr. Lars Lindkvist, for his efficient and valuable help in both the planning and writing of the thesis, as well as administrative and software issues. Lastly, Assistant Professor Dr. Martin Fagerström at Chalmers also deserves appreciation for his help in providing me with software for composite pre-processing and guidance in the application of this. iii iv Nomenclature and Abbreviations t Time [s] ∆t Time step [s] n Vertical loading factor [−] Veq Equivalent airspeed [m/s V Velocity [m/s] a Acceleration [m/s2] s Distance or stretch [m] g Gravitational constant acceleration [m/s2] ε Failure strain [m/m] C Speed of sound [m/s] P Contact force [N ] k Contact stiffness [Nm−3/2] α Indentation [m] R Radius of curvature [m] E Young’s modulus [N/m2] ν Poisson’s ratio [−] T0 Stagnation temperature [K] T Ambient temperature [K] M Mach number [−] K Global stiffness matrix [N/m] u Global nodal displacement vector [m] f Nodal force vector [N ] M Mass matrix [kg] ü Nodal acceleration vector [m/s2] C Matrix of damping coefficients [kg/s] u̇ Nodal velocity vector [m/s] τ∆t Duration of time step [s] θw Weighting parameter [−] ωmax Maximum eigenvalue of an element [Hz] Le Characteristic element dimension [m] cd Dilatational wave speed [m/s] ε Strain vector [m/m] S Compliance matrix of a laminate [m2/N ] σ Stress [N/m2] G Shear modulus [N/m2] C Material stiffness matrix [N/m2] τ Shear stress [N/m2] θ Pitch angle [deg] f Time step safety factor [−] h Characteristic length of element [m] ρ Density [kg/m3] m Mass [kg] v FEM Finite Element Method FEA Finite Element Analysis FE Finite Element UAV Unmanned Aerial Vehicle UAS Unmanned Aircraft System RPAS Remotely Piloted Aircraft System RPV Remotely Piloted Vehicle DDD Dull Dirty Dangerous SI Spark Ignition CFD Computational Fluid Dynamics GPU Graphics Processing Unit GFRP Glass-Fiber-Reinforced Polymers CFRP Carbon-Fiber-Reinforced Polymers 1D, 2D, 3D One, Two, Three-Dimensional CPU Central Processing Unit CG Center of Gravity CAD Computer Aided Design CAE Computer Aided Engineering CAM Computer Aided Manufacturing KDS Kongsberg Defence Systems FPF First-Ply Failure LPF Last-Ply Failure HVI High Velocity Impact LVI Low Velocity Impact STEP STandard for the Exchange of Product model data BC Boundary Condition PC Patch Conforming PI Patch Independent CFL Courant-Friedrichs-Lewy vi Contents Abstract i Preface iii Acknowledgements iii Nomenclature and Abbreviations v Contents vii 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.4 Unmanned Aerial Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.5 Existing LocalHawk UAV Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Literature Review 5 2.1 Fuselage Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Loading of Fuselages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Fuselage Structural Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.4 Belly Landing of an Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Low-Velocity Impact Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Low-Velocity Impact Failure Modes for Composites . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3 Contact Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 Fiber-Reinforced Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.3 Structural Composites - Laminates and Sandwich Constructions . . . . . . . . . . . . . . . . . . 11 2.3.4 Designing with Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Explicit/Implicit Transient Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.3 Selecting Software Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Method 17 3.1 Landing Parameter Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Design of Skin and Internal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.1 Concept Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.2 Computer Aided Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Material Selection and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.1 Composite Skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.2 Internal Stiffening Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4.1 Material Definition and Geometry Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4.2 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4.3 Composite Modeling using ANSYS ACP Composite PrepPost . . . . . . . . . . . . . . . . . . . . 27 3.4.4 Common Boundary Conditions and Analysis Settings . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.5 Density Modification and CG Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4.6 Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.4.7 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 vii 4 Results 33 4.1 Landing Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.1.1 Pitch (θ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.1.2 Descend Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2 Design of Skin and Internal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.1 Concept Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.2 Computer Aided Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.3 Orthotropic Constants Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.4 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4.1 Stacking Sequence Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.4.2 Pitch Angle (θ) and Descend Velocity Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5 Discussion 53 5.1 Concept Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.3 Future Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6 Conclusion 55 Appendices 61 A Explicit Analyses 63 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.2 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.2.1 Materials Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.2.2 Geometry Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.2.3 Contacts and Body Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 A.2.4 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 A.2.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 A.2.6 Analysis Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 A.3 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.3.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.3.2 Evaluating Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 B Sample Case - Explicit Analysis Walk-through 69 B.1 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 B.2 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 B.2.1 Material Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 B.2.2 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 B.2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 B.2.4 Analysis Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 B.3 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 B.3.1 Low-Velocity Impact (LVI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 B.3.2 High-Velocity Impact (HVI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 C Defining Composites in ACP (pre) 85 C.1 Creating Fabrics and Verifying Imported Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 C.2 Importing CAD Geometry for Cutoff Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 C.3 Rosettes and Oriented Element Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 C.4 Modeling Ply Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 D Orthotropic Constants Study 91 E Stacking Sequence Test Results 93 F Pitch (θ) and Descend Velocity Test Results 103 viii G Fuselage CAD Figures 109 ix x 1 Introduction This chapter aims to give the reader an introduction to the background, aim, and limitations of the thesis. In addition to this, it includes a short section about the history and modern-day application of UAVs, as well as a section summarizing the work done in the LocalHawk summer student project 2012. 1.1 Background In 2008, Kongsberg Defence Systems (KDS), department of Missile Systems, started a summer student project called LocalHawk. Initially, the purpose was to let students apply their knowledge to practical problems: making a Unmanned Aerial Vehicle (UAV) operate autonomously and be able to recognize objects. Fast forward to 2012, and the scope of the project was extended to include development and building of a UAV which was supposed to fly autonomously and be used for civil purposes, such as sporting events. During the summer of 2012, the mechanics team of the LocalHawk project developed in total three concepts for the airframe of the UAV. Estimated at total weights of 12.5 [kg], all concepts had belly landing as a conceptual solution for landing the UAV. Being limited to a short period of time, no study was conducted to establish the feasibility of belly landing as a conceptual solution. 1.2 Aim The aim of this thesis is to fulfill the need for a feasibility study of the belly landing solution, given the parameters and design developed during the summer of 2012 in Kongsberg. To achieve this, an explicit Finite Element (FE) solver will be applied to simulate the low-velocity impact of the UAV landing on a surface. A go/no-go decision to either continue with the design as it is, or to make alterations to the design to facilitate belly landing, possibly even scrapping the solution, will be the main output of this thesis. As a bi-product, the documented use of an explicit solver will provide knowledge about the process and how it differs from implicit methods. Existing design of the UAV includes only external surfaces, therefore, two concepts for skin and internal structure will be developed. Summarized, this thesis aims to answer the following questions: • Is belly landing as a conceptual solution feasible for the LocalHawk UAV? • If not, what changes could be performed to facilitate belly landing? • How does the different skin and internal structure concepts perform during belly landing? • How can an explicit solver successfully be applied to simulate the low-velocity impact of the UAV? 1.3 Limitations This study has been limited to only one of the three concepts, concept number three (see section 1.5), and the fuselage of this concept. The main reasons for this limitation were that, firstly, airframe concept #1 (see section 1.5) was deemed too conventional, and secondly, airfame concept #2 had issues with too little generated lift. Adding to these reasons, was a perceived reduced complexity of the third concept relative to the second. In addition to this limitation of one concept, development of concepts for skin and internal structure was in the end limited to not include any alterations of the basic shape of the UAV’s external fuselage surface. Other limitations include the use of a simple, rigid, and flat surface without any modeled interaction between the fuselage and the ground except for the deformation of the fuselage, i.e. no friction, and no deformation of the ground. For the composite components, perfect draping was assumed. 