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- Permanent Link:
- https://ufdc.ufl.edu/UFE0042430/00001
## Material Information- Title:
- Experimental Characterization and Multidisciplinary Conceptual Design Optimization of a Bendable Load Stiffened Unmanned Air Vehicle Wing
- Creator:
- Jagdale, Vijay
- Place of Publication:
- [Gainesville, Fla.]
- Publisher:
- University of Florida
- Publication Date:
- 2010
- Language:
- english
- Physical Description:
- 1 online resource (146 p.)
## Thesis/Dissertation Information- Degree:
- Doctorate ( Ph.D.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Mechanical Engineering
Mechanical and Aerospace Engineering - Committee Chair:
- Ifju, Peter
- Committee Co-Chair:
- Sankar, Bhavani V.
- Committee Members:
- Haftka, Raphael T.
Brennan, Anthony B. - Graduation Date:
- 12/17/2010
## Subjects- Subjects / Keywords:
- Aerodynamics ( jstor )
Aircraft wings ( jstor ) Airfoil camber ( jstor ) Airfoils ( jstor ) Buckling ( jstor ) Design optimization ( jstor ) Modeling ( jstor ) Remotely piloted vehicles ( jstor ) Sweepback ( jstor ) Velocity ( jstor ) Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF aircraft, bendable, buckling, compact, compliant, design, experimental, foldable, mav, optimization, storage, uav, unmanned, wing City of Gainesville ( local ) - Genre:
- Electronic Thesis or Dissertation
born-digital ( sobekcm ) Mechanical Engineering thesis, Ph.D.
## Notes- Abstract:
- Demand for deployable MAVs and UAVs with wings designed to reduce aircraft storage volume led to the development of a bendable wing concept at the University of Florida (UF). The wing shows an ability to load stiffen in the flight load direction, still remaining compliant in the opposite direction, enabling UAV storage inside smaller packing volumes. From the design prospective, when the wing shape parameters are treated as design variables, the performance requirements : high aerodynamic efficiency, structural stability under aggressive flight loads and desired compliant nature to prevent breaking while stored, in general conflict with each other. Creep deformation induced by long term storage and its effect on the wing flight characteristics are additional considerations. Experimental characterization of candidate bendable UAV wings is performed in order to demonstrate and understand aerodynamic and structural behavior of the bendable load stiffened wing under flight loads and while the wings are stored inside a canister for long duration, in the process identifying some important wing shape parameters. A multidisciplinary, multiobjective design optimization approach is utilized for conceptual design of a 24 inch span and 7 inch root chord bendable wing. Aerodynamic performance of the wing is studied using an extended vortex lattice method based Athena Vortex Lattice (AVL) program. An arc length method based nonlinear FEA routine in ABAQUS is used to evaluate the structural performance of the wing and to determine maximum flying velocity that the wing can withstand without buckling or failing under aggressive flight loads. An analytical approach is used to study the stresses developed in the composite wing during storage and Tsai-Wu criterion is used to check failure of the composite wing due to the rolling stresses to determine minimum safe storage diameter. Multidisciplinary wing shape and layup optimization is performed using an elitist non-dominated sorting genetic algorithm: NSGA-II. Simultaneous maximization of aerodynamic efficiency and aggressive flight load carrying capacity are chosen as two design objectives. The design points on the Pareto optimal front thus achieved are compared with a baseline design to observe some designs with improved performance both aerodynamically and structurally. Reliability based optimization concludes the work where uncertainties in design variables, design parameters and modeling are considered to achieve designs satisfying specified reliability constraint. ( en )
- General Note:
- In the series University of Florida Digital Collections.
- General Note:
- Includes vita.
- Bibliography:
- Includes bibliographical references.
- Source of Description:
- Description based on online resource; title from PDF title page.
- Source of Description:
- This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
- Thesis:
- Thesis (Ph.D.)--University of Florida, 2010.
- Local:
- Adviser: Ifju, Peter.
- Local:
- Co-adviser: Sankar, Bhavani V.
- Statement of Responsibility:
- by Vijay Jagdale.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Jagdale, Vijay. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 741565063 ( OCLC )
- Classification:
- LD1780 2010 ( lcc )
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PAGE 1 1 EXPERIMENTAL CHARACTERIZATION AND MULTIDISCIPLINARY CONCEPTUAL DESIGN OPTIMIZATION OF A BENDABLE LOAD STIFFENED UNMANNED A IR V EHICLE WING B y VIJAY N ARAYAN JAGDALE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 PAGE 2 2 2010 V ijay Narayan Jagdale PAGE 3 3 To my idol and inspiring father Late Narayan L Jagdale; my caring mother Kaushalya N. Jagdale; my loving wife Ujwala ; my supportive sister Balika and her family ; and my brother Shridhar and his family PAGE 4 4 ACKNOWLEDGMENTS I would like to thank my adviser Dr. Peter Ifju, for his support, guidance and motivation throughout my PhD studies. I would also like to thank him for his patience and allowing me to work with freedom, injecting ideas at appropriate stages. I would like to thank my committee co chair Dr. Bhavani Sankar for serv ing on my committee and advising me on the research. Many thanks to Dr. Raphael Haftka for supporting me, serving on my committee and providing me with invalu able inputs and guidance during my research Thank you to Dr. Anthony Brennan for serving on my co mmittee for his valuable inputs and to allow me to use his lab facilit ies I would also like to acknowledge Dr. Nam Ho Kim for his useful inputs. Thanks to Dr. Bret Stanford for his valuable inputs, discussions and help in the research. Thank you to Dr. Roberto Albertani for his help and allowing me to use the wind tunnel facility at REEF. Many thanks to my past and present lab mates in the Experimental Stress Analysis Lab for their help and making the lab fun and exciting work place. Thank you to Abhishek Patil, Dr. Weiqi Yin Dr. Enoch Chen, Dr. Mulu geta Haile Yaakov Abudaram and other graduate students in the department: Dr. Felipe Viana Anurag Sharma and Dr. Prasanna Thiyagasundaram Thanks to my many wonderful to be lifelong friends that I made during my stay at Gainesville. Finally many thanks to my loved family members who constantly encouraged me during my studies and for their patience and support. PAGE 5 5 TABLE OF CONTENTS ACKNOWLEDGMENTS ........................................................................................................... 4 page LIST OF TABLES ...................................................................................................................... 7 LIST OF FIGURES .................................................................................................................... 9 ABSTRACT ............................................................................................................................. 13 CHAPTER 1 INTRODUCTION ............................................................................................................. 15 Bendable UAV Wing Design ............................................................................................. 16 Problem Statement ............................................................................................................. 18 Approach ........................................................................................................................... 21 2 LITERATURE REVIEW ................................................................................................... 24 UAV Wing Designs to Reduce Storage Volume ................................................................. 24 Compliant Wings ........................................................................................................ 24 Mechanically Deployable Wings ................................................................................. 25 Inflatable Wings .......................................................................................................... 27 Low Aspect Ratio (LAR), Low Reynolds Number (LRN) Aerodynamics ........................... 28 Low Aspect Ratio Studies ........................................................................................... 28 Low Reynolds Number Studies ................................................................................... 29 LAR and LRN Combined Studies ............................................................................... 29 Wing Airfoil and Planform Parameters Affecting Aerodynamics ........................................ 30 Wing Optimization Studies ................................................................................................ 31 University of Florida Flexible Wing MAV ......................................................................... 34 3 EXPERIMENTAL CHARACTERIZATION ..................................................................... 36 Design and Manufacturing of Experimental Wings ............................................................ 39 Visual Image Correlation (VIC) ......................................................................................... 40 Wing Compliance in the Folding Direction ........................................................................ 43 Wing Load Stiffening Ability in Positive Flight Load Direction ......................................... 45 Wind Tunnel Aerodynamic Measurements ......................................................................... 51 Storage Induced Creep Deformation Measurement ............................................................ 54 Material Creep Characterization ......................................................................................... 57 Experimental Setup ..................................................................................................... 58 Data Analysis .............................................................................................................. 59 Experimental Characterization Conclusions ..................................................................... 66 PAGE 6 6 4 MULTIDISCILINARY SHAPE AND LAYUP OPTIMIZATION ..................................... 68 Wing Model ....................................................................................................................... 72 Wing Analysis Techniques ................................................................................................. 74 Aerodynamic Analysis ................................................................................................ 74 Structural Analysis Limit Flight Velocity Calculation ............................................... 79 Storage Analysis Minimum Safe Storage Diameter Calculation ................................ 90 Wing Manufacturing Layup Orientation and Opt imization Considerations ......................... 93 Optimization Problem Formulation .................................................................................... 97 Optimization Algorithm ..................................................................................................... 99 Results an d Discussion ..................................................................................................... 101 5 DESIGN OF BENDABLE WING UNDER UNCERTAINTY ......................................... 111 Uncertainty Quantification and Propagation ..................................................................... 113 Reliability Based Design Optimization (RBDO) of Bendable Wing ................................. 117 Design Space Reduction and RBDO Problem Formulation ........................................ 117 Response Surface Approximations ............................................................................ 118 Results and Discussion ..................................................................................................... 122 6 CONCLUSIONS AND FUTURE WORK ........................................................................ 130 LIST OF REFERENCES ........................................................................................................ 136 BIOGRAPHICAL SKETCH ................................................................................................... 