Analysis and Design of a Morphing Wing Tip using Multicellular Flexible Matrix Composite Adaptive Skins by Tyler Lee Hinshaw Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering Dr. Michael K. Philen, Chair Dr. Rakesh K. Kapania Dr. William H. Mason July 1, 2009 Blacksburg, Virginia Keywords: Morphing Wing, Skins, Intelligent Structures Copyright 2009, Tyler Lee Hinshaw Abstract The material presented in this thesis uses concepts of the finite element and doublet panel methods to develop a structural-aerodynamic coupled mathematical model for the analysis of a morphing wing tip composed of smart materials. Much research is currently being performed within many facets of engineering on the use of smart or intelligent materials. Examples of the beneficial characteristics of smart materials might include altering a structure’s mechanical properties, controlling its dynamic response(s) and sensing flaws that might progressively become detrimental to the structure. This thesis describes a bio-inspired adaptive structure that will be used in morphing an aircraft’s wing tip. The actuation system is derived from individual flexible matrix composite tube actuators embedded in a matrix medium that when pressurized, radical structural shape change is possible. A driving force behind this research, as with any morphing wing related studies, is to expand the limitations of an aircraft’s mission, usually constrained by the wing design. Rather than deploying current methods of achieving certain flight characteristics, changing the shape of a wing greatly increases the flight envelope. This thesis gives some insight as to the structural capability and limitations using current numerical methods to model a morphing wing in a flow. i Acknowledgments I would like to thank Dr. Michael Philen for presenting me with the opportunity to perform this research under your advisement. Through all of my dim-witted questions in our countless meetings and all of the assistance in debugging the model, you were always patient and never made me feel pressured in any situation. The knowledge I have gained from working under you is invaluable and I will be forever grateful for the time I spent studying under you. I would also like to thank my coworkers whom I shared an office with, Mr. Zhiye Zang and Mr. Daewon Kim. All of the long days that turned into nights that we spent in the office together made the workload always seem easier with you there to talk to. I most certainly would not have been able to accomplish this research without your help. Last but not least I would like to thank my parents, Barry and Sherry Hinshaw. The unconditional love and support you have showed me over the continuation of my education has allowed me to accomplish all of my goals set for myself. You were always there for me when I needed it and for that I thank you. I am proud to be called your son. ii Contents Abstract ........................................................................................................................... i Acknowledgments......................................................................................................... ii Contents ........................................................................................................................ iii List of Figures ............................................................................................................... v List of Tables ................................................................................................................ ix Nomenclature ................................................................................................................ x Chapter 1 Introduction and Literature Review ............................................................ 1 1.1 History of Wing Morphing ........................................................................... 2 1.2 Current Morphing Research ....................................................................... 4 1.3 Morphing Wing Skin Materials ................................................................... 6 1.4 Similar Work .............................................................................................. 9 1.5 Adaptive Structures ................................................................................. 11 1.6 Motivation ................................................................................................ 14 1.7 Thesis Overview ...................................................................................... 17 Chapter 2 Model Development ................................................................................... 19 2.1 Displacement-Based Elements ................................................................ 20 2.1.1 FMC Material Model and Actuation Formulation ........................... 21 2.1.2 The Stiffness Matrix ...................................................................... 29 2.2 The Flat Shell Element............................................................................. 30 2.2.1 The Bilinear Isoparametric (Membrane) Element .......................... 30 2.2.2 The Kirchhoff Plate Element ......................................................... 34 2.2.3 Actuation Forces ........................................................................... 38 2.3 Global Assembly ...................................................................................... 43 iii 2.4 Applying Boundary Conditions ................................................................. 47 2.5 Aerodynamic Model – Calculation of Aerodynamic Loading .................... 50 2.5.1 Kutta Condition.............................................................................. 54 2.6 Weight Force ........................................................................................... 58 2.7 Pressure Optimization.............................................................................. 59 Chapter 3 Model Verification ...................................................................................... 62 3.1 Structural Verification ............................................................................... 62 3.2 Aerodynamics Verification ....................................................................... 67 Chapter 4 Parameter Studies ..................................................................................... 72 4.1 Design Region Determination .................................................................. 74 4.1.1 Design Region Selection ............................................................... 77 4.2 Test Setup ............................................................................................... 79 4.3 Results ..................................................................................................... 82 4.3.1 Constrained Actuation Pressure Performance .............................. 83 4.3.2 Unconstrained Actuation Pressure Performance Comparison ...... 86 4.3.3 Aerodynamic Performance ............................................................ 88 4.3.4 Maximum Pressure and Weight .................................................... 90 Chapter 5 Conclusions and Future Work .................................................................. 93 5.1 Thesis Overview and Conclusions ........................................................... 93 5.2 Future Work ............................................................................................. 94 Bibliography .............................................................................................................. 101 iv List of Figures Figure 1.1 The Bell X-5 with Variations of Wing Sweep [10] ........................................... 3 Figure 1.2 Bald Eagle Configurations: a. Landing b. Loiter c. Dash [14] ......................... 4 Figure 1.3 Lockheed Martin's Proposed Baseline Morphing Concept [15, 16] ................ 5 Figure 1.4 Multiple Exposure of LM MAS Model's Different Configurations [2] ............... 5 Figure 1.5 Preliminary Tests for Skin Selection [22] ........................................................ 8 Figure 1.6 Initial SMP Prototype [22] ............................................................................... 9 Figure 1.7 Inflatable Wing [24] ...................................................................................... 10 Figure 1.8 FMC Actuators Converting Internal Pressure to Axial Contraction/Extension and Torsion ................................................................................................................... 13 Figure 1.9 Analysis and Frames From Demonstration Video of a Multicellular FMC Adaptive Structure Performing Bending and Twisting Maneuvers ................................ 14 Figure 1.10 Typical Sail Plane Flight ............................................................................. 15 Figure 1.11 Proposed Morphing Wing Tip for Long Endurance UAV ............................ 15 Figure 1.12 The HP-18 Sail Plane ................................................................................. 16 Figure 1.13 The Wortmann FX-67-K-150 Airfoil ............................................................ 16 Figure 2.1 Full Model Derived in Chapter 2 With All Forces Depicted ........................... 20 Figure 2.2 FMC Tubes Embedded in a Matrix Material ................................................. 22 Figure 2.3 Material Axes for