1 1.4 Unmanned Aerial Vehicles Unmanned Aerial Vehicle (UAV), Unmanned Aircraft System (UAS), Remotely Piloted Aircraft System (RPAS), Remotely Piloted Vehicle (RPV), and drone are all names that can be, and are being, used to describe an aircraft that operates without any on-board personnel. Choosing a simplistic path that conforms with general knowledge of these types of systems, the term Unmanned Aerial Vehicle, or rather the shortening UAV, will be used in this report. The history of UAVs goes back to the mid 19th century, two years into the American civil war, when Charles Perley registered a patent for a UAV bomber (PBS Nova 2002). Perley’s bomber consisted of a hot-air balloon that carried a basket filled with explosives attached to a timing mechanism. During the second World War, Nazi Germany’s V-1 (Vergeltungswaffe-1 English: ”Revenge weapon”-1) spread terror among the Allies with its purpose; to target non-military targets among the population of Hitler’s enemies. Though being a horrible testimony of the cruelty of man, it proved how effective UAVs could be used in combat. From the American civil war, UAVs have evolved to become highly complex systems with a wide array of application areas. Although many associate modern UAVs with headlines such as ”Pakistan Says U.S. Drone Kills 13”, (Shah 2009), and ”Precisely Wrong: Gaza Civilians Killed by Israeli Drone-Launched Missiles”, (HRW 2009), UAVs are currently being used in a wide variety of civil applications such as: • Oil, gas, and mineral exploration activities (Barnard 2010) • Climate research (NASA Dryden Flight Research Center 2013) • Art/Construction(Guizzo 2011) • Search and rescue (Austin 2010) • Wildlife conservation (BBC News 2012) • Fire detection (Austin 2010) • Road traffic control (Austin 2010) From the list above, it is possible to conclude that civil applications plays a major role in the presence, and future, of UAVs. An interesting notion was brought forth by The Economist, a weekly news and international affairs publication (Wikipedia 2013), in the article published November 2012 which presented the possibility of unmanned civilian passenger flights being commercialized before autonomous cars (The Economist 2012). The purpose of producing and operating UAVs as opposed to manned aircraft have been discussed for a long time (Austin 2010). Generally, UAVs have been developed for roles which are dull, dirty, and dangerous (DDD), but Austin (2010) argues that covert, diplomatic, research, and environmentally critical roles should be added to the list. Some examples of DDD applications (Austin 2010): • Surveillance, either civilian (e.g. livestock) or military, over a long time can be dull, handing the task over to UAVs could allow personnel to focus on other tasks. • Operating manned aircraft in dirty environments, for instance areas contaminated by radioactive spillage/waste, places the operating personnel in harms way. By possibly increasing safety for humans, the application of UAVs in dirty environments have obvious advantages over manned flights. • Dangerous: could refer to either defense operations in areas where the aircraft might be attacked by hostile forces, or inspection of power lines and forest fires. As for applications in dirty environments, UAVs represents an increase in safety for personnel which have obvious advantages over manned flight. 2 1.5 Existing LocalHawk UAV Design This section summarizes the work done by the Mechanics team the summer of 2012 in the LocalHawk student project at KDS. The aim of this section is to provide insight into the development process and understanding of why concept three looks the way it does. Most of the information presented in this section is based on the author’s own experience during the 2012 LocalHawk student project. The major requirements, put forth by the project owner, which affected the Mechanics team were the minimum payload carrying capacity, desired flight time, operating conditions, and the decision that the UAV should be able to fit in a 0.7x0.7x1.5m crate when disassembled. A minimum payload carrying capacity of 2.5kg, excluding fuel/batteries and motor, meant that the resulting UAV design would be of a considerable size (relative to small hand-launched concepts carrying a payload of less than 0.5kg). One of the earliest decisions made, was to focus on developing a UAV propelled by an electric engine instead of a spark-ignition (SI) engine running on liquid fuel. This decision highly simplified design work as the designers would not have to worry about reduction in mass during flight, or designing fuel tanks that corresponded with safety regulations for highly flammable liquids. The concept development work consisted of applying Product Development methodology. Starting with a requirement specification for the UAV airframe, the requirements stated by the project owner were developed further and supplemented with requirements from other LocalHawk-internal teams (Cybernetics, Electronics, etc.), legal restrictions, other stakeholders at KDS, and tips given by experienced radio controlled aircraft builders. Based on the requirements specification, a Morphological matrix was used for both idea generation (with the focus on each function individually) and concept synthesis (with the focus being on the overall value of the concept when combining function solutions) as proposed by Almefelt (2011). Several ideas were proposed, resulting in seven concepts. A coarse selection process was completed using a Systematic selection chart as proposed by Pahl, Beitz, Feldhusen & Grote (2007). The coarse selection shortened the total number of concepts to four. These remaining concepts were put through a finer selection, specifically, the evaluation matrix proposed by Pugh (1990), which resulted in two remaining concepts. Work then proceeded to sizing of the concepts by using the conceptual design methodology for aircraft proposed by Raymer (2012). When the sizing process was completed, focus shifted to designing the concepts in Catia V5. The CAD work comprised the bulk of the effort done during the summer of 2012. With two remaining concepts after the concept selection, each designer worked on his/her own concept. Aiding the CAD work, Computational Fluid Dynamics (CFD) analyses, performed by the supervisor of the mechanics team, helped in refining the shape of the airframes. Nearing completion of the 2012 part-project, the two concepts were presented to the stakeholders. A desire of more radical designs was put forth. Heeding this desire, as well as a need for more lift (wing area), the designers developed concept three using the second concept as a reference. In Figure 1.1, the third concept can be seen, while in Figure 1.2 a side cut-view of the fuselage can be seen with the placement of the internal components. Figure 1.1: Rendering of the third LocalHawk airframe concept 3 Figure 1.2: Cut-view of the third LocalHawk airframe concept showing the position of the internal components A major cause of uncertainty during the entire design process was the size of the payload components. The Image-processing team responsible for the choice of on-board camera and Graphics Processing Unit (GPU) board, had a hard time specifying the dimensions of the GPU board as it had not yet been released to the market. An overly-pessimistic estimation was performed, which resulted in the fuselage designs being bulky and taking up much of the reference area for the wings. In turn, this meant that, with the size restrictions of the carrying crate, the UAV design concepts would not fly with an estimated total weight of 12.5kg. Modifications were performed, and late information from the GPU board manufacturer considerably reduced the size estimate, so that the fuselage designs could be narrowed and more stream-lined. 4 2 Literature Review This chapter contains the theoretic background that will provide a foundation for the rest of the thesis work. The aim is to give the reader an introduction to necessary theory in such a way that he/she is able to understand and interpret the selected methods, and obtained results. 2.1 Fuselage Structures In this section, an introduction to some of the important characteristics of aircraft fuselages is presented. General loading of fuselages is included to provide the reader with a picture of what a fuselage is subjected to during its flight cycle. Continuing, section 2.1.3 contains standard solutions of fuselage structural components designed to accommodate the previously described loads. 2.1.1 Introduction Firstly, a distinction between the term ”airframe” and the term ”fuselage” needs to be done: According to the Merriam-Webster online dictionary, an airframe is defined as: ”the structure of an aircraft, rocket vehicle, or missile without the power plant” (Merriam-Webster 2013a). While fuselage is defined as: ”the central body portion of an aircraft designed to accommodate the crew and the passengers or cargo” (Merriam-Webster 2013b). In other words, the fuselage is part of the airframe and refers only to the central body of the aircraft. As stated by the Merriam-Webster dictionary definition of fuselages, the main task of the fuselage is to carry the payload of the aircraft. Megson (2010) adds that the basic functions of an airframe are to transmit and resist the applied loads, to provide an aerodynamic shape, and to protect onboard passengers, systems, as well as other payload against environmental conditions. 2.1.2 Loading of Fuselages Franklin (2010) divides the loads experienced by aircraft into two categories; external loads and internal loads. External loads include aerodynamic and inertia loads, while internal loads refer to loads distributed within the airframe, carried by the structural components. While the wing sections of the airframe are subjected to elevated aerodynamic forces from the pressure distribution generating lift, the aerodynamic loading on the fuselage is relatively low (Megson 2010). The dominating internal loading of the fuselage is the concentrated loads originating from the supports of wings, tail, and undercarriage. Adding to these loads is the external inertia loads stemming from the mass of the airframe, power plant, and payload. The general aerodynamic and inertial loading of an airframe during flight can be presented using a V-n diagram, describing the flight envelope of the aircraft. A V-n diagram gives the maximum design, positive and negative, vertical load factor, commonly referred to as g-forces, as well as the maximum velocity and stall lines of the aircraft (Franklin 2010). An example V-n diagram is shown in Figure 2.1. 5 Figure 2.1: Example V-n diagram Inertial loads are described using Newton’s second law (F = ma), and originates from various maneuvers and external accelerations such as gusts (Raymer 2012). According to Raymer (2012), the critical loads for the fuselage of a L1011 transport aircraft is maneuvering (positive, negative, yaw, and lateral) as well as braking and gusts (positive dynamic and lateral). These loads are all by definition inertial loads (originating due to an acceleration), and the load severity is assumed to be transferable to a subsonic UAV. Most likely, without a landing gear, whose objective it is to reduce the landing load to an acceptable level (Raymer 2012), the landing-impact load could be added to this list. Impact theory is treated in detail in section 2.2. 