146 PAGE 7 7 LIST OF TABLES Table page 31 Spanwise strain measurements during the creep study. ................................................... 55 32 Observed glass transition temperatures based on DMA test data .................................... 60 41 Multimesh extrapolation mesh sizes used ...................................................................... 83 42 Candidate layups that can be used for wing manufacturing ............................................ 95 43 Candidate layups considered during the wing optimization study ................................... 96 44 Side constraints for design variables. ............................................................................. 98 45 Objective function and constraint values for designs noted in Figure 419. .................. 102 46 Variable values for pareto front designs and the baseline wing noted in Figure 419. ... 103 47 Design variable and objective function values for the Pareto design points noted in Figure 422 .................................................................................................................. 108 48 Design variable and function values for the Pareto design points noted in Figure 4 24 110 51 Uncertainties in random design variables ..................................................................... 114 52 Uncertainties in random parameters ............................................................................. 114 53 Computational Model Uncertainties ............................................................................. 115 54 Uncertainties for the deterministic Pareto front designs noted in Figure 5 1 ................. 116 55 Current probability of failure for Pareto optimal designs noted in Figure 51 ............... 117 56 RBDO: side constraints for the design variables .......................................................... 118 57 Surrogate models with associated PRESSRMS and PRESSRMS (%) ................................ 122 58 Design variable and objective function values for the Pareto design points noted in Figure 52 .................................................................................................................... 124 59 Design variable and objective function values for the Pareto design points noted in Figure 52 .................................................................................................................... 125 510 Design variable and objective function values for the Pareto design points noted in Figure 54 .................................................................................................................... 127 PAGE 8 8 511 Design variable and objective function values for the Pareto design points noted in Figure 54 .................................................................................................................... 128 PAGE 9 9 LIST OF FIGURES Figure page 11 Typical NACA 4 digit airfoil (top), Example of a thin airfoil utilized in present research (bottom). .......................................................................................................... 16 12 Applied Research Associates Inc. Nighthawk MAV [128] incorporates a bendablewing (left) that can be folded for compact stor age (right). .............................................. 17 13 Addition of curvature and sweep provides dissimilar bending stiffness. Beams are bendable / foldable in low be nding stiffness direction. ................................................. 17 14 Pocket MAV (left): 13 inch span bendable wing rolled and stored in a parallelepiped container (inset). UFs 2006 IMAVC endurance MAV (right): 6 inch span wi ng rolled into 1 inch diameter. ............................................................................................ 18 15 Major concerns for bendable wing design: a) Initial rolling for storage induced stress failu re, b) Creep due to storage inside a canister, c) In flight buckling due to aggressive flight loads. .................................................................................................. 20 21 BYUs IRIS UAV segmented rolling wing concept (Landon [11]). Wing laid flat (left), one side rolled under (center), both sides rolled under (right). .............................. 25 22 Advanced Ceramics Research Coyote UAV [19] utilizes scissor wing concept. ............. 26 23 ILC Dover Inflatable UAV Wing [28] : Wing in deplo yed condition (left), wing packed in the fuselage (center), wing construction (right). ............................................. 27 31 Bendable wing. The chord wise shape of the airfoil can be seen with respect to the straight edge (left). Once bent, the airfoil shape becomes completely flat (right). ........... 37 32 Straight and swept camber wing molds (top) and the wing planforms (bottom). ............. 40 33 Speckled straight camber wing (left) viewed from top. Folded wing (right). .................. 44 34 Compliant nature of bendable wings. Upon folding root airfoil flattens out in straight cambered wing (left) and in swept cambered wing (right). ............................................. 45 35 straight camber wing (left) and on swept camber wing (right). ....................................... 46 36 Three point bend test. Test schematic (top), test setup (left), supports are positioned at the center of pressure for each wing half (right). ........................................................ 47 37 Chord normalized (z/c) shape of straight wing: initial shape (left) and buckled shape (right). ........................................................................................................................... 48 PAGE 10 10 38 Chord normalized (z/c) shape of swept wing: initial shape (left) and buckled shape (right). ........................................................................................................................... 48 39 Chord Normalized camber (left), and normalized displacement at the loading point (right). ........................................................................................................................... 49 310 Graphical depiction of the root airfoil camber. The exaggerated camber for both straight camber (left) and swept camber (right) wings throughout the range of loading. ......................................................................................................................... 50 311 Lift coefficient vs AOA (left) and Drag coefficient vs Lift coefficient (right) at Re = 7x104 ............................................................................................................................. 53 312 L/D ratio vs Lift coefficient (left) and Pitching moment coefficient vs Lift coefficient (right) at Re = 7x104 ...................................................................................................... 53 313 Measured out of plane creep deformation of the straight camber wing (top) and swept camber wing (bottom) after being stored at 70 C for 24 hour (picture 1 hr after unfolding). ............................................................................................................. 56 314 DMS 110U equipment used in the study (left), composite specimen inside the sample holder (right). ................................................................................................................ 58 315 DMA test specimen : 0/90 specimen (left), 45 specimen (right). .................................. 59 316 DMA test data : 1 Hz frequency slice. Storage modulus and tan delta versus the test temperature. ................................................................................................................... 60 317 Creep compliance curves at different isothermals for 0/90 specimen. ............................. 62 318 Master creep curve for 0/90 orientation specimen (Tref = 30C). .................................... 63 319 Creep compliance curves at different isothermals for 45 specimen. .............................. 63 320 Master creep curve for 45 orientation specimen (Tref = 30C). ..................................... 64 321 Comparison of normalized master creep curves for 45 and 0/90 specimen (Tref = 30C). Curves are normalized using their respective initial creep compliance values and show % change in the creep compliance values. ...................................................... 65 41 Wing root airfoil control variables. ................................................................................ 73 42 Wing planform shape control variables. ......................................................................... 73 43 Example of equally spaced panel distribution (left), same number of panels with chord wise cosine and span wise half sine spacing (right). ............................................. 76 44 Change in aerodynamic coefficient predictions for straight camber wing with the inverse of the number of panels. .................................................................................... 77 PAGE 11 11 45 Change in prediction error with the inverse of the number of panels (left), Tradeoff between prediction error and computational cost (right). ................................................ 78 46 Comparison of results from aerodynamic model and wind tunnel testing of straight camber wing at Re = 7x104. (Model uses 14x24 cosine/half sine panel distribution). ..... 79 47 Completely buckled shape of the baseline wing (left), buckling analysis possible win g structural behavior plots (right). ............................................................................ 82 48 Singly curved specimens: 45 deg and 60 deg (left) [94] and the three point bend test sch ematic (right). ........................................................................................................... 84 49 Comparison of experimental and model predictions for 60 deg singly curved specimen. ...................................................................................................................... 85 410 60 deg singly curved specimen: tradeoff between prediction error and element size (left), tradeoff between prediction error and normalized computational cost (right). ....... 86 411 Comparison of experimental and model predictions for 40, 45 and 60 deg singly c urved specimen three point bend test. ........................................................................... 86 412 Comparison of experimental observations and model predictions (20x36 mesh) for straight and swept camber wing three point bend tests detailed in Chapter 3. ................. 87 413 Straight camber wing: tradeoff between predicti on error and element size (left), tradeoff between prediction error and normalized computational cost (right). ................ 88 414 Comparison of wind tunnel test data and the results from analysis model. ...................... 89 415 Rectangular strain rosettes G1, G2 and G3 are mounted on the un derside of the swept camber wing .................................................................................................................. 91 416 Predicted and measured chord wise strains for different folding diameters (left), similar measurements for span wise strains (right). ........................................................ 92 417 Model percent prediction error in chord wise strains for different folding diameters (left), similar measurements for span wise strains (right). .............................................. 93 418 Bending force required for flat plate wing laminate layup s (left) and diameter to which wings can be folded without bending stress induced failure (right). ..................... 96 419 Pareto optimal front: tradeoff between Limit flight velocity and L/D ratio. .................. 101 420 Root airfoil shapes (top), curvatures along root airfoils (left) and planforms of semi wings for designs A, B, C, D, E and baseline wing. ..................................................... 104 421 Wing flight load analysis for the baseline design and Pareto front designs A, B, C, D and E. .......................................................................................................................... 105 PAGE 12 12 422 Pareto optimal front: Effect of fixing layup and geometric twist angle = 0. .................. 107 423 Root airfoil shapes (left) and planforms of semi wings for designs 1, 1, 2, 3 and baseline wing noted in Figure 4 22. ............................................................................. 108 424 Pareto optimal fronts: effect of Cm constraint. .............................................................. 