2.1.3 Fuselage Structural Components The overall purpose of the structural components of a fuselage is to provide load paths which connect opposing forces (Raymer 2012). Although they all aim to meet the same end goal, several different solutions have been developed to best resist the applied loads, and are now standard structural components. The loads presented above result in bending, torsion, and shear, all of which the structural components must be designed for. Presented in Figure 2.2 are the most common solutions for providing resistance towards bending (Raymer 2012). Figure 2.2: Common structural components. Left: Stringers, mid: Keelson, right: Longerons. Inspired by Raymer (2012). Being a relatively large, solid beam, the keelson provides a great deal of longitudinal stiffness and prevents bending in the lower part of the fuselage (Raymer 2012). Longerons fulfil the same purpose as the keelson, providing bending resistance, but are used either in combination with a keelson (Raymer 2012), or without any supplementary elements (Franklin 2010). According to Raymer (2012), longerons are used in fuselages that are subjected to highly concentrated loads and which have relatively many cutouts (ex: fighter jets). Stringers on the other hand, are used in fuselages that have relatively few cutouts and concentrated loads (ex: transport aircraft). By applying stringers instead of longerons, it is possible to increase the spacing between the frames (Franklin 2010). The stringers and longerons are placed around the circumference of the fuselage as can be seen from Figure 2.2. Common for all of the longitudinal stiffening elements are the design goal of keeping them as straight as possible to reduce weight (Raymer 2012). 6 An alternative solution to the longerons, keelson, and stringers, is the sandwich-skin approach (Franklin 2010). Compared to the stringers and longerons approaches, a sandwich skin increases the necessary spacing between frames, ultimately reducing the total number of frames. A sketch of the sandwich-skin approach can be seen in Figure 2.3. Figure 2.3: The sandwich-skin fuselage with frames included in the sketch. Inspired by Franklin (2010). 2.1.4 Belly Landing of an Aircraft Loading experienced by the fuselage during a belly landing generally varies with the flight-approach parameters such as descent velocity (vertical velocity), approach velocity (horizontal velocity), and pitch angle (θ). A study of the effects these parameters have on the impact loading will be performed using a simplified model in an explicit Finite Element (FE) solver. Landing surface also play a major role, it is easy to imagine the difference between landing, and skidding, on soft grass as opposed to hard tarmac or coarse gravel. For more information on impact loading see section 2.2. 2.2 Low-Velocity Impact Theory This section aims to give the reader an introduction to the basic theory of Low-Velocity Impacts. It is included here to provide an insight into what the UAV will experience during landing. 2.2.1 Introduction The term impact describes the collision between two bodies identified by a generation of relatively high forces over a short period of time (Meriam & Kraige 2008). According to Meriam & Kraige (2008), impacts are complex processes involving material deformation and transformation of mechanical energy to sound and heat. Impact processes are generally classified by the degree of kinetic energy that is conserved after the impact (Lien & Løvhøiden 2001): • Elastic - Total conservation of kinetic energy • Inelastic - A part of the kinetic energy is conserved, the rest is transformed into other states of energy • Totally Inelastic - Maximum transformation of kinetic energy, the two objects stick together and move with a common velocity Another method of classifying impact processes is by using impact velocity, i.e. low and high velocity impacts (Richardson & Wisheart 1996). The transition between low and high velocity depends on the target stiffness, material properties, and the impactor’s stiffness and mass. A high-velocity impact is dominated by the propagation of an impact stress wave, resulting in localized damage. This process is independent of boundary conditions as the material does not have time to react. Richardson & Wisheart (1996) presents several views on how to define low-velocity impacts: • Sjöblom, Hartness & Cordell (1988) argues that for low-velocity impacts, it is possible to model the impact process using a quasi-static approach. For a stiff, light-weight structure this ”may be on the order of tens of m/s”. 7 • Cantwell & Morton (1991) describes several impact testing procedures for composites. Charpy pendulum, the Izod impact test, Drop-weight impact tests, and hydraulic test machines are all methods for testing low-velocity impacts, which Cantwell & Morton (1991) defines as being up to 10 m/s. • Robinson & Davies (1992) presents a relation between the failure strain ε, impact velocity V0, and the speed of sound in the material C: ε = V0 C (2.1) For failure strains in composites on the order of 0.5−1.0%, the resulting transition from low to high-velocity impacts occurs between 10− 20 m/s (Robinson & Davies 1992). The LocalHawk UAV has an assumed descend-velocity of much less than 10 m/s, which according to the above-presented views, classifies it as a low-velocity impact event. 2.2.2 Low-Velocity Impact Failure Modes for Composites Richardson & Wisheart (1996) argue that the dynamic response of the structure is important in low-velocity impacts since the impact duration is long enough for the entire structure to react. Since the impact spreads energy throughout the entire structure, it is not only the surface in direct contact with the impactor/target that is susceptible to damage. For a composite structure, there are four main modes of failure (Richardson & Wisheart 1996): • Matrix cracking • Delamination • Fibre breakage • Penetration Matrix cracking is normally the first failure mode to occur in a composite subjected to transverse low-velocity impacts (Richardson & Wisheart 1996). The cracks appear due to mismatched properties of the fibers and the matrix, and they grow parallel to the fiber orientation. Delamination between fibers occurs due to off-axial loading, i.e. loading not parallel to the fiber orientation (see section 2.3.2) (Zenkert & Battley 2011). In a laminate structure, the crack will grow in the interface between the matrix and the fiber. Richardson & Wisheart (1996) adds that the crack grows between plies of different fiber orientation, and not between lamina in the same ply group. Fiber failure occurs only in the late stages of the total failure, after the matrix has cracked and delamination has taken place, and is the last failure mode before total penetration (Richardson & Wisheart 1996). The fibers fail beneath the impactor due to localized high stresses and indentation, but also on the opposite side of the structure due to bending. Penetration is the last stage of failure and occurs when the extent of fiber failure in the impact zone is great enough for the impactor to fully penetrate the material (Richardson & Wisheart 1996). At this point, the structure is ruined and efforts must be made to prevent the extent of the damage ever reaching this stage. 2.2.3 Contact Mechanics According to Abrate (2001), local indentation has a major influence on the contact force. He argues that the contact phenomenon is generally assumed to be rate independent so that statically determined contact laws can be used. The impact can be divided into two phases; loading and unloading. Contact force during the loading phase is calculated using the formula (Abrate 2001): P = kα 3 2 (2.2) Where α is the indentation and k, the contact stiffness, is given by: k = 4 3 ER 1 2 (2.3) 8 Where the R and E parameters are defined as: 1 R = 1 R1 + 1 R2 (2.4) 1 E = 1− ν2 1 E1 + 1− ν2 2 E2 (2.5) Here, R is the radius of curvature, E is the Young’s modulus, ν is the Poisson’s ratio, and subscripts 1 & 2 de- notes indentor and target respectively. Equation (2.2) is usually called the Hertzian law of contact (Abrate 2001). Although ending this very short introduction to contact mechanics here, it is possible to identify some general trends from equations (2.2) through (2.5): • The contact force is proportional to the radius of curvature for a given indentation. If equation (2.2) is turned around to return the indentation for a given contact force, it is inversely proportional to the radius of curvature for both indentor and target, highlighting the importance of a smooth impact area to reduce indentation. • The contact force is proportional to the Young’s modulus of the indentor & target materials, which means that the ”stiffer” the material, the higher contact force the bodies will experience for a given indentation. 2.3 Material Selection This section addresses the topic of choosing the material of the different sections of the LocalHawk UAV fuselage. If all possible materials were to be considered, this could be the topic for an independent thesis. Therefore, this section will be limited to evaluating glass-fiber-reinforced polymers (GFRP, fiberglass) and carbon-fiber-reinforced polymers (CFRP). 2.3.1 Introduction Materials chosen for manufacturing of the LocalHawk UAV will have to facilitate the type of loading presented in sections 2.1.2 and 2.2. Some of the more important design parameters for materials used in aircraft design is specific strength and specific stiffness, here, specific signifies the property in relation to the density of the material. Specific strength is defined as the ultimate tensile strength divided by the material density, and specific stiffness is defined as the Young’s modulus of the material divided by density (Franklin 2010). This specification of properties relative to the mass of the material is in accordance with the all-important requirement when designing aircraft: keeping the weight at a minimum level. Other factors that should be considered when choosing materials for an aircraft are temperature and corrosion. Galvanic corrosion could be a risk for electrically dissimilar materials such as aluminum and carbon-fiber composites (Raymer 2012). Determining the actual skin temperature is difficult as one has to take into consideration airflow conditions, surface finish, and atmospheric conditions. However, the highest theoretical skin temperature is determined using the stagnation temperature (Raymer 2012): T0 = T ( 1 + 0.2M2 ) (2.6) Where the ambient temperature, T , is specified in [K], and M is the flight Mach number. Operating at low altitudes and with a relatively low flight Mach number, problems regarding skin temperature are assumed to be negligible for the LocalHawk UAV. However, the internal engine mounts could experience elevated temperatures, especially for maneuvers requiring maximum thrust. Material selection for the engine mounts should therefore be performed with this in mind. 9 2.3.2 Fiber-Reinforced Composites The main purpose of the fiber phase of a fiber-reinforced composite is to provide strength (Callister 2007). There are two main types of fiber-reinforced composites; chopped-fiber reinforced (whisker) or filament reinforced (fiber) (Raymer 2012). Both types consist of fibers enveloped in a matrix, but for the whisker-reinforced composite, short fibers randomly oriented in the matrix are applied which results in an isotropic material. A fiber-reinforced composite on the other hand, utilizes fibers that are longer and oriented in a non-arbitrary direction. As opposed to whisker-reinforced composites, fiber-reinforced composites are anisotropic, meaning their physical properties (here: strength) are dependent on material direction (Oxford Dictionary of Physics 2005). Fibers come in several forms ready for manufacturing, the most common are loose or batting (for whisker reinforcement), unidirectional tape, unidirectional fabric, and bidirectional fabric (Raymer 2012). The unidirec- tional tape consists of continuous fibers pre-impregnated with a polymer resin which is only partially cured; unidirectional tape is often called prepreg (Callister 2007). Fabrics can also be prepreg and comes either with a unidirectional (all fibers in the same direction) or in a bidirectional (0 deg, 90 deg) layup (Raymer 2012). The matrix phase serves several purposes, firstly, it binds the fibers together and transfer loads to the fibers (Callister 2007). Secondly, it protects the fibers from surface damage and hinders the propagation of brittle cracks from fiber to fiber. GFRP composites, or more commonly known as fiberglass, are the most produced type of composites (Callister 2007). Fiberglass consist of glass fibers either oriented continuous (fiber-reinforced) or discontinuous (whisker-reinforced) in a polymer matrix. According to Callister (2007) there are several reasons for why glass is used as a fiber-reinforcement material: • Molten glass is easily drawn into fibers. • Easily accessible and cheap to manufacture using various techniques. • High strength, when used in a polymer matrix, the result is a composite with a high specific strength. • GFRP composites are applicable in corrosive environments due to the glass and polymer composite being chemically inert. According to Megson (2010), GFRP composites were used at the introduction of composite materials to the aircraft-manufacturing industry. However, GFRP composites do unfortunately possess a low level of stiffness, so that application areas in fixed-wing aircraft are limited (Megson 2010). However, many small or medium sized UAV designs are built using GFRP composites instead of CFRP composites due to their inherent damping capabilities (much lower Young’s modulus) and low cost (Austin 2010). CFRP composites consist of carbon fibers in a polymer matrix and are the most used advanced1 composite material (Callister 2007). Several properties have made CFRP composites so popular (Callister 2007): • Of all fiber-reinforcing materials, carbon fibers have the highest specific Young’s modulus and specific strength. • Even at elevated temperatures, carbon fibers keep their high strength. • Carbon fibers does not react, at room temperature, with many solvents, acids, bases, and is unaffected by moisture. • Many manufacturing methods have been developed, thereby reducing the cost of production. However, Raymer (2012) reports that in 2012, the cost of CFRP composites was approximately twenty times that of aluminum (please note that the material waste is less for composites than for metals during manufacturing). Another possible drawback with using CFRP composites is their brittleness which results in a sudden failure instead of plastic yielding in zones of load concentrations (Megson 2010). Adding to this is the poor resistance to impacts which may result in internal damage not visible under normal inspections. According to Megson (2010), CFRP laminates have approximately a Young’s modulus of three times that of GFRP laminates, but the strength does not differ that much. 1According to Callister (2007), advanced here translates to not fiberglass 10 2.3.3 Structural Composites - Laminates and Sandwich Constructions As mentioned in section 2.3.2, laminates are built up by first stacking plies of oriented fibers in a predetermined sequence and then cementing (curing) the plies together to form a laminate (Callister 2007). The stacking sequence determines the strength properties of the laminate and can be performed in infinitely different combinations (Raymer 2012). Ply orientation is up to the designer to decide, but some of the more common methods are (Raymer 2012): • 0 deg, provides strength in the direction of the principal axis. • 0 deg /90 deg, provides strength in both the direction of the principal axis and the transverse direction. • ±45 deg: Two plies provides some strength in the direction of the principal axis and good shear strength in the principal axis direction. Also used for structures subjected to torque. • 0 deg / ± 45 deg /90 deg: The four ply orientations provide good strength in both the principal axis direction and the transverse direction, as well as good shear strength. A preliminary-design rule-of-thumb, the Ten-Percent Rule proposed by Hart-Smith (1992), states that for 0 deg /± 45 deg /90 deg laminates, the 0 deg ply contributes 100% strength in the principal (0 deg) direction, while the other plies contributes with 10% strength in the principal direction each. Sandwich panels consist of two sheets bonded, using an adhesive or welding, to a thicker core (Callister 2007). The sheets are usually made of a stiff and strong material, such as fiber-reinforced polymers, while the core could either be a honeycomb structure or a solid material such as foam or balsa wood. Having a much higher Young’s modulus than the core, the purpose of the skin is to cope with stress due to tension and compression, as well as in-plane shear loads, while the core provide (out-of-plane) shear strength and resistance towards buckling (Franklin 2010). In addition, the core provides thickness between the faces, thereby increasing the second moment of area for resistance against bending. By binding the two sheets together, the core also provides shear continuity so that the sandwich acts as one structural entity. Joining the sheets to the core is of paramount importance for a sandwich structure (Franklin 2010). For composite sheets, an adhesive bond is normally applied. Franklin (2010) stresses the importance of taking into consideration the weight of the adhesive when deciding whether to apply sandwich structures instead of other alternative structures, as the total weight can be significant for a large area. Raymer (2012) reports that for aircraft applications, the core normally is a honeycomb structure made of aluminum or a phenolic material, but that for home-built aircraft, rigid foam is often used instead. This is supported by the design-proposition made by Austin (2010) in section 2.3.4. Although sandwich structures could provide good specific-strength properties, there are some possible drawbacks related to the application of sandwich structures (Franklin 2010): • Moisture could become trapped between the core and the sheets. If subjected to below-freezing tempera- tures, this moisture could freeze, causing separation between the sheet and the core. • If the sheets are very thin, damage from impacts could be severe. However, Franklin (2010) stresses that these drawbacks could be mitigated by ”proper design practices”. 2.3.4 Designing with Composites Designing with composites as opposed to metals can provide a weight saving for the structural parts of 25% (Raymer 2012). However, optimal weight-saving depends on the designer designing with composites in mind from the outset of the design process. Maximizing the potential of composites requires an understanding of how the material is manufactured and how it influences the design. The most basic difference is, as presented in section 2.3.2, that the fiber-reinforced composite materials are anisotropic, as opposed to an isotropic metallic material. Fiber orientation determines the direction in which the material is strongest, and therefore also in which direction the material is weakest (Franklin 2010). Also important to remember, is that composites generally perform poorly when subjected to concentrated loads (Raymer 2012). Therefore, joints and fittings that evenly distribute the loads should be applied. 11 An example of a common fuselage design for small or medium UAV designs, presented by Austin (2010), is the application of fiberglass to produce the skin, which is then supported by stringers made up of a stiff plastic foam core wrapped with carbon-fiber tape. This reduces cost drastically as the fiberglass is much cheaper than carbon fiber, and the carbon-fiber tape is cheaper than carbon-fiber cloth. A sought-after property of this design is the inherent damping capabilities of fiberglass as opposed to the stiffer carbon fiber, making the structure less prone to shattering upon an impact. 2.4 Finite Element Analysis This section contains an introduction to the basic theory of the Finite Element Method (FEM) and how this is applied when performing a Finite Element Analysis (FEA). The aim of this section is to give the reader an understanding of why the chosen software and solution method is selected, as well as a basic understanding of the theory which is the foundation for the Finite Element Method. 2.4.1 Introduction FEM is used in a wide variety of applications such as structural engineering, thermodynamic, bio-medical engineering, mechanical design, hydrodynamics, electromagnetic analyses, as well as other areas (Rao 2011). The basic idea of FEM is to simplify a physical problem by dividing the problem geometry/area into several smaller sub-elements which are connected to each other (Rao 2011). This process is in FEM called meshing, and consists of building a representation of the geometry (for non-field problems, for example: structural analysis) using a variety of elements. The elements can either be 1D (beam, truss elements), 2D (quadrilateral, triangular elements), or 3D (tetrahedron, cubic elements), see Figure 2.4 for a sketch showing the most basic 1D, 2D, and 3D elements. Figure 2.4: Basic FEM elements. Top: five two-noded 1D elements, mid left: quadrilateral 2D element with four nodes, mid right: triangular 2D element with three nodes, bottom left: cubic eight-noded 3D element, bottom right: tetrahedral 3D element with four nodes. By applying this simplification it is possible to obtain an approximate solution to the physical problem, and often it is possible to increase the accuracy by increasing the number of elements. As an example of accuracy when it comes to geometry representation, the effect of a mesh refinement, when using elements with straight edges only, is shown in Figure 2.5. 