109 425 Root airfoil shapes (left) and planforms of semi wings for designs 4, 5, 6, 7 and baseline wing noted in Figure 4 24. ............................................................................. 110 51 Selected Pareto optimal design points a1, a2 and a3 for uncertainty propagation and probability of failure study. .......................................................................................... 115 52 Pareto optimal fronts: Deterministic designs compared with RBDO designs of different levels of reliability index constraint. .............................................................. 123 53 Root airfoil shapes (left) and planforms of semi wings for designs R1, R2, R3 and baseline wing noted in Figure 5 2. ............................................................................... 125 54 Pareto optimal fronts: Deterministic designs compared with RBDO designs of different levels of reliability index constraint. .............................................................. 127 55 Root airfoil shapes (left) and planforms of semi wings for designs R4, R5, R6, R7 and baseline wing noted in Figure 54. ......................................................................... 128 PAGE 13 13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EXPERIMENTAL CHARACTER IZATION AND MULTIDISCIPLINARY C ONCEPTUAL DESIGN OPTIMIZATION OF A BENDABLE LOAD STIFFENED UNMANNED AIR VEHICLE WING By Vijay Narayan Jagdale December 2010 Chair: Peter G. Ifju Cochair: Bhavani V. Sankar Major: Mechanical Engineering Demand for deployable MAVs and UAVs with wings designed to reduce aircraft storage volume led to the development of a bendable wing concept at the University of Florida (UF) The wing shows an ability to load stiffen in the flight load dire ction, still remaining compliant in the opposite direction, enabling UAV storage inside smaller packing volumes. From the design prospective, w hen the wing shape parameters are treated as design variable s the performance requirements : high aerodynamic ef ficiency, structural stability under aggressive flight loads and desired compliant nature to prevent breaking while stored in general conflict with each other Creep deformation induced by long term storage and its effect on the wing flight characteristic s are additional considerations. Experimental characterization of candidate bendable UAV wings is performed in order to demonstrate and understand aerodynamic and structural behavior of the bendable load stiffe n ed wing under flight loads and while the win gs are stored inside a canister for long duration in the process identifying some important wing shape parameters A multidisciplinary multiobjective design optimization approach is utilized for conceptual design of a 24 inch span and 7 inch root chord b endable wing. Aerodynamic performance of the wing is PAGE 14 14 studied using an extended vortex lattice method based Athena Vortex Lattice (AVL) program. An arc length method based nonlinear FEA routine in ABAQUS is used to evaluate the structural performance of the wing and to determine maximum flying velocity that the wing can withstand without buckling or failing under aggressive flight loads. An analytical approach is used to study the stresses developed in the composite wing during storage and Tsai Wu criterion is used to check failure of the composite wing due to the rolling stresses to determine minimum safe storage diameter. M ultidisciplinary wing shape and layup optimization is performed using an elitist non dominated sorting genetic algorithm: NSGA II. Simultaneous maximiz ation of aerodynamic efficiency and aggressive flight load carrying capacity are chosen as two design obj ectives. The design points on the Pareto optimal front thus achieved are compared with a baseline design to observe some designs with improved performance both aerodynamically and structurally. Reliability based optimization concludes the work where uncert ainties in design variables, design parameters and modeling are considered to achieve designs satisfying specified reliability constraint. PAGE 15 15 CHAPTER 1 INTRODUCTION R econnaissance, surveillance and target acquisition (RSTA) mission requirements have been a driving force in the development of unmanned air vehicles (UAV) and micro air vehicles (MAV) over the years. From the initial definition of Micro Air Vehicle [1] being an aircraft with less than 15.24 cm (6 inch) wing span weighing less than 90 gms (~ 3 oz), research is now moving towards Nano Air Vehicles (NAV) [2] [3] having less than 7.5 cm wing span and weighing less than 10 grams. MAVs are envisioned to be inexpensive and expendable vehicles that may be equipped with visual, acoustic, chemical, or biological sensors, and are able to fly autonomously or remotely by a pilot. Apart from militar y and defense RSTA applications; examples being over the hill and aroundthe corner battlefiel d surveillance, bomb damage assessment, chemical weapon detection, etc, MAVs are useful for civil and commercial applications as well such as wild life stud ies, environmental, agriculture and traffic monitoring. On the lift generation concept side, the res earch community ha s been focusing on the development of MAVs using fixed wings while parallel recent developments have been made on morphing wing concepts, flapping wings and rotary wing concepts. The University of Florida (UF) has been active in the annu al International Micro Air Vehicle Competitions (IMAVC) since its start in the year 1997 and has won the competition eight times from year 199 9 to 2006. Various unique wing concepts have been developed while participating in these competitions as well as to meet requirements of various externally funded projects ; the bendable wing is one such exciting concept that helped UF w i n the 2006 IMAVC. The requirement for a flying vehicle that has highest endurance per unit storage volume motivated the development of aerodynamically efficient bendable wing which can be rolled around the air vehicle fuselage for storage into small volume canisters. PAGE 16 16 Bendable UAV Wing Design The concept of rolling under cambered, thin flexible, monolithic composite wing around the fus elage, to reduce packing volume of small UAVs or MAVs, is very unique to University of Florida bendable wing micro air vehicle designs As opposed to conventional airfoils, the wings utilize a thin airfoil which has thickness to chord ratio of 0.24 to 0.3 %. Depending on the air vehicle configuration the airfoils also use a reflex (negative camber) towards the trailing edge to reduce wing pitching moment (Refer Figure 11). Figure 11. Typical NACA 4 digit airfoil (top), Example of a thin airfoil utilized in present research (bottom). Such wings are typically constructed from monolithic bi directional plain weave graphite/epoxy composite shells, and can be rolled around the fuselage of the vehicle, an example as seen in Figure 12. The structural behavior of the wings is similar to a tape measure. In a tape measure, the addition of curvature increases the bending stiffness and makes the tape stiff in one direction but it still remains compliant and bendable in the other direction (refer PAGE 17 17 Figure 13). Presence of camber in the bendable wing creates similar effect. Addition of sweepback is found to further increase the wing stiffness (refer Figure 13). Figure 12. Applied Research Associates Inc. Nighthawk MAV [128] incorporates a bendablewing (left) t hat can be folded for compact storage (right). Figure 13. Addition of curvature and sweep provides dissimilar bending stiffness Beams are bendable / foldable in low bending stiffness direction. This bendable wing concept have been demonstrated and used on air vehicles that range in size from 6 to 36 inch wingspans and are capable of being packed within volumes of 3 to 300 cubic inch [4] [5] The UF team has a US patent on the bendable wing concept [6] Such a compact air vehicle configuration is desirable for a number of potential applications. These PAGE 18 18 vehicles can be stored in a canister within the platform of a manned air vehicle or a larger UAV. Upon release from the can ister, the wings will spring back to the desired aerodynamic shape, and then air vehicle will fly to and around the area of interest. Vehicles have also been constructed with a bendable wing in order to fit them into the cargo pocket of a soldiers battle field uniform, providing reduced storage space and easy at will access to over the hill surveillance capabilities ( Figure 14 left). UFs 2006 international micro air vehicle competition endurance MAV ( Figure 14, right) utilizes the bendable wing technology to minimize the total aircraft packed size, resultant highest endurance per unit packing vol ume lead to UF winning the competition [7] Figure 14. Pocket MAV (left): 13 inch span bendable wing rolled and stored in a parallelepiped container (inset). UFs 2006 IMAVC endurance MAV (right): 6 inch span wing rolled into 1 inch diameter. Problem Statement The bendable wing design considerations incorporate numerous challenges. To enable the UAV to fit inside a storage can ister, the wing is rolled/bent around the fuselage into a cylindrical shape. This may introduce large amount of strains in the wing and depending on the initial wing geometry and the number of composite layers used in the wing manufacturing, may result in the laminate failure ( Figure 15a). Depending on the mission mode, the application conditions may PAGE 19 19 require storage of the bendable wing along with the UAV from negative temperatu res to elevated temperatures for extended periods of time. The high initial folding strains, viscoelastic nature of the material of construction ( carbon/epoxy composite) combined with the potentially extended storage duration at elevated temperatures will give rise to creep strains and creep deformations ( Figure 15b) The excessive creep deformations may affect the wing aerodynamics (especially wing pitching moment) and interfe re with the aircraft trim settings, potentially leading the vehicle away from the intended target location or imposing difficulty in navigating the air vehicle. This necessitates creep characterization of the wing For thin walled structures, like bendabl e wing s the bending stiffness (corresponding to out of plane deformation) is several orders smaller than the membrane stiffness (corresponding to the inplane deformation). During the aggressive flight maneuvers, due to the nature of the aerodynamic loadi ng, for bendable UAV wings the wing bending stiffness becomes important. In the initial generations of the bendable wing designs, which used shallower airfoils with straight quarter chord camber (all airfoils positioned at different spanwise stations are a ligned in a same line at their individual quarter chord locations), insufficient bending stiffness resulted in the in flight snap through buckling of the wing root airfoil section during aggressive flight maneuvers During pull up maneuvers when the wing e xperiences multiple G load factor (3 to 4 times normal flight load), the wing would lose its camber at the root airfoil section and snap through buckle ( Figure 15c). This resu lted in excessive post buckling wing deformations where the wing could no longer generate adequate lift and therefore lost controllability. This observation resulted in a need for increasing the wing bending stiffness to develop more stable flying structure capable of withstanding aggressive flight loads. To increase the stiffness of the wing, the wing geometry was modifi ed and quarter chord sweep back was added: the resulting wing geometry PAGE 20 20 shows load stiffening ability. Increasing wing airfoil quarter chord camber and washout is also found to help increase the wing s stiffness and its flight load carrying capacity. Fig ure 1 5. Major concerns for bendable wing design: a) Initial rolling for storage induced stress failure, b) Creep due to storage inside a canister, c) In flight buckling due to aggressive flight loads. B y having different wing shape s (airfoil and planform ) it is possible to obtain varying wing designs some that are easy to bend and would not fail when rolled for storage but which may also eas ily buckle under aggressive flight loads O ther wing designs are also possible that have high load carrying capac ity but which may fail (laminate failure) when rolled into desired packing diameter. From a structural point of view, a bendable wing design that has higher load carrying capacity (that would not buckle under aggressive flight loads), one that will not fai l when rolled into cylindrical shape for storage and has minimum storage induced creep deformation, is desired. From aerodynamic point of view, we would