12 Figure 2.5: Mesh refinement; left: original geometry, second from left: coarse FE mesh, second from right: medium-coarse FE mesh, right: very fine FE mesh. Mesh produced using Ansys 14.5 Academic Research License. Although very important and directly linked to CPU solve time, the size of the mesh generally does not solely dictate the possible scope of an analysis anymore. Modern computers and their computational capabilities have allowed the main focus to shift to whether or not the problem is modeled correctly. Modeling is the process where the physical problem is reproduced in a modeling environment, for instance FEA software. Correct definitions of contacts, boundary conditions (forces, supports, temperature etc.), and simplifications are essential to obtain a realistic approximation. For a static structural analysis the global equation to be solved is (Rao 2011): Ku = f (2.7) Where K is the global stiffness matrix, u is the global nodal displacement vector, and f is the nodal force vector. By inverting the stiffness matrix and multiplying each side of equation (2.7) with it, the nodal displacement can be found: u = K−1f (2.8) For a linear structural analysis these displacements could then be used to calculate the element strains and stresses (Rao 2011). For a more in-depth explanation of the Finite Element Method, please see a textbook devoted to FEM such as Liu & Quek (2003), Rao (2011), or Taylor, Nithiarasu & Zhu (2005). During this thesis project, a commercial pre-/post-processing software and solver will be applied to conduct the FEA. Utilizing commercial software eliminates the need to write a solver script from scratch, and greatly increases the possible scope of the project. Numerous different software solutions are available, and most of them fulfills the requirements of this project, but they are not necessarily readily available with a student/academic license without constraining limitations. These limitations could be a maximum number of nodes, availability of specific solvers, and/or period of license validity. The choice of software package is addressed in section 2.4.3. 2.4.2 Explicit/Implicit Transient Dynamic Analysis Transient problems are characterized by dynamic, time-dependent loads exerted on the structure. Often, a method called direct integration is used to solve these types of problems due to its intuitiveness (Liu & Quek 2003). The basic ordinary differential equation this method aims to solve is (Taylor et al. 2005): Mü + Cu̇ + Ku + f = 0 (2.9) Where M is the mass matrix, C is the matrix of damping coefficients , K is the stiffness matrix, f is the nodal force vector, ü is the nodal acceleration vector, u̇ is the nodal velocity vector, and u is the vector containing the displacement of all the nodes. Direct integration can be divided into two different main categories: implicit and explicit (Liu & Quek 2003). According to Liu & Quek (2003), implicit methods are generally preferable for application in slow problems, while explicit methods are preferable for rapid phenomena such as impacts. To explain the difference between implicit and explicit methods, a derivation of a first-order transient equation to obtain an approximation of un+1, where the subscript n + 1 indicates the displacement for the next time step, is performed (Taylor et al. 2005): Cu̇ + Ku + f = 0 (2.10) 13 Assuming that u follows a polynomial, the lowest, linear, expansion gives: u ≈ û(t) = un + τ∆t ∆t (un+1 − un) (2.11) Where τ∆t is the current duration of the time step in question; τ∆t = t− tn (see Figure 2.6). Figure 2.6: Time step in a transient FEM analysis. Inspired by Taylor et al. (2005). It can be shown that the weighted equation to be solved is (Taylor et al. 2005): ∆t∫ 0 W (τ∆t) [ C ˙̂u + Kû + f ] dτ∆t = 0 (2.12) Introducing a weighting parameter θw: θw = 1 ∆t ∆t∫ 0 W (τ∆t)τ∆t dτ∆t ∆t∫ 0 W (τ∆t) dτ∆t (2.13) we get: 1 ∆t C (un+1 − un) + K [un + θw (un+1 − un)] + f̄ = 0 (2.14) where f̄ is an average value of f: f̄ = ∆t∫ 0 W f dτ∆t ∆t∫ 0 W dτ∆t (2.15) f̄ = fn + θw (fn+1 − fn) (2.16) Solving equation (2.14) for un+1 gives: un+1 = (C + θw∆tK) −1 [ (C− (1− θw) ∆tK) un −∆t̄f ] (2.17) From equation (2.17) it is possible to conclude that for values of θw > 0, a matrix inversion needs to be performed, such methods are called implicit. When θw = 0, and C is replaced by a lumped equivalent matrix, no matrix inversion is needed and this is called explicit methods (Taylor et al. 2005). A ”lumped” matrix is the opposite of a ”consistent” matrix which consists of off-diagonal elements (Taylor et al. 2005). For a mass matrix one assumes that the material on the mean locations on either side of the nodal displacement in question, behaves like a rigid body, and the rest of the element does not participate in the motion, thereby excluding the dynamic coupling that exists between the element displacements (Rao 2011). This assumption ”removes” the off-diagonal terms in the mass matrix, making it ”lumped”. According to Imaoka (2001), the most CPU demanding operation is matrix inversion, and Rao (2011) argues that a diagonal matrix requires less storage space than a matrix with off-diagonal terms, thus underlining the 14 numerical benefit of replacing matrix inversion with matrix multiplication. The difference between explicit and implicit methods could be summarized to the following; implicit methods involve unknown parameters for time-step n+ 1 in the calculation of un+1 while explicit methods rely solely on known parameters. This could be exemplified by inserting eq. (2.16) into eq. (2.17): un+1 = (C + θw∆tK) −1 [(C− (1− θw) ∆tK) un −∆t (fn + θw (fn+1 − fn))] (2.18) From eq. (2.18), it is possible to conclude that for values of θw 6= 0, unknown values of f̄ (fn+1) is included in the calculation. Inserting θw = 0 into eq. (2.18) yields: un+1 = C−1 [(C−∆tK) un −∆tfn] (2.19) By inspecting eq. (2.19), and assuming that C is calculated using only known values, it is possible to conclude that an explicit method does not require any iteration since all elements of the equations are known. One advantage of implicit methods is that they are unconditionally stable, which in practice means that the size of the time steps can be relatively large (Taylor et al. 2005). This makes the implicit method good for long lasting, smooth transient problems. The explicit methods are on the other hand conditionally stable, meaning that they have a maximum limit for the size of the time step. According to Sun, Lee & Lee (2000), the maximum ∆t must be less than the shortest time it takes a dilatational wave to cross any element in the mesh: ∆t ≤ 2 ωmax (2.20) Where ωmax is the maximum eigenvalue of the element. A conservative estimate of the time increment is the minimum value for all elements (Sun et al. 2000): ∆t = min ( Le cd ) (2.21) Where Le is the characteristic element dimension and cd the dilatational wave speed in the material. According to Ansys (2012), the time increment for an explicit analysis, which is constrained to facilitate stability in a commercial solver, is proportional to the smallest element dimension, and inversely proportional to the speed of sound in the material used. Simulia (2012) states that an implicit analysis including complex contact and/or material definitions could require many iterations which would increase solve time. In such a situation, they argue that an explicit solver would be preferable as it does not iterate but advances explicitly through the time steps. Sun et al. (2000) reported in their comparison of explicit and implicit finite element methods for dynamic problems, that for fast contact problems (here: 0.002s as opposed to 1s which was considered slow), the computational cost for explicit methods were about one tenth that of implicit methods. However, Sun et al. (2000) continues with reporting that for a given slow problem, explicit methods resulted in a CPU time of 1 h and 17 min while application of implicit methods took 10 min. Deciding whether to apply an implicit or explicit solver depends on the problem at hand. For an impact analysis of a short duration, the choice falls on an explicit method. This is due to the advantages an explicit solver has when it comes to dealing with large deformations, highly dynamic events, and the reduced cost relative to an implicit solver for a short, highly dynamic event. The decision to utilize an explicit solver for an impact analysis of a UAV during belly landing, match the decisions of Yüksel (2009) and Akhilesh, Sathyamoorthy, Bharath & Laxminarayan (2012). 2.4.3 Selecting Software Package A commercial pre-/post-processor as well as solver will be used to perform the analyses. Important factors for choosing software are accessibility, performance capabilities, student/academic license limitations, and ease-of-use. The FE software packages Abaqus/CAE, MSC Patran/Nastran, and Ansys Workbench have been examined. ”Accessibility” refers to whether or not a license is available, either through Chalmers, Kongsberg Defence Systems, or a general student license. Depending on the license, limitations of model size (total number of 15 nodes), analysis types available, and available support may exist. As discussed in section 2.4.2, the software should include an explicit solver. MSC Patran/Nastran is available for students with a general student license applying limitations to the total number of nodes to 5000, as well as excluding the SOL 700 explicit analysis. MSC’s on-line student center offers an extensive set of tutorials. However, considering the limitations included in the student license, MSC Patran/Nastran is found unfit for this project. Dassault Systèmes, Simulia, offers Abaqus/CAE with Abaqus/Explicit and a maximum node limitation of 1000 nodes. As reported by Yüksel (2009), 1000 nodes could result in inaccurate results for a problem of this nature. Taking the node limitation into consideration, Abaqus is also found unfit for this project. Chalmers has an Academic Research license available for Ansys which includes the explicit dynamics toolbox Autodyn. Combining the explicit capabilities with unlimited nodes and available tutorials through their on-line support center, Ansys Workbench is found to be the preferred software solution. 16 3 Method This chapter contains a step-wise description of the methods utilized in this thesis. Starting out with a study of how different landing parameters influence the UAV during landing, critical parameters and design cases for the FEA were identified. Basic concept development methodology was applied in the design of the internal structure before the concepts were modeled and made ready for FEA using CAD software. Manufacturers of composite materials were contacted to obtain parameters for eligible prepreg materials, based on input from a manufacturer, both in the form of parameters and qualitative recommendations, a material for the UAV’s skin was chosen. Laminate definition was performed using the ACP Composite PrepPost tool for Ansys 14.0. Different stacking sequences were examined, scrutinizing the strength of each test sequence lead to a preferred stacking sequence tailored for the belly-landing of the LocalHawk UAV. Using this preferred laminate, tests with varied descend velocity and pitch angle created a set of results used to evaluate concept viability. 3.1 Landing Parameter Study A landing-parameter study was conducted with the aim of identifying conditions under which the UAV would experience desirable or undesirable loading conditions. Approaching the problem conservatively dictates that the most undesirable loading conditions, within the UAV’s operational range, should be modelled in the FEA. Benefits of approaching the problem conservatively include that a fuselage designed for the worst case scenario is inherently capable of dealing with more preferable loading conditions. However, an overly-conservative approach may result in unnecessary structural reinforcement which increases weight and could render the UAV unfit for flight. A hollow model of the basic UAV fuselage, without any cutouts, was imported into an explicit analysis environment in Ansys 14.5 and appointed an isotropic material. The fuselage had a thickness of 3 [mm], and the geometry also included a thin, rigid section representing the ground. Being a simplistic analysis with the intent of solely investigating the influence of landing parameters on the loading experienced by the UAV during landing, no absolute values of stress or strain were noted. Normalizing all results enabled a straight-forward presentation which was easily interpreted. Pitch angle θ, and descend velocity Vz were the parameters of main concern. Thus, two independent test cases were defined. For the first, the pitch angle was varied between zero and ten degrees while descend velocity and approach velocity were kept constant at 5 [m/s] and 11.11 [m/s] (40 [km/h]) respectively. As the UAV fuselage has its largest cross section relatively close to the nose with a steadily decreasing cross-sectional area from there until the aft section, it was assumed that the most favorable loading conditions would occur for a pitch angle greater than zero. This assumption was made due to the increase in area of contact between the fuselage and the ground, thereby decreasing the surface load, for pitch angles larger than zero. In Figure 3.1, a comparison of θ = 0 deg and θ = 5 deg is depicted. Figure 3.1: Difference in landing surface area for pitch values of θ = 0 deg (bottom) and θ = 5 deg (top). For the descend velocity tests, the pitch angle and approach velocity were held constant at θ = 0 deg and 17 Vx = 11.11 [m/s] respectively while the descend velocity varied between Vz = 2.5 [m/s] and Vz = 10 [m/s]. From the UAV’s point of view, a low descend velocity as possible is desirable to reduce the impact load. Experienced operators manually controlling the UAV during landing should be able to facilitate a smooth landing. However, unfavorable landing conditions such as wind, gusts, turbulence, difficult approach path, and a short landing strip are all factors which could result in a hard landing. 3.2 Design of Skin and Internal Structure Using product development methodology, a proposed skin and internal structure were developed. Concept development was followed by designing of the chosen concepts using the Computer Aided Design (CAD) software Catia V5R20. 3.2.1 Concept Development Functional Analysis A functional analysis was performed to identify critical functions of the UAV’s fuselage as well as their possible solutions. Specifically, a function tree model was utilized, which resembles but differs from the Concept Classification Tree proposed by Ulrich & Eppinger (2012) in the way that it addresses the main function, means to fulfill said function, functions related to said means and so on until a desired level of specification has been reached, instead of focusing on the main function followed by means only. As suggested by Almefelt (2011), all functions were defined using a verb and a noun, specifying what should be done to which part of the UAV. Morphological Matrix From the Functional Analysis, key functions, along with their related means, were transferred to a morphological matrix for concept synthesis. Concepts were built up by the partial solutions (means) identified in the Functional Analysis. Throughout the process, focus was placed on identifying possible synergy between partial solutions. The morphological matrix was of the form suggested by Almefelt (2011), with the main functions listed in the first column with the corresponding proposed solutions placed horizontally to the right in columns 2−?, depending on how many different solutions were proposed. The question mark is used to represent the varying number of partial solutions assigned to each function. Starting from the top, moving down, one partial solution was chosen for each function, resulting in a concept proposal. See Chapter 4 for the resulting Morphological matrix and the partial solutions related to each key function. Concept Evaluation Results from the concept synthesis were subjected to evaluation with the intent of focusing further development on promising concepts and removing potential dead-ends. Instead of applying well-known methods such as the evaluation matrix proposed by Pugh (1990), a review involving experienced professionals at KDS was conducted. This limitation to applied concept evaluation methodology was done partly due to geographical constraints (Gothenburg in Sweden, Kongsberg in Norway), and partly due to the author being the only student invested in this project. Organizing a group event with the time it would take to do so was deemed too costly, in terms of time, relative to the perceived gains. The experience of the KDS employees and their ability to unbiased evaluate feasibility, advantages, and disadvantages regarding the concepts was thought to be sufficient for this evaluation. 3.2.2 Computer Aided Design Computer Aided Design (CAD) has become an irreplaceable tool for Product Developers, severely shortening development lead times and costs. An array of CAD tools are available for engineers, however, since the LocalHawk UAV was designed using Catia V5R20, and Chalmers Univ. of Technology has licenses for Catia available for students, it was the chosen CAD tool for this thesis work. Being a spin-off concept of the original second concept (see Chapter 1), rapidly developed in the late stages of the LocalHawk 2012 summer project, concept three’s CAD model was not as described as the other concepts. Specifically, all that was CAD-modelled were the surfaces, roughly describing the outer shape of the airframe. Roughly, because joints between wings, fuselage, and tail were not developed, neither were fillets between these 18 bodies. Focus was directed towards the fuselage, with the fuselage’s bulge being the first area, of two, immediately possible to identify as an area at risk of failure during belly landing. The other area being the joints between the wings and the fuselage which could break due to wing bending at the moment of impact (inertia effects). One of the identified possible problem areas of the fuselage was the nose section which had a bulky geometry. Concerns about the producibility of the nose geometry were raised and lead to the decision to improve the design of the nose. Using Catia’s Generative Surface Design module, the surface model was modified to produce a surface which had a smoother transition from the fuselage’s main body to the nose. After modifications to the existing fuselage model were performed, the design effort moved to modeling of the two proposed concepts for the skin and internal stiffening structure. For the Multiframe concept, a skin thickness of between 1 [mm] and 2 [mm] was recommended by Kristiansen (2013). Describing outer dimensions, the fuselage surface defined in Catia had an offset surface created in the inwards direction. The offset was set equal to the target skin thickness for the concept in question, so that thickness could be applied in the FE model in the outwards direction. By ensuring the skin surface was in contact with the frames, prior to applying thickness to the surfaces, mesh connectivity was possible during the FE modelling. For the sandwich concept, the frames were a bit more complexly modelled. Instead of several transverse frames, the sandwich concept relied on only two, larger frames, separately supporting the batteries and the payload, see Chapter 4 for the resulting CAD models. 3.3 Material Selection and Parameters This section covers the work done to select materials for the different structures. It is divided into two sections; section 3.3.1 Composite Skin, and section 3.3.2 Internal Stiffening Structure. Section 3.3.1 describes the process of selecting composite material for the fuselage skin, but also gives an introduction to orthotropic material parameters and how they are defined for the FEA (see section 3.4 for more info about FEA). Section 3.3.2 briefly discusses limitations regarding the representation of internal components, and contains a brief discussion about the topic of designing internal stiffening structure. 3.3.1 Composite Skin As described in the Literature Review (Chapter 2), laminates are built up by plies with specific fiber orientations. The result is an orthotropic material, meaning that the parameters of the material (strength, stiffness etc.) depends on the direction, and that the material consists of three orthogonal symmetry planes (Sundström 2007). As opposed to isotropic materials which only requires a general Young’s modulus E and Poisson’s ratio ν (alternatively Bulk modulus K, or Shear modulus G) to describe elastic behavior, orthotropic materials require Young modulus, Poisson’s ratio, and Shear modulus defined in each principal direction or material plane. The constitutive equation for orthotropic materials is (Sundström 2007): ε = Sσ (3.1) Where ε is the strain vector, S is the laminate’s compliance matrix, and σ is the stress vector. Equation (3.1) written out becomes: ε11 ε22 ε33 2ε23 2ε31 2ε12  =  1 E11 − ν21 E22 − ν31 E33 0 0 0 − ν12 E11 1 E22 − ν32 E33 0 0 0 − ν13 E11 − ν23 E22 1 E33 0 0 0 0 0 0 1 G23 0 0 0 0 0 0 1 G31 0 0 0 0 0 0 1 G12   σ11 σ22 σ33 σ23 σ31 σ12  (3.2) 19 From equation (3.2), it is possible to conclude that 12 constants are required to define an orthotropic material. However, a relationship between some of the constants exists (Sundström 2007): ν12 E11 = ν21 E22 (3.3) ν31 E33 = ν13 E11 (3.4) ν32 E33 = ν23 E22 (3.5) Thereby reducing the total number of independent constants to 9 for an orthotropic material. Equation (3.1) can be written on a stiffness form by inverting the compliance matrix: σ = Cε (3.6) Where C is the material stiffness matrix: C = S−1 (3.7) The material constants are determined from various physical tests which requires different test fixtures/jigs, and several runs to establish values that can be trusted from a statistically point of view. Instead of manufac- turing and testing a material, professional manufacturers were contacted and inquired about material data for applicable materials. In accordance with desires put forth by KDS, to facilitate the production process by simplifying composite production wherever possible, prepreg materials were the main focus (see the Literature Review, Chapter 2, for more info about prepregs). Prepreg materials were considered an effective solution because of not having to impregnate a matrix with fibers. To reduce costs, fiberglass prepregs were preferred over carbon-fiber prepregs. Ideally, a material used in an explicit analysis is defined elastically, plastically, and with failure criteria. Generally, for composite materials, a linear material model with failure includes the parameters presented in equation (3.2), as well as strength parameters (stress/strain limits) accompanied by a failure criterion. For laminates (plate theory), the necessary elastic parameters are reduced to the Young’s Modulus E and Poisson’s ratio ν in the 11 and 22 directions, as well as the in-plane shear modulus G12 (Sundström 2007). The properties of the selected composite material is presented in Table 3.3, Section 3.4.1. Tsai-Wu Failure Criterion The failure criterion proposed by Tsai & Wu (1971), is commonly used to predict failure of composite materials. Their model assumes that there exists a failure surface in the stress-space on the following form: f (σk) = Fiσi + Fijσiσj = 1 (3.8) Where repeated indices indicate summation, and i, j, k = 1, 2, . . . 