desire a wing that has high aerodynamic efficiency resulting in higher endurance or lower power require ment for the same flight duration. Minimizing the storage volume requirement constrains the physical dimensions PAGE 21 21 of the horizontal stabilizer present on the air vehicle and its chordwise position with respect to the wing. This limits the pitching moment neu tralization offered by the horizontal stabilizer and requires the wing to have close to zero pitching moment at level flight; in essence we require a flying wing. Selection of wing airfoil with appropriate reverse camber or reflex towards the trailing edge and a wing sweepback would help in meeting this requirement, although presence of reflex and sweepback might reduce the aerodynamic efficiency of the wing. No single wing design is thus expected to satisfy all the structural as well as aerodynamic perform ance requirements and a Pareto front tradeoff study between different competing performance requirements / objectives would be required. On such Pareto front no single wing design is better than other design unless some additional criterion are specified, e.g. mission requirement on minimum endurance, maximum expected flying speed, built in additional payload carrying capacity, etc. Approach Due to the potential non convex and discontinuous design space (wing layup scheme) involved, gradient based optimizers would not work and multiobjective evolutionary algorithm based global optimizers will be better suited for the present research. In the optimization effort, in order to keep the computational cost to a minimum, identifying the lowest order numerical and analytical models that explain the underlying structural or aerodynamic behavior appropriately is an important first step. For aerodynamic analysis use of inviscid vortex lattice method is explored. For the wing aspect ratio considered in the present stud y and the aerodynamic parameters studied, use of low cost medium fidelity panel methods over costly high fidelity Navier Stokes solvers (more appropriate for investigating unsteady aerodynamics) is justified. Wind tunnel testing is used to validate the aer odynamic performance prediction model utilized. PAGE 22 22 The buckling of the wing is associated with loosing the wing root airfoil camber under aggressive flight loads While amount of lift generated varies with change in camber, the amount of camber change that the wing undergoes before buckling is considered and experimentally observed to be small and as a result the pressure distribution over the wing is assumed to be unchanged throughout the buckling analysis. The experimental validation of this technique then becomes the second important step. For analyzing wing failure due to rolling stresses, an experimentally validated strain superposition approach is used and a classical laminate theory based analytical method is utilized to calculate the minimum safe diameter to which the wing can be cylindrically rolled/bent without the occurrence of laminate failure (first ply failure). To minimize the storage induced creep deformations, experimental creep measurement observations are used to constrain the wing design space such that during the optimization study wing designs will be selected that would undergo minimum creep deformations. The o bjectives of the present study are thus twofold. First, e xperimentally characterize the candidate baseline bendable wing designs to demonstrate the wings unique l oad stiffen ing ability under aggressive flight loads the compliant nature in the folding direction and storage induced creep deformations, in the process identif ying important wing design parameters that give the wing highe r load carrying capacity and lower creep deformation s Aerodynamic characterization is performed to study effect of addition of sweepback on the wing aerodynamics. The wing buckling behavior under incrementally aggressive flight speeds is also studied in t he wind tunnel. The experimental work is used to identify and validate appropriate structural and aerodynamic numerical and analytical model s for further optimization studies The second objective is to develop a conceptual design framework that would take into consideration the multidisciplinary nature of the design problem with a large number of design variables (wing PAGE 23 23 shape and manufacturing layup scheme ). A method is developed to completely and uniquely defin e the type of wing airfoil shape utilized in t he study Standard wing planform definition parameters are utilized. The wing design p roblem is treated as a constrained multiobjective optimization problem, simultaneously maximizing wing aerodynamic efficiency (wing lift/drag ratio) and the flight veloci ty the wing can sustain without buckling or failing (laminate failure) in flight, while satisfying a storage diameter constraint and other important aerodynamic constraints detail ed later in appropriate section Such a design tool is expected to develop de sign guidelines and avoid or reduce experimental trial and error based bendable wing development Finally while considering uncertainties in the design variables, design parameters and modeling, optimization of the bendable wing is performed to achieve certain reliability in the designs. The write up is organized as follows. A review of the relevant literatur e is provided in Chapter 2. Details of the experimental characterization techniques and results are given in Chapter 3. Multidisciplinary, multiobjective deterministic optimization method used for conceptual design of bendable wing and results are detailed in Chapter 4. Details of the reliability based design optimization scheme where uncertainties in wing design variables, design parameters and modeling are considered to achieve wing designs that satisfy specified reliability requirements is provided in Ch apter 5. Work is summarized in Chapter 6 with suggestions for future research. PAGE 24 24 CHAPTER 2 LITERATURE REVIEW UAV Wing Designs to Reduce Storage Volume Compliant Wings The concept of a rolling flexible, monolithic, cambered, thin, wing, that is manufactured from composite material, around a fuselage, without mechanically folding or collapsing it, to reduce packing volume of small UAVs or MAVs, is v ery unique to the University of Florida micro air vehicle designs. In the literature, only few examples can be found that conceptually propose the use of compliant wings to reduce storage volume, but no working examples could be located. A 1973 patent [8] proposed the use of flexible and resilient metallic wings secured to fuselage on a glider or a self propelled aircraft, with wings that can be folded around fuselage for storage. Another 1984 patent [9] proposes using a roll able airfoil wing filled with a suitable filler material between an upper elastic cambered skin and a lower stretchable straight skin. The wing was proposed to be made in such a way as to break the upper skin camber and rolling the entire wing spanwise into a coil to reduce storage volume. No real life working wing examples of such concepts could be found in literature from the respective authors. Landon et al. of BYU Compliant Mechanisms Research group [10] discussed some compliant mechanism concepts that can be used in the design of deployable wing mechanisms for small UAVs. The proposed compliant mechanisms could be used in place of rigid bo dy joints for deployment of rigid wing segments. Various types of wing deployment motions are possible using such compliant mechanisms [11] e.g. folding, rotating segmented rolling, continuous rolling, in plane bending, sliding, telescoping and tucking. The c ompliant mechanism joint stiffness and potential for resulting wing flutter is one of the main mechanism design PAGE 25 25 consideration s along with the weight addition caused by such mechanisms. A suitable mechanism selection process is demonstrated, resulting in selection of a segmented rolling wing concept for a 45 cm wing span BYUs IRIS small UAV [11] The middle 15 cm of the wing span (occupied by electronic components) is rigid polystyrene foam and the outer halves of the semiwings are divided into 1 cm wide segments of polystyrene foam that are glued using epoxy on a com pliant Kevlar fabric ( Figure 21) Figure 21. BYUs IRIS UAV segmented rolling wing concept (Landon [11] ) Wing laid flat (left), one side rolled under (center), both sides rolled under (right). The gap between segments enables the wing to be rolled down to reduce storage volume. The limitation of this design is its load carrying capacity. In the deployed condition the wing is expected to withstand 3.01 g of turning acceleration, mainly governed by the compressive strength of the polystyrene used [11] Even though segmented rolling is possible with this wing design, a locking mechanism is needed for holding the wing in the in flight configuration. Flying examples of this design could not be located. Mechan ically Deployable Wings Conventional methods used on some of the small UAVs depend on a mechanical approach for storing wings in smaller packing volumes. Spanwise mechanical wing folding has been proposed by many inventors [12] to [14] Researchers at Massachusetts Institute of Technology (MIT) and the Charles Stark Draper Laboratories developed a folding wing to be used on a PAGE 26 26 cannon launched reconnaissance air vehicle [15] [16] The wing utilizes pivots between six spanwise segments of each semi wing that enable the wing to transition from stowed nested wing segments to a deployed aerodynamic surface. The MIT researchers claimed their wing assembly is able to withstand 15000 gs of forward acceleration during the initial canon launch phase [17] Such spanwise folding wings come with a wei ght penalty due to the folding mechanism. Each additional fold while reducing storage volume also increases total weight. Deployment mechanisms become complicated with each additional fold raising doubts about reliability of such mechanisms. A second set of mechanisms, found in the literature, use wing sweep or scissor wing methods to store wings inside the aircraft fuselage. The span and chord lengths of such wings is limited by the length and the width of aircraft fuselage, respectively. Even though su ch mechanisms give rapid deployment of wings, there is an associated weight penalty due to heavier and stronger hinges that are required to carry the entire wing root bending moment. Stowable aircraft structure [18] and Coyote UAV ( Figure 22) from Advanced Ceramics Research (now part of BAE Systems, Inc.) [19] are some examples of such a concept. Figure 22. Advanced Ceramics Research Coyote UAV [19] utilizes scissor wing concept. Wings swing back for storage PAGE 27 27 Telescopic wing concepts [20] although used to improve aircraft aer odynamic efficiency over large mission spectrum, can also be used for reducing aircraft storage volume. Associated weight penalty of the mechanism is one of the design considerations. Inflatable Wings Inflatable wing concepts have been proposed [21] to [24] and som e unique wing configurations has been in use for a long period of time with applications in manned aircraft [25] munition control surfaces, lighter than air vehicles [26] and UAVs [27] In their Apteron UAV (5.1 feet wing span), ILC Dover Inc uses i nflatable wings [28] which are engineered textile and membrane structures that are deployed and supported by inflation pressure ( Figure 23) With such a wing stiffness is directly related to the inflation pressure. An increase in the wing loading requires an increase in inflation pressure and possibly an increase in the wing material thickness. This in turn increases wing weight as well as reduces aerodynamic efficiency caused by thicker airfoils. Figure 23. ILC Dover Inflatable UAV Wing [28] : Wing in deployed condition (left), wing packed in the fuselage (center), wing construction (right). Inflatable and rigidizable composite wings that do not require sustained inflation pressure after deployment have also been developed [29] By rigidization the flexible inflatable wing is co nverted into a rigid composite structure by using several possible mechanisms, such as, thermalchemical reactions, UV chemical reactions and inflation gas chemical reactions. The University of Kentucky Big Blue UAV (6 ft wing span) program uses such an PAGE 28 28 in flatable/rigidizable wing [30] The limited aggressive flight load carrying capacity is one of the limiting factors of such a wing concept. Low A spect R atio (LAR), L ow Reynolds N umber (LRN) A erodynamics Literature on the small unmanned air vehicle and micro air vehicle wing aerodynamic studies is focused on the characterization of low aspect ratio wings at low Reynolds number s (Re) A wing with 24 inch wing span and 7 inch root chord would have an aspect ratio = span2/wing planform area, (b2/S) of 3.4 to 4.6, depending on the taper ratio of 1 or 0.5, respectively. For a flight velocity range of 10 to 20 m/s, root chord Reynolds number for such wings ranges from 1.2x 105 to 2. 