6. Expanded, eq. (3.8) becomes: F1σ1 + F2σ2 + F3σ3 + F4σ4 + F5σ5 + F6σ6 + F11σ 2 1 + 2F12σ1σ2 + 2F13σ1σ3 + 2F14σ1σ4 + 2F15σ1σ5 + 2F16σ1σ6 + F22σ 2 2 + 2F23σ2σ3 + 2F24σ2σ4 + 2F25σ2σ5 + 2F26σ2σ6 + F33σ 2 3 + 2F34σ3σ4 + 2F35σ3σ5 + 2F36σ3σ6 + F44σ 2 4 + 2F45σ4σ5 + 2F46σ4σ6 + F55σ 2 5 + 2F56σ5σ6 + F66σ 2 6 = 1 (3.9) For a 3D shell element of a orthotropic material, plane stress, eq. (3.8) is reduced to (Liu & Tsai 1998) & (Ansys 2012): F11σ 2 1 + F22σ 2 2 + F66τ 2 12 + F1σ1 + F2σ2 + 2F ∗ 12 √ F11F22σ1σ2 = 1 (3.10) 20 Where: F11 = 1 σt1σc1 (3.11) F22 = 1 σt2σc2 (3.12) F66 = 1 τ2 t (3.13) F1 = 1 σt1 − 1 σc1 (3.14) F2 = 1 σt2 − 1 σc2 (3.15) In equations (3.11) through (3.15), σti indicates the material’s tensile strength in the i direction, σci indicates the material’s compressive strength in the i direction, and τt is the in-plane shear strength of the material. The coupling parameter F ∗ 12 is often decided by the user to fit the failure surface to experimental results (biaxial stress tests), but to ensure a closed failure-surface envelope, the following requirement exists (Liu & Tsai 1998): −1 ≤ F ∗ 12 ≤ 1 (3.16) However, according to Liu & Tsai (1998), F ∗ 12 could be set to an average value of −1/2, which they refer to as the generalized von-Mises model. Ansys Workbench uses ”Tsai-Wu Constants” in combination with ”Orthotropic Stress Limit” to model this plane stress failure criterion (Ansys 2012). The coupling parameter is replaced with Cxy (or C12) which is twice the F ∗ 12 value (ANSYS.NET 2002). For Explicit Dynamics analyses in Ansys, the Tsai-Wu constant, Cxy, is automatically set to −1, no matter what the user has defined (Ansys 2012). Since Cxy is set to −1 automatically by Ansys Workbench, any Explicit Dynamics analyses employ the generalized von-Mises model for F ∗ 12. First-Ply Failure (FPF) is the easiest and most conservative approach to modeling the failure of laminate structures. As the name suggests, the composite is considered to be failed when the first ply of the laminate experiences failure. Tolson & Zabaras (1991) describes FPF as occurring when ”initial failure of a single layer in a laminate fails in either the fiber direction or in the direction perpendicular to the fibers”. On the other end of the scale, is Last-Ply Failure (LPF). Last-ply failure evaluates the failure of all plies and includes a material model for estimating stiffness based on the parameters and stackup of remaining plies. LPF is defined by Tolson & Zabaras (1991) to occur when the structure has degraded to a point where it no longer can support any additional load. Orthotropic Constants Study Unfortunately, none of the manufacturers contacted about material data offered the full set of nine elastic constants required to describe orthotropic elasticity in Ansys. Therefore, a short study was performed to investigate how the different unknown parameters affected the solution of a thin composite plate structure being hit by a spherical impactor. The plate was modelled as a curved surface and meshed using shell elements, see Appendix D for more information about the test setup. Five plies of one of the woven prepreg materials supplied by a manufacturer with a stacking sequence of [0, 45, 0, 45, 0] comprised the composite material, see Table 3.3, Section 3.4.1 for material parameters. The spherical impactor was modelled as a rigid body made up of structural steel, and assigned an impact velocity of 7.5 [m/s]. Elastic constants not supplied included the through-thickness Young’s modulus, Ez or E33, and out-of-plane Poisson’s ratios νyz or ν23 and νxz or ν13. Values were assigned to each of these constants, creating a reference result. Assigned values were relatively low ”guesstimates”, the Poisson’s ratios were set to 0, 001 and the through-thickness Young’s modulus was set to 1 [MPa]. Values of 0.001 were chosen for the Poisson’s ratios instead of 0 because, according to Lauth (2013), an inserted value of 0 for Poisson’s ratio will automatically be changed to 0.3 by Ansys. Several tests were performed, varying each constant independently as well as combined tests where all constants were given a high value. See Table 3.1 for test cases. 21 Table 3.1: Test settings for the Orthotropic Constants Study Test Ez [GPa] νyz νxz 1 0.001 0.001 0.001 2 10 0.001 0.001 3 10 0.1 0.001 4 10 0.1 0.1 5 20 0.1 0.1 6 20 0.499 0.1 7 20 0.499 0.499 8 0.001 0.499 0.499 9 0.001 0.001 0.499 10 10 0.122 0.122 3.3.2 Internal Stiffening Structure The internal stiffening structure supports the payload, batteries, and engine. Being relatively small additions, mass wise, the camera and engine were not included in this project. This simplification was done to avoid spending time on designing detailed fixtures for these, more complex, installations. These are more complex because, it should be possible to install the camera in different angles with a free view of the ground, and the engine represents a source of elevated temperatures requiring cooling. Since the main goal of this thesis was to investigate the belly-landing concept, resource spending (time) on design of internal stiffening structures was limited to the structure supporting the payload (electric cabinet) and the batteries. Therefore, only frames for those two components were modeled (except for the Multiframe concept which also had frames not connected to the internal components). The number of frames was a result of a discussion between the stakeholders at KDS and the author of this thesis. Operating with the mindset that internal access to the UAV’s components should be available through cut-outs in the top of the UAV, all frames were designed so that internal components could be lowered into them, and not inserted from the front/side/rear/bottom. 22 3.4 Finite Element Analysis CAD-files generated during the CAD phase were imported into the FEA software Ansys as STEP (.stp) files. STEP (Standard for the Exchange of Product Model Data, ISO 10303) is a neutral file format for transfer of CAD/CAM/CAE geometry and product data between different systems (SCRA 2006). For a more thorough explanation of functions and controllers used in Ansys, see Appendix A. In Appendix B, a sample case for an explicit analysis is solved step by step. Since it being a significant contribution to the thesis text, the Pre-Processing work has been divided up into several sections. The term Pre-Processing encompasses all of the work done to enable the FE Analysis to run and achieve realistic, sound results. It is the most input demanding part of the FEA and involves defining material, body contacts, mesh, boundary conditions (BC) such as loads and supports, analysis settings, and any modifications to the geometry. Last-minute access was granted to Ansys ACP Composite PrepPost v14.0. This module was used to model the composite laminates in Ansys. Unfortunately, since it was version 14.0 and not 14.5, post-processing of Explicit Dynamics’ results using ACP was not available. The ACP pre-processing modeling environment consists of four components; Engineering Data (material definition), Geometry (import of CAD geometry or modeling geometry using Design Modeler), Model (meshing, boundary conditions, and analysis settings), and Setup (composite modeling). These are then linked to one or more analysis systems (here: Explicit Dynamics), and the composite information is automatically imported as a Layered Section, see Figure 3.2 for an overview from Ansys Workbench. Figure 3.2: ACP (pre) linked to Explicit Dynamics in Ansys Workbench Another limitation affiliated with version 14.0 is the restriction of not being able to do explicit analyses of models with meshes consisting of both shell elements and solid elements. Although possible for other types of analyses, the Explicit Analysis system in Ansys Workbench cannot have a combined model input from an ACP (pre) system (shell elements) and a Model system (solid elements). Due to this limitation, all bodies were simplified using surfaces which were then imported into ACP (pre) and applied thickness. 3.4.1 Material Definition and Geometry Preparation Utilizing input received from Gurit, RE210 SE70 unbalanced, woven fiberglass prepreg was chosen as the skin material. SE 70 was chosen for its toughness and availability in light-weight reinforcements, suitable for UAV structures in the LocalHawk’s size range (Armstrong 2013). Based on the input, orthotropic elasticity as well as orthotropic strength could be modeled for composite shell elements (that is, the elastic constants provided by Gurit were complemented by the parameters decided using the results of the Orthotropic Constants Study, section 3.3.1, results are in Chapter 4). As described in section 3.3.1, the Tsai-Wu failure criterion was used to determine whether or not a ply had failed. Upon failure, the AUTODYN solver (for explicit analyses) in Ansys removes the element’s capability to sustain any shear stresses or negative pressures (Ansys 2011). In Ansys, the composite material definition was achieved by applying the material parameters specified in Table 3.2. Please note that the densities presented in Tables 3.2 through 3.4, were not the densities used in the final analyses, they are the actual densities, pre-modification. Densities had to be modified so that the total weight 23 of the wing-less models represented actual condition, section 3.4.5 explains this in more detail. Table 3.2: Material parameters composite skin RE210 SE70 Unbalanced Woven E-Glass Prepreg Property/Parameter Value/Setting Unit Density 1867 [ kg m3 ] Ply Type Woven [−] Orthotropic Elasticity Young’s Modulus x-dir 27180 [MPa] Young’s Modulus y-dir 18120 [MPa] Young’s Modulus z-dir 10000 [MPa] Poisson’s Ratio xy 0.122 [−] Poisson’s Ratio yz 0.122 [−] Poisson’s Ratio xz 0.122 [−] Shear Modulus xy 3806 [MPa] Shear Modulus yz 3460 [MPa] Shear Modulus xz 3460 [MPa] Orthotropic Stress Limits Tensile Strength x-dir 407.7 [MPa] Tensile Strength y-dir 271.8 [MPa] Tensile Strength z-dir 0 [MPa] Compressive Strength x-dir 366.9 [MPa] Compressive Strength y-dir 244.6 [MPa] Compressive Strength z-dir 0 [MPa] Shear