4x 105. Aerodynamics at such low Reyno lds number is dominated by viscous flow effects and bound ary layer separation behavior of airfoils is an important aspect to be considered in this flight regime. Low A spect R atio S tudies Early experimental studies of aerodynamics of low aspect ratio wings by Zimmerman [31] and Winter [32] showed the measured lift to be higher than one predicted by linear aerodynamic theories [33] for finite wings at high angles of attack. This sparked an interest in the study of low aspect ratio wing aerodynamics. T ests by Winter [32] were done at Reynolds number range of 0.3x106 to 1.7x106. As the aspect ratio is reduced, high lift co efficient was observed near stall angles for low aspect ratio wings (AR = 1 to 1.25). This was attributed to the strong wing tip vortices interfering with the longitudinal wing circulation. The downward momentum of the tip vortices may keep the flow attached to the upper surface of the wing, increasing stall angle of attack (AOA) [34] The spanwise pressure distribution measureme nts by Sathaye [35] using an array of pressure ports showed the lift distribution for AR=1 wing to deviate from the elliptic lift distribution predicted by the lifting line theory A large reduction in pressure was observed on the upper surface of the wing near the wing tip area indicating the presence of tip vortices. PAGE 29 29 Low Reynolds N umber S tudies The i mportance of the effects of low Reynolds number on the wing aerodynamic performance has been studied by numerous researchers. A irfoils designed to perform at greater than 5x105 Reynolds number, do not perform well as Reynolds number decreases below 5x105 [36] because of boundary layer separation. For low aspect ratio flat plate wings, Mueller and DeLaurier [34] named aspect ratio as the most important design variable affecting wing aerodynamics, followed by wing planform and the Reynolds number. Trailing edge geometry was reported to be a non factor, and the Reynolds number was mentioned to be only important near stall. A survey of low Reynolds number (0.3x105 to 5x105) airfoils by Carmichael [37] indicates that for Re < 0.5x105, laminar separation is a problem and thicker sections (6% and above) can have a significant sized transitional separation bubble (15% to 40% of the airfoil surface) and hysteresis in lift and drag forces. Stall occurs when this bubble has extended to the trailing edge (at high angles of attack). In the range of 0.7x105 Re 2x105, extensive laminar flow can be obtained and airfoil performance improves. A laminar separation bubble can still present problems for a particular airfoil. For Re > 2x105, airfoil performance improves as separation bubble becomes shorter. LAR an d LRN Combined S tudies A large collection of experimental results on different airfoils was published by Selig [38] This has served as a starting point of airfoil designs for many MAV designers. Bastedo and Mueller [39] studied FX63137 airfoil wings with aspect ratios from 3 to 5.4 (close to our study) at Reynolds numbers from 0.8x105 to 2x105. For Re < 1.5x105, they observed highly nonlinear lift curves. While for Re > 1.5x105, lift curves were more linear. The CLmax increased and CD decreased as Reynolds numbers increased. The changes in performance parameters due to PAGE 30 30 change in Re were smaller as aspect ratio was decreased. Increasing the aspect ratio of wing increased the lift curve slope. Torres [40] studied flat plate wings of AR = 0.5 to 2 at Re of 0.7x105, 1x105 and 1.4x105. Zimmerman, inverse Zimmerman, elliptical and rectangular planforms were studied. Torres found wings of aspect ratio below 1.25 to have highly nonlinear lift curves with high AO A at CLmax. For aspect ratios > 1.25, most planforms exhibited more linear lift curves. For aspect ratio < 1.0, Zimmerman planform perfo rmed the worst. For higher aspect ratios, the elliptical planform is seen to be more efficient (higher L/D) than others. Wing A irfoil and P lanform P arameters A ffecting A erodynamics Experimental work on rigid wings by numerous researchers suggested that cambered and thin airfoils would achieve good low Reynolds number performance. Torres [40] found that wings with camber (4% circular) have higher lift and L/D ratio than flat plate wings for the same planforms. The values of CLmax and AOA at CLmax ( CLmax) also increased for the camber ed wings, indicating low aspect ratio wings at low Reynolds numbers benefit from camber as much as high aspect ratio wings at the higher Reynolds numbers. Pelletier and Mueller [41] in their experimental study of 2% thick wings with aspect ratio from 0.5 to 3 tested at Reynolds numbers from 6x104 to 2x105, also found that cambered wings (4%) offer better aerodynamic characteristics (CL, CD, Cm/4) than the flat plate wings for given Reynolds numbers and aspect ratio. Laitone [42] in his wind tunnel testing showed cambered wings to have higher lift to drag ratios other than obvious increase in the lift. Dodbele and Plotkin [43] in their three dimensional inviscid simulations and Kellogg and Bowman [44] in their two dimensional viscous simulations conducted using XFOIL, showed the superiority of thin wings for MAV applications, where the drop in the adverse pressure gradients increases the lift and decreases the drag towards stall. PAGE 31 31 Letko and Goodman [45] performed a wind tunnel investigation on wings of NACA 23012 airfoil with different swe ep back angles of 0, 30, 45 and 60 deg with aspect ratios of 4.13, 4.36, 4.13 and 2.52 respectively. Tests were performed at Reynolds number of 0.99x106 to 1.98x106. With increase in the sweep back, the lift coefficient was found to decrease while the drag coefficient remained nearly the same. Aerodynamic efficiency, as a result, was found to decrease with increase in the sweepback. The slope of the lift curve decreases with increased sweepback and the angle of attack corresponding to the maximum lift coeff icient increases. A large amount of sweepback adversely affects the longitudinal stability of wings near stall, as also indicated by Shortal and Maggin [46] Similar observations were made by Goodman and Brewer [47] for untapered wings of aspect ratios 1. 34, 2.61 and 5.16. The adverse effects of increased sweepback were predominant with the increase of the aspect ratio. Increased sweepback however helped in delaying stall and increasing the maximum lift coefficient. It also helps in increasing the flight R eynolds number while the wing operates at a lower Reynolds number, as famously known. Letko and Cowan [48] tested three wings of taper ratio 1, 0.5 and 0.25 having 2.61 aspect ratio (NACA 0012 airfoil) with a constant quarter chord line sweepback of 45 degree. The test Reynolds number range was 1.1x106 to 1.23x106. At the angles of attack less than 12 and the lift coefficient of 0.52, there is seemingly no differenc e caused by the taper ratio on the lift and the drag characteristics of the wing. Beyond an AOA of 12 however, the wing with higher taper ratio shows marginally higher lift coefficient (CL = 1 for 1 taper ratio versus CL = 0.9 for 0.25 taper ratio). Also for CL > 0.7, aerodynamic efficiency was found to increase with increase in the taper ratio until stall. Wing O ptimization S tudies Apart from configuration and path planning, n umerous studies can be found in the literature with multiobjective optimization of the shape and size the MAV and UAV wings Due PAGE 32 32 to the large number of function evaluations required during optimization these studies typically use low fidelity analytical or numerical models for aerodynamic and structural analysis. Such low fidelity aer odynamic models, for example, may not be able to account for the complicated flow behavior associated with low aspect ratio wings flying at low Reynolds number and may have limited applicability range (low angles of attack) but such studies give good insi ght into the interactions between various shape /sizing design variables and studied objective functions. Use of low fidelity tools can be found in the work of Morris [49] and Raise Rohani and Hicks [50] Morris [49] performed a study to find the smallest vehicle (smallest wing) that will satisfy give n mission constraints throughout a theoretical mission, using different empirical and analytical expressions for the aerodynamic, structural weight and propulsion performance evaluation. Whereas, Rais Rohani and Hicks [50] minimized the size of a biplane MAV (wing and vehicle overall dimensions) using an extended interior penalty function method. A vortex lattice method with coarse grid was used for aerodynamic and s tability performance evaluation and well developed empirical equations were used in the propulsion and weights module. Use of high fidelity aerodynamic models can be found in the w ork of Sloan et al. [51] Lian et al. [52] and Park et.al [53] Sloan et al. [51] used a combined 2D thin layer Navier Stokes model and a 3 D panel method to construct a response surface for aerodynamic parameters to optimize the wing geometry for minimum power consumption. The study reveals the superiority of thin wings, and finds that optimal airfoil shapes are insensitive to aspect ratio. Lian et al. [52] conducted gradient based shape optimization of a rigid wing as surrogate for flexible membrane wing to maximize its aerodynamic efficiency. Six points on the wing surface (making sixe design variables) were used to modify wing shape from a baseline shape using thin plate spline interpolation. Moving grid technique and full Navier Stokes solver was used for PAGE 33 33 aerodynamics evaluation. By reducing the camber from 7.5% to 4.8% near the root and increasing from 2% to 4% near the tip the amount of flow separation and form drag is reduced to achieve efficiency improvement. Park et.al [53] in their high aspect ratio (AR = 17.5) long endurance UAV aerodynamic optimization stu dy used the wing airfoil, taper ratio and sweep angle as design variables. Wing sectional airfoil is parameterized with four Bezier curves. A high fidelity Navier Stokes solver is used for aerodynamic predictions. Multiobjective genetic algorithm is used t o simultaneously maximize lift coefficient, lift to drag ratio while minimizing the pitching moment. The p resence of high dimensional design space is reasoned as motivation for use of genetic algorithm for optimization. The s tudy observed the tradeoff betw een pitching moment and other objectives. Use of genetic algorithms in the optimization study can also be found in the work of Torres [40] Lundstrm and Krus [54] Aksugur and Inalhan [55] and Ng et al. [56] Torres [40] used a genetic algorithm to minimize a weighted combination of payload, endurance, and agility metrics, with various discrete (wing and tail planform) and continuous (aspect ratio, propeller location, angle of attack, etc) variables. A c ombination of experimental data and analytical methods were used for aerodynamic analysis. Aksugur a nd Inalhan [55] used multiobjective genetic algorithm and different empirical and analytical expressions for the structural weight and aerodynamics performance evaluation to maximize payload and cruise durat ion of a hybrid propulsion driven tailsitter UAV. Ng et al. [56] optimized a flying wing MAV configuration with winglets using six design variables: angle of atta ck, main wing twist angle, winglet span, main wing chord length, main wing taper ratio and winglet taper ratio Wing shape was optimized to achieve maximum aerodynamic efficiency while attaining specified longitudinal static stability, performance and phys ical constraints. V ortex lattice method was utilized for PAGE 34 34 aerodynamic analysis The a uthor indicated that genetic algorithms are more suited for the potentially disjointed design spaces presented by such MAV optimization efforts and emphasizes that genetic algorithm may only be feasible for lower fidelity tools, due to the large number of function evaluations required for convergence. University of Florida F lexible Wing MAV The velocity scale of the atmospheric turbulence is comparable to the flight speeds of the micro air vehicles. Due to their small size and low inertia, the gust rejection ability and maintaining smooth controllable flight is an important design issue. Low aspect ratio and resulting large wing tip vortex swirling system makes flight contro l of micro air vehicles challenging. Some of the unmanned air vehicles designed at the University of Florida use active morphing mechanisms [57] to solve dynamics a nd control issues while some designs use flexible membrane skin [58] for passive shape adaptation to eliminate the sudden gust effects. The flexible wing design uti lizes two versions : batten reinforced (BR) wing and perimeter reinforced (PR) wing. The BR wing utilizes thin strips (battens) of unidirectional carbon fiber imbedded in the chordwise direction within the membrane skin. The trailing edge of the wing is un constrained, and the resulting nose down geometric twist of each flexible wing section alleviates the flight loads: decrease in CD, decrease in C, delayed stall (as compared to a rigid wing) [59] The p erimeter reinforced wing design leaves the interior of the membrane skin unconstrained, while sealing the perimeter of the skin/ wing using a thin curved strip of carbon fiber. Both the leading and the trailing edges of each membrane section are constrained by the relatively stiff carbon fiber. The positive camberin g (inflation) of the wing lead s to an increase in CL and a decrease (more negative) in C [60] Albertani [61] performed aerodynamic measurements for both BR and PR wings, with dramatic improvements in longitudinal stati c stability of both membrane wings over their rigid counterpart. The BR wing has a noticeably PAGE 35 35 smoother lift behavior in the stalled region, though neither deforms into a particularly optimal aerodynamic shape: both incur a drag penalty. Systma [62] conducted oil surface, laser sheet flow visualization on rigid and perimeter reinforced LAR wings to study separation bubble behavior. For optimizing the morphing wing sha pe controlled by 2 or 3 actuators positioned along root chord to maximize aerodynamic efficiency, Boria et al [63] used wind tunnel hardware in the genetic algorith m based optimization loop and demonstrated feasibility of such an approach. Stanford [64] developed numerical modeling tools for aerodynamic analysis and structura l analysis of flexible membrane wings. Aerodynamic analysis was performed using a steady laminar Navier Stokes solver. Discrete Kirchhoff triangle plate elements were used to model the composite laminate shells, while a nonlinear finite element model was u sed to capture the membrane behavior. These tools were used in aeroelastic tailoring and multiobjective topology optimization studies to identify some interesting looking BR and PR wings performing better than the baseline designs. PAGE 36 36 CHAPTER 3 EXPERIMENTAL CHARACTERIZATION The bendable wing has a unique combination of compliant nature in the folding direction and load stiffening ability in the flight load direction. The camber built into the wing airfoil provides dissimilar stiffness in these two directions Addition of quarter chord sweepback is found to help increase the flight load carrying capacity. To demonstrate these effects experimental characterization of candidate bendable wings was carried out. A n a dditional objective of the experimental study is to identify important wing design parameters that help increase load stiffening ability and reduce strains when the wing is rolled / stored inside a canister, in the process developing bendable wing structural behavior experimental database; a reference to be matched by the numerical / analytical wing analysis models. A comparative study between two wings, one with straight camber and an other with swept camber was conducted. The w ing compliant nature, its load stiffening ability and full field basis permane nt deformation caused by long term creep were measured. Wind tunnel testing wa s conducted to quantify the effect of the addition of sweepback on the wing aerodynamic performance. The bendable wings utilize an under cambered airfoil with reflex towards the trailing edge (TE) to reduce t he need for a horizontal stabilizer. Previous studies [65] have shown thin under cambered wings to be more efficient than those with significant thickness. Wings used in the present study utilize a maximum camber of 6% located at 22% chord and 2% reflex located at 83% chord, although different configurations are possible and might be useful from an increased load stiffening ability poi nt of view. Camber and reflex values are defined as percent of the airfoil chord length. The airfoil ha s been developed by researchers [66] at UF, initially optimi zing it for maximum L/D ratio at fixed angle of attack (6) and Reynolds number (105). Reflex was later added in the airfoil to reduce the wing pitching moment. Due to smaller packing PAGE 37 37 requirements of the MAV/UAV there are limitations on the horizontal stab ilizer dimensions and its downstream spatial location. The addition of reflex in the wing design helps ease and meet these limitations. The resultant airfoil has been used successfully in the past on a wide variety of aircraft including UFs 2005 Internat ional Micro Air Vehicle Competition ( IMAVC ) winning entries [4] Depending on the wing and the payload size, t he bendable wings use one or more layers of plain weave carbon fiber epoxy composite with fibers running in 45 orientation with respect to the wing center chord line. S tress analysis [5] [67] favors a 45 orientation over a 0/90 orientation owing to significantly lower stresses in 45 orientation wing when it is packed inside a canister. Also, the reduced bending stiffness of 45 orientation wing makes it easier to roll and allows its storage in weaker canisters. The shape and corresponding structural behavior of the wing then resemble s a tape measure. A curved spring steel tape measure has the distinct character istic of having high bending stiffness in one direction yet being complian t in the other direction. Compliance arises when the curved cross section flattens out under a bending moment, effectively reducing the moment of inertia of the cross section. Likew ise, the bendable wings can be curled downward, which flattens the camber and the airfoil of the wing ( Figure 31). Figure 31. Bendable wing. The chord wise shape of the airfoil can be seen with respect to the straight edge (left). Once bent, the airfoil shape becomes completely flat (right). PAGE 38 38 The bendable wings also exhibit high stiffness in the positive flight load direction (upward force in level flight) Initial generations of the bendable wing with straight camber experienced structural instability (snap through buckling) during extreme positive loads, e.g. pull up maneuvers. To increase the stiffness of the wing, quarter chord sweep i s added whi le keeping the airfoil constant along the span: the resulting geometry has load stiffening ability and is capable of withstanding larger flight loads When a positive load is applied to the wing, the leading edge ( LE ) of the center portion of the wing woul d deflect downward, increasing the wings centerline camber and moment of inertia. This results in a stable wing structure which becomes stiffer as the positive load is increased. Catastrophic b uckling has never been encountered in flight with similarly lo ad stiffened wing designs. Quantitative analysis of this loadstiffened geometry is presented later in the text. Although sweep back helps in increasing load carrying capacity, it may reduce aerodynamic efficiency of the wing [68] which is investigated here through wind tunnel tests. S torage induced creep deformation is another concern. Depending on the mission mode, the application conditions may require storage of the vehicle from negative temperatures to elevated temperatures for extended periods of time. Initial rolling of the wing for storage i nto a c anister introduces high bending strains in the wing. This combined with the viscoelastic nature of the material o f construction ( carbon/epoxy composite) and the potential extended storage at elevated temperatures necessitates creep characterization of the wing. Wing creep deformations might be excessive, affecting wing flying characteristics and potentially rendering the aircraft unusable or unable to reach the intended target. The remainde r of the c hapter is organized as follows: a brief description of the expe rimental wings is given followed by a description of the experimental setup and the results. PAGE 39 39 A comp arative study between two wings, one with straight camber and another with swept camber is carried out. While both the wing geometries are bendable, the win g with swept camber is an example of a bendable load stiffened wing Wing compliant nature is demonstrated its load stiffening ability and full field basis permanent deformation caused by storage induced creep are measured. The work concludes with a serie s of wind tunnel test results, comparing the aerodynamic performance of the experimental wings. Design and Manufacturing of Experimental Wings For quantitative comparison, two wings are designed, one with a straight camber (0 sweepback ) and other with a s wept camber ( 15 sweepback measured at the quarter chord location). The wings have a 24 inch (61 cm) wing span, 7 inch (17.78 cm) root chord and an aspect ratio of 4.36. The wings can be rolled and stored in a canister of 4.5 inch (11.43 cm) inner diamete r. Both the wings are designed with the same airfoil shape, discussed in the earlier section, at each spanwise station. The sole difference between the two wings is the sweepback angle When the same composite material, layup orientation and number of layers (two) are used for manufacturing, any difference in the structural or aerodynamic behavior can be attributed to the addition of the sweepback angle alone. Wing geometries were designed using in house design software [69] and the layup tools/molds were machined on a 3axis computer numerically controlled ( CNC) milling machine. The mold s are machined from high density tooling board. After machining on the CNC mill, the wing mold s were not perfectly smooth due to the scalloping of the ball end mill and so slight sanding was required for a smooth finish. Accuracy is achieved by first app lying a light trace coat of black spray paint to the mold surface and then sanding until all painted regions are gone. Figure 32 shows the wing mold s (pictured after wings are manufactured). Two layers of T300/934 plainweave carbon fiber epoxy prepreg composite are then la id on the Teflon PAGE 40 40 covered mold and the wings are oven cured under vacuum, at 126C for 4 hours using appropriate vacuum bagging consumables Both the c omposite layers are laid in a 45 orientation with respect to the wing center chord line due to considerations discussed earlier. Figure 32. Straight and swept camber wing mold s (top) and the wing planforms (bottom). Visual Image Correlation (VIC) Experimental characterization of bendable wings involves full field shape and deformation measurements of the wing. Continuous monitoring of the root airfoil and the complete wing shape is required during the compliance check, the load st iffening ability study, as well as the long term storage induced creep deformation measurement studies. A need for full field basis nonintrusive experimental measurement techniques limits the selection to non contacting optical methods, several of which have been reported in the literature. Ifju [66] Albertani [61] and Stanford [64] were among the first researchers to use visual image correlation (VIC) techniqu e [70] for the full field basis deformation measurement of rigid and flexible MAV wings inside and outside the wing tunnel. Galvao et al. [ 72] use d stereo PAGE 41 41 photogrammetry for displacement measurements of a 12.9 cm by 5.9 cm membrane wing. With a camera spatial resolution of 0.2 mm per pixel and direct linear transformation to achieve marker co plane measurements and of plane measurements. Data is available at discrete markers placed along the wing. Jacob et al. [29] also use photogrammetry to measure the deformed wing shape of inflatable wings to quantify the effect of wing warping on its aerodynamics. Fleming et al. [73] use projection moir interferometry (PMI) that requires no such marker placement (a fringe pattern is projected onto the wing surface), and the resulting data set achieved is full field. However, wit h camera spatial resolution on 0.22 mm/pixel, displacement resolutions reported are camera system must be rotated during the angle of attack sweep, and only out of plane data is available, making in plane strain calculati ons, if required, impossible. In the present study, a visual image