strength xy 41.5 [MPa] Shear strength yz 0 [MPa] Shear strength xz 0 [MPa] Tsai-Wu Constants Coupling xy −1 [−] Coupling yz −1 [−] Coupling xz −1 [−] Non-Composite Material Definition Table 3.3 contains the material parameters for the material selected to represent the internal stiffening components (frames). This material was selected due to its light weight and excellent damping capabilities (Rohacell 2013). Table 3.3: Material parameters foam frames Rohacell 110IG Property/Parameter Value/Setting Unit Density 110 [ kg m3 ] Ply Type Isotropic Homogenous Core [−] Isotropic Elasticity Young’s Modulus 160 [MPa] Poisson’s Ratio (Calc) 0.33 [−] Shear Modulus 60 [MPa] Bulk Modulus (Calc) 160 [MPa] 24 For the rigid bodies, aluminum as described in Ansys’ material library was used. Table 3.4 presents the material parameters for the rigid bodies (ground, payload, and batteries). Table 3.4: Material parameters rigid bodies Aluminum Property/Parameter Value/Setting Unit Density 2770 [ kg m3 ] Ply Type Isotropic [−] Isotropic Elasticity Young’s Modulus 71000 [MPa] Poisson’s Ratio 0.33 [−] Bulk Modulus (Calc) 69608 [MPa] Shear Modulus (Calc) 26692 [MPa] Please note that material definition for the frames, payload, batteries, and ground were rudimentary due to them not being scrutinized. Material data for the frames were collected from the website of Rohacell (2013), however, the shear modulus was modified to get a Poisson’s ratio ν < 0.5. Geometry Preparation Due to unsuccessful attempts to combine solid geometry (from a Mechanical Model system) and surface geometry (from the ACP (pre) system) in an Explicit Dynamics system, all bodies were simplified, and represented by surfaces. However, since no detailed representations of neither the payload nor the internal components were included in the original CAD import, it could be argued that this simplification did not affect the results in a significant manner. To accommodate meshing and solve issues related to relative-to-the-skin frame/payload movement, the skin, payload, batteries and the frames were combined into a multi-body part. Line/edge to surface contact definition is not supported for Ansys’ Explicit Dynamics system, and surface to surface contact definitions between the frames and the skin were not enough for the frames to maintain their position relative to the skin. As described in section 3.2.2, the frames for the Sandwich concept were more complex than the frames for the Multiframe concept. This complexity hindered accurate representation of the geometry of the frames. However, since the main focus was on the response of the skin to the impact with the ground, this reduced accuracy in frame representation was considered of little importance and thus an acceptable approximation. The resulting simplification using surfaces is compared to the original geometry in Figure 3.3. Figure 3.3: The Sandwich Skin concept’s frames. Top: Before simplification. Bottom: After being simplified using surfaces 25 3.4.2 Meshing To avoid non-physical results due to movement of frames/payload/batteries relative to the fuselage’s skin, all moving bodies were combined into a multi-body part. This was combined with a Joint description between the frames and the skin, creating common boundary edges to fully ensure mesh connectivity. Figure 3.4 depicts the connected mesh between the aft closing section and the skin, although being surface bodies, thickness is displayed to visualize relative size and distance. Figure 3.4: Meshes for the aft section and skin connected It is also important to stress that since the meshing took place inside an ACP (pre) system, physics preference for the meshing algorithm was, manually, set to Explicit (since it was not set by default, as it would have been inside an Explicit Dynamics system). See Appendix A for a more in-depth explanation of what Explicit meshing preferences represent. Sizing was globally controlled using the global sizing controller defined under Mesh-Sizing-Min Size and Max Face Size, these were set to 2.5 [mm] and 20 [mm] respectively. A result of trial and error, the part-specific method and sizing settings can be seen in Table 3.5 for both the Sandwich Skin concept and the Multiframe concept. Table 3.5: Mesh method, sizing, and sequence for each part Part Method Sizing [mm] Sequence Multiframe Concept Skin Quadrilateral Dominant 5 hard 3 Frame 1-9 Uniform Quad/Tri 5 4 Aft Section Uniform Quad/Tri 5 5 Payload Mapped Face Meshing 10 soft 1 Batteries Mapped Face Meshing 10 soft 2 Ground Mapped Face Meshing 15 soft 6 Sandwich Skin Concept Skin Quad. Dominant (All quad) 5 hard 1 Payload Frame Uniform Quad/Tri 10 2 Batteries Frame Uniform Quad/Tri 10 4 Payload Mapped Face Meshing 10 soft 3 Batteries Mapped Face Meshing 10 soft 5 Ground Mapped Face Meshing 15 soft 7 Aft Section Uniform Quad/Tri 5 6 Not directly a part of the meshing, creating named selections was the last step performed prior to opening the model in the ACP (pre) environment. When importing a mesh into the ACP (pre) environment, the mesh is imported as one entity, no matter if the meshed bodies are connected or not. Therefore, it is necessary to 26 define the elements and nodes which make out parts of the mesh that needs to be distinguished from the other elements and nodes. Named selections created in the Mechanical (meshing) environment are imported into ACP (pre) and allows the user to separate the bodies from each other. All bodies were assigned a named selection, and in addition, lines going from the nose of the fuselage to the aft section were also assigned a named selection each. These lines were used to define the principal direction for the plies in the ACP (pre) system. 3.4.3 Composite Modeling using ANSYS ACP Composite PrepPost Using the ACP (pre) system instead of the Layered Section option which is native in Ansys Mechanical, allowed for much better control and easier definition of plies and their respective orientation. After importing the surface mesh and named selections described in section 3.4.2, fabrics were defined using the materials presented in section 3.4.1. Although consisting of isotropic materials, the frames, payload, batteries, and ground were modeled using plies defined in the same way as orthotropic laminates due to the aforementioned limitation associated with v14.0 of not being able to combine solid and shell elements. However, since these bodies consisted of isotropic materials, rosette (coordinate systems, rosettes are used to describe reference directions in ACP) definition was arbitrary for all of these bodies. Orientation Direction, defined during creation of Oriented Element Sets, determines the stacking direction for a laminate/composite structure, and was in that way used to determine in which direction thickness was applied to a surface mesh. For surfaces that were a result of a mid-surface simplification, as opposed to surfaces created from a face or created in CAD to be an external face, two Oriented Element Sets were created, one for each direction to apply thickness. Reference fiber direction (0 deg direction) for the skin was defined using the imported Edge Sets (from named selections consisting of edges) to be along the skin, from front to aft. An example of the resulting reference direction and fiber directions are shown for two plies, [45,−45], of the skin of the Multiframe concept in Figure 3.5. Figure 3.5: Reference direction (yellow) and fiber direction (green) for the two plies [45,−45] (left, right), rear of the skin The complete process is described in more detail in Appendix C, where a step-by-step guide is presented for the Sandwich Skin. 3.4.4 Common Boundary Conditions and Analysis Settings In all cases, the ground was applied a fixed support, locking all degrees of freedom. Moving parts (skin, frames, payload, and batteries) were assigned the same velocity whose directional components were defined using a coordinate system which was normal to the ground. By defining the direction of the velocity vector using a relative-to-the ground coordinate system, it was assured that all tests had the same velocity relative to the ground (except for those where descend velocity varied). A standard earth gravity was applied to all bodies, this also being defined by the ground coordinate system. Utilizing Ansys’ advice on settings for low-velocity impact simulations, the analysis settings presented in Table 3.6 were used, see Ansys (2011). As will be described in section 3.4.7, mass scaling was applied to shorten the solution time by increasing the time step (Appendix A explains the theory behind mass scaling in more 27 detail). To facilitate the use of mass scaling, mass after meshing never exceeded 12.49 [kg], since mass scaling would add a fractional mass. Table 3.6: Analysis Settings Setting Value Mass Scaling Yes Precision Double Beam time step safety factor 0.1 Hex integration 1pt Gauss Shell sublayers 3 Tet integration Nodal Strain Hourglass Damping Flanagan Belytschko Stiffness coefficient 0.1 Viscous coefficient 0.1 Save results on 100 equally spaced points Save result tracked data per 10 cycles Body self contact No Element self contact No By default, when applying Flanagan-Belytschko hourglass damping, which is based on the paper presented by Flanagan & Belytschko (1981), the viscous coefficient is set to 0. However, localized energy oscillations, see Figure 3.6, led to this being set to 0.1. Figure 3.6: Energy oscillations at late stages of an analysis 3.4.5 Density Modification and CG Positioning Tests were performed without any wing or tail geometry due to them not being modeled with internal structure, and to allow for shorter solve times due to the reduced model complexity. As mentioned in Appendix A, correct representation of the bodies’ mass is very important due to the dynamic nature of explicit analyses. Therefore, since there were no wings nor a tail included in the model, modifications to the density of existing materials were performed. Had these modifications not been implemented, results would have been invalidated as the analyses had included an unrealistically light-weight structure, grossly underestimating actual loads. Except from the solver time step, see the Literature Review Ch. 2 or Appendix A for explanation why, and of course the mass of the bodies, this density modification was assumed to not affect the solution’s accuracy in a noticeable manner. To reach the goal of 12.5 [kg], which was the estimated total weight of the LocalHawk UAV, 28 the density of all materials were modified with the same constant, thereby ensuring no major offsets in mass distribution. Being a UAV, the center of gravity (CG) is one of the most important parameters used to evaluate stability during flight. Positioning of internal components had been meticulously carried out during design of the three UAV concepts to ensure that the UAVs were stable. Simplifying the model to what was used in this thesis, and using thickness applied to a surface to individually replicate the mass of the payload and batteries, resulted in an offset in the position of the CG. Tuning the thickness va