correlation system, originally developed by researchers at the University of South Carolina [70] and now commercially available from Correlated Solutions Inc, is used to measure wing geometry and displacements. VIC makes use of stereo triangulation: recovering 3 D structure from two imaging sensors, similar to human vision. The first step is to calib rate the VIC system using a known fixed grid of black and white dots. This gives the VIC system information concerning the length scale (pixel spacing) and the locations of the camera with respect to the experimental space. The specimen surface is painted with a random speckle pattern and its images are taken before and after the deformation. By tracking a subset in the images, stereo correlation matches the two 2D images taken simultaneously by the twin cameras to reconstruct the 3D geometry (spatial match ing). Then temporal matching is utilized; by tracking a subset, at a time, of the reference image (taken with no load) to the region PAGE 42 42 in the deformed image that maximizes a normalized cross correlation function [71] full field basis displacements are calculated. As it is unlikely that the deformed coordinates will directly fall onto the sampling grid of the image a dditional accurate grey value interpolation schemes [74] are implemented to achieve optimal sub pixel accuracy without bias. Typical data results that can be obtained from the VIC system consist of the geometry of the surface in discrete x, y, and z coordinates (where the origin is located at the centroid of the speckled area of interest, and the outward normal points towards the cameras, by default), and the corresponding displacements along the wing (u, v, and w). The VIC system places a grid point every N pixels, where N is user defined. A final post processing option involves calculating the in plane strains xxyyxy) if so desired This is done my mapping the displacement field onto an unstructured triangular mesh, and conducting the appropriate numerical differentiation (the complete definition of finite strains is used). VIC Theoretical Accuracy Estimation of theoretical in plane displacement accuracy [61] is possible with the knowledge of the VIC setup. The following imaging parameters need to be defined: Field of view (FOV): L by L (m2) Recording resolution: N by N (pixels2) Subset size (SS): m by m (pixels2) Image displacement accu racy: 1 (pixels) Image speckle dimension: 1 (pixels) Object speckle dimension: 0 (m) With these definitions, we can determine parameters that are commonly used in computer vision: Magnification factor, MT (pixels/m) MT = L/N (3 1) PAGE 43 43 Object d 0 (m): 0 1 1 *MT (3 2) Considering the typical values for the MAVs tested during this work, we have a FOV of 0. 76 X 0.76 m2 and N about 1000. Assuming for the cameras used an image displacement accuracy of 0.01 pixels, using Equation (3 2) we obtain the best theoretical target displacement accuracy of 0.0076 mm Out of plane displacement accuracy is about twice t he inplane displacement accuracy, also reported by Albertani [61] and Stanford et al. [75] Though not nondimensional parameter independent of speckle size), a high value (compared to few microstrains resolution of strain gages, for example) owing to the differentiation methods used. Wing Complian ce in the Folding Direction In this compliance study, each wing is clamped on a long C shaped structure at its two mounting points to enable free rolling of the wings without introducing any rigid body motion due to movement of the support points. The wing upper surface is coated with an even thin coat of flat white paint and the random speckles are created using a flat black spray paint ( Figure 33). A h igh resolution visual image correlation technique i s used to study the compliant nature of the bendable wings. T win synchronized cameras, each looking from a different viewing angle, are installed above the wing. The wing is normally mounted on the fuselage through two holes that are drilled into the root airfoil section ( Figure 33). The chordwise position of these hole s bound an imaginary line on the root airfoil which is approximately straight when the wing is in the deployed condition and also remains straight after the wing is rolled for storage. Such a mounting enables easy wing bending without introducing significa nt chordwise strains caused by chordwise pushing or pulling offered by mounting points on the wing or vice versa. PAGE 44 44 Figure 33. Speckled straight camber wing (left) viewed from top. Folded wing (right). After calibration of the VIC camera system, a reference image for individual wings is taken when the wings are in a deployed condition. Appropriate rolling moments are applied on the individual wings while monitoring the section of the wing close to its root airfoil. Upon application of a bending moment for folding, both; the straight and swept cambered wing, showed compliant nature. On initial application of the rolling moment and at the start of the folding, t he root airfoil flattens out, as shown in Figure 34 Further application of the rolling moment causes the local airfoils at various spanwise locations to progressively flatten out, enabling the wing to be rolled into a cylindrical shape and stor ed inside a canister. The swe pt cambered (load stiffening) wing requires a marginally higher rolling moment than the straight cambered wing, but both the wings could be easily rolled with little human effort. The observation of seemingly two step result: first flattening of root airfo il and then cylindrical rolling of the wing can be utilized to develop an analytical model based on strain superposition principle to perform stress analysis of the wing during folding process Initial flattening of the root airfoil would introduce chordw ise strains and further cylindrical rolling would introduce PAGE 45 45 spanwise strains. Superposition of these strains and knowledge of laminate layup can be used to perform laminate failure analysis at the wing root to find out safe storage diameter for a given wing. Figure 34. Compliant nature of bendable wings. Upon folding root airfoil flattens out in straight cambered wing (left) and in swept cambered wing (right) Wing Load Stiffening Ability in Positive Flight Load Direction To study the behavior of th e bendable wings under various (positive) loading conditions, a special three point bend test fixture i s developed for testing wings on a MTI universal tensile PAGE 46 46 testing machine. In the load stiffening study, the individual wings are supported at two locatio ns and a downward force is applied at the aircraft center of gravity location (close to the wing roots quarter chord location). To determine the two support points on the wing, both the straight and the swept camber wings are analyzed with Athena Vortex L attice (AVL) [76] program AVL employs an inviscid, extended vortex lattice model for the lifting surfaces and is useful for the aerodynamic and flight dynamic ana lysis of aircraft of arbitrary configuration. In AVL, wing geometry at various spanwise stations is defined along with the normal flight conditions. AVL gives wing aerodynamic coefficients as well as the Cp) distribution over the wing as an output. Figure 35 shows the Cp distribution on semi wing planforms Figure 35. output from AVL straight camber wing (left) and on swept camber wing (right). The effective center of pressure on each wing half is then calculated and used as a support location during the bend test. The test setup i s configured in order to f ix the stereo cameras looking down on the speckled wing test specimen upper surface ( Figure 36). Individual wings are fixed at the root airfoil section on a C shaped bracket through their fuselage mounting holes and the loading point is adjusted to apply the load at the center of gravity location of the vehicle. This is thought to closely simulate the actual flight condition loading on the wing. A downward PAGE 47 47 pulling load is applied at the wing center section using an MTI universal testing machine ( Figure 36). An initial preload is applied on individual wings to force the m to touch the supports and attain a stable configuration for further loading. Loads a re measured using a standard calibrated load cell of 1000 lbf (~ 4500 N) capacity available from Interface Inc. The rated maximum error in the load measurement is 0.1 lbf ( 0.45 N). The VIC setup permit s the accurate measurement of the three dimensional geometry of the wing under each loading condition. Figure 36. Three point bend test. Test schematic (top), test setup (left), supports are positioned at the center of pressure for each wing half (right). First, the undeformed shape of the straight camber wing and the swept camber wing i s measured. I ncreasing loads a re applied to the center section and the new shapes a re compared with the undeformed shapes Figure 37 shows the initial undeformed (z/c) shape and final buckled shape o f the straight camber wing, while Figure 38 shows that for swept camber wing. As can be seen, due to the nature of loading, the tip area moves up and in the bu ckled stage both the wings lose their camber at the root airfoil while maintaining their camber in the tip region. PAGE 48 48 Figure 37. Chord normalized (z/c) shape of straight wing: initial shape (left) and buckled shape (right). Figure 38. Chord normalized (z/c) shape of swept wing: initial shape (left) and buckled shape (right). Using VIC, the change in the camber of the wing root airfoil is monitored throughout the loading history. The out of plane (w) displacement of the loading point loc ation on the root airfoil is also monitored. Loading i s co ntinued until the wings buckle at the root area, marked by a loss of the wing camber at the root airfoil: the structure is no longer able to sustain the applied loads (change in slope or negative sl ope of the load versus displacement graph). Figure 39 PAGE 49 49 shows the plot of applied center load versus change in chord normalized camber at the root airfoil (left) as well as the plot of the applied load versus chord normalized out of plane displacement of the loading point location on the root airfoil (right). Figure 39. Chord Normalized camber (left), and normalized displacement at the loading point (right). Due to the preloading used in the experiment, the initial camber at the root airfoils is slightly different than the design camber. The starting camber is consistent with the structural behavior shown by two wing geometries throughout the loading history. On the initial load application, the straight camber wing starts to lose its camber at the root airfoil whereas; the swept camber wing gain s camber. As the load increases in the swept camber wing, the leading edge of the root airfoil moves downward, incr easing its moment of inertia and the wing stiffness. The root camber of the swept camber wing is found to increase ( Figure 39, left, red line against dashed vertical blue straight line), as a result, a higher incremental load is needed for additional incremental displacement of the loading point ( Figure 39, right). T he swept camber (load stiffening) wing continued to increase its root camber as the load i s increased before buckling at a higher load than what the straight camber wing could support. The wing structural behavior is termed snap through PAGE 50 50 buckling here, due to the nature of the experimentally observed load deflection and load camber plot. The stiffness of the wing and the slope of the load response curve are found to decrease with increasing load. At the limit load the curves has zero slope and beyond the s nap through point load deflection curve shows negative slope. As can be seen in Figure 39, the straight camber wing can support a maximum load of 9 N (2 lbs) be fore buckling, whereas the swept camber wing can support a maximum load of 30.74 N (6.91 lbs). Based on the UAV maximum take of weight of approximate ly 0.44 kg (~ 4.3 N) this provide s a load factor greater than 7 Gs for the swept camber wing as compared to vertical load factor of 2 for the straight camber wing. The plot of load versus change in chord normalized root camber ( Figure 39, left) captures the load s tiffening behavior of the wing and gives the maximum load carrying capacity of the wing. For further optimization studies, analysis of such a plot alone would help understand and compare load stiffening abilities and load carrying capacities of different w ing geometries. The actual shape of the root airfoil is shown in Figure 310 for each wing as the center load is increased. Figure 310. Graphical depiction of the root airfoil camber. The exaggerated camber for both straight camber (left) and swept camber (right) wings throughout the range of loading. PAGE 51 51 The location of the fuselage mounting holes on the wing also plays an important role in deciding t he maximum load carrying capacity or buckling load, as termed in this study. Straight forward testing shows that moving the front mount ing hole forward towards the leading edge helps in increasing the buckling load carried by the wing Wind Tunnel Aerodyna mic Measurements As discussed earlier, while sweepback helps in providing the load stiffening ability, it might reduce aerodynamic efficiency (L/D ratio) of the wing. The aerodynamic performance of both the wings is studied in a low speed, low turbulence ( LSLT), open jet wind tunnel. The wind tunnel has a bell mouth inlet of 3.7 m x 3.7 m cross section. A flo w conditioning section, consisting of honeycomb screens and mesh structures positioned ahead of a contraction section provides uniform, low turbulent incoming flow to a 1.1 m x 1.1 m test section The open jet test section is enclosed by a 3.4 m high x 3.7 m wide x 4.6 m long rigid enclosure. A diffuser section installed at the downstream of the open jet test section make s a transition from a square cro sssection to a 1.5 m diameter circular section which houses an axial fan driven by a 50 HP e lectric motor. The wind tunnel is capable of test speeds ranging from 0 to 22 m/s with turbulence levels below 0.16%. The wind tunnel flow velocity is monitored by a pitot probe installed in the inlet of the test section, and the air temperature is monitored by a resistance temperature detector (RTD) sensor mounted on the inside of the test section. Further details of the wind tunnel are given by Albertani et al. [77] A calibrated six component strain gauge internal sting balance is used to measur e the aerodynamics coefficients. The rated maximum error in force and moment measurements is about 0.075% of full scale (45 N normal and 22.25 N axial force). A s ampling rate of 1000 Hz is used and at each angle of attack data is averaged based on a 2 second sampling time. To reduce bias and hysteresis effect s introduced due to the monotonically increasing AOA, the AOA PAGE 52 52 sweep is randomized. Three repetitions are performed at each AOA and Reynolds number setting. Considering the error in AOA, wing area, chord measurement and standard deviation of repeat measurements the expected maximum uncertainty (95% confidence interval) in the aerodynamic coefficient measurement is estimated to be 5% for CL, CD, Cm and 7% for L/D ratio Both of the wings are tested at mean aerodynamic chord based Reynolds number of 5x104 and 7x104. Aerodynamic behavior at both these Reynolds numbers is essentially the same. Data corresponding to Re = 7x104, after streamline curvature correction and downwash correction is presented below. Pitching moment coefficients reported are measured about 25% of the mean aerodynamic chord. No noticeable difference is observed in the lift characteristics of both the wings until near the stall region ( Figure 311). The initial l ift curve slope (C) for both the wings is observed to be the same. Between 11 to 14 AOA the swept camber wing is found to generate higher lift ( CLmax of 1.09) than the straight camber wing (CLmax of 1.05). At low AOA, the swept camber wing showed margi nally higher drag (CD) than the straight camber wing. Lift, drag and resultant L/D ratio behavior ( Figure 312) can be divided into two segments until the stall For CL < 0.6, the drag for the swept camber wing is higher, resulting in marginally lower aerodynamic efficiency. In this segment, the highest L /D ratio for the straight camber wing is 8.4 while for the swept camber wing it is 8.27, observed at CL ~ 0.55 (corresponding to AOA ~ 5). In the second segment of CL > 0.6 and before the stall, the lift characteristics for both the wings are similar whil e the drag behavior and as a result L/D ratio curves for both the wings are intertwined. At high AOA the aerodynamics is dominated by laminar separation effects finally resulting in stall. The swept camber wing shows an important advantage in terms of high er static longitudinal stability ( Figure 312), offering higher dCm/dCL derivative. With the increased sweepback angle PAGE 53 53 aerodynamic center of the wing is expected to move aftwards improving the wing static stability margin. Addition of sweepback angle is thus found not to affect the aerodynamic efficiency of the wing much while improving its static longitudinal stability. Figure 311. Lift coefficient vs AOA (left) and Drag coefficient vs Lift coefficient (right) at Re = 7x104 Figure 312. L/D ratio vs Lift coefficient (left) and Pitching moment coefficient vs Lift coefficient (right) at Re = 7x104 PAGE 54 54 Storage Induced Creep Deformation Measurement The carbon/epoxy composite used for manufacturing the bendable UAV wings possesses viscoelastic behavior. Application conditions may require storage of the bendable UAV wing in the rolled condition inside a canister for an extended period of time. Due to creep effects, after extended storage, the wing may not deploy to the desired shape. This might affect the aerodynamic performance of the UAV in a negative manner if the creep deformations of the wing are excessive. Straight Camber and Swept Camber Wing Co mparative Study To quantify the creep deformations and to check if introduction of sweepback plays any role in increasing or decreasing creep deformation/residual strains, a creep deformation measurement study on straight camber and swept camber wings is p erformed. For this study, both the wings are rolled and stored inside a 4.5 inch diameter composite canister. The canister is then kept inside an environmental chamber at 70 C for 24 hours duration. The 2200 watt environmental chamber has a resolution of 0.02 C and can maintain the set temperature within 1 C. Considering the time temperature superposition principle [125] and the creep master curve developed for the material (detailed in later section), the storage conditions used in the study are expected to simulate approximately 20 months of storage at room temperature. To monitor folding and later residual strains, a CEA 06250UR 350 rectangular strain rosette available from Vishay Micro Measurements is used. The strain rosette is bonded on the underside (pressure side) of the wing, close to the individual wing mid span and mid chord location. Strains are monitored throughout the storage duration, as is the res idual strain when wing is deployed after the storage period. Table 3 1 details spanwise strains observed in the wings. The previously detailed VIC experimental setup is utilized to study full field basis creep deformation of the PAGE 55 55 wings. An image is taken before rolling/storing and another is taken after the storage period: correlation of the two gives the out of plane deformation/permanent set caused by creep. Since the strain ros ette is on the underside of the wing, the observed strain readings are compressive in nature. Upon initial folding, strains along the spanwise direction are observed to be of similar magnitude for both the wings. After 1 h ou r of recovery, residual strain i n the swept camber wing was lower than the straight camber wing, which might indicate that increased stiffness due to addition of sweepback helps in reducing the residual strains. Table 3 1. Spanwise strain measurements during the creep study. Event Straight camber Swept camber Unstrained condition (deployed wings) 0 0 Storage inside canister at Room Temp (folded wings, 24 C ) 4078 4047 After 24 hours, still inside canister, at Room Temp 4539 4449 1 hour after removing from canister, at Room Temp (deployed wings) 360 288 The out of plane creep deformations (w in mm) measured after 1 hour of recovery, are shown in Figure 313. Both the w ings show a small spanwise unsymmetry (about the root airfoil) in the measured creep deformations. When the wing is folded into the storage canister, one wing tip is forced to lie inside the other tip, which presumably corresponds to the slight difference in the creep deformation pattern across the halves of the wing. For the straight camber wing, VIC measurements indicated maximum positive o ut of plane deformation of +1. 42 mm (red area) near the leading edge (bending up in normal flight condition), while the trailing edges at the tip show a 1.6 mm (light blue area) deformation of the wing (remain bent down in normal flight condition). For the swept camber wing, a maximum positive deformation of +1.9 mm is observed at the leading edge near the root airfoil and a 3 mm deformation is observed near the leading edge of the tip The deformations for both the PAGE 56 56 wings near the root airfoil leading edge and trailing edge follow the expected pattern. When the wing is rolled to fit inside a cylinder, the leading edge of the wing near the root area moves up and the trailing edge moves down so as to flatten out the airfoil (see Figure 34). Due to the creep e ffects, the leading edge does not completely recover and remains up, showing positive deformation. Similarly, the trailing edge shows a negative deformation. Figure 313. Measured out of plane creep deformation of the straight camber wing (top) and swe pt camber wing (bottom) after being stored at 70 C for 24 hour (picture 1 hr after unfolding). The negative deformation of the leading edges in the tip area for the swept camber wing is emblematic of the complex behavior of a three dimensional wing shape when it is stored inside the canister. Due to sweepback the wing is stiffer and thus has a greater tendency to spring back to its original shape. Simultaneously, the inside surface of the canister is forcing the top point PAGE 57 57 (maximum camber point) of the tip airfoil down, thus twisting the wing. The incomplete recovery of this twist causes negative deformations to appear near the leading edge of the tip area. The overall creep deformation s in both the wings are relatively small however, and are not expected to affect the wing aerodynamics significantly. The pitching moment change caused by the creep deformations is expected to be in the operating range of the small horizontal stabilizer incorporated on the actual MAV/UAV. Material Creep Characterization In the effort of the conceptual design of a bendable wing, along with other considerations such as the aerodynamic performance and structural stability, minimum creep deformation is one of the important factors. A bendable wing designed to have minimum creep defo rmation for the given storage conditions would be highly desirable. This necessitates creep predictive capabilities and a need for developing a creep master curve and a viscoelastic material model for the material of construction. The material model can th en be used along with a nonlinear finite element analysis technique to predict the long term storage induced creep deformations. Creep testing was performed on the composite material in the 0/90 fiber direction as well as in the 45 direction, both being t he candidate design fiber orientations for the bendable wing. Here the creep master curves are developed leaving other tasks as a future work. The conventional method of directly measuring the response of the viscoelastic material over long periods of time is time consuming. Using accelerated aging processes during short term testing to obtain the creep properties, has been used by numerous researchers [116] [118] Gibson. et.al, [119] [120] used dynamic test methods to study the viscoelastic behavior of polymer ma trix composites. Li Rongazhi [121] used combined dynamic testing using dynamic mechanical analyzer (DMA) and a time temperature superposition (TTSP) technique to study the glass tr ansition temperature of plastic materials. The advantages of using DMA include PAGE 58 58 automated testing, better control of the test environment, ease of including a TTSP technique and simple p reparation of the test specimen Experimental S etup In the present stu dy, dynamic mechanical analyzer, DMS 110U ( Figure 314), was used to measure the viscoelastic creep properties. As the bendable wing creep deformation is due to the flexural mode of loading, material specimens were also tested in flexural mode in the DMA. The material was tested along 0/90 direction and along 45 direction (also the orientation used to manufacture wing). Figure 314. DMS 110U equipment used in the study (left), composite specimen inside the sample holder (right). A 0/90 orientation 2 layer T300/934 composite laminate was laid up and cured under vacuum at 266 F (130C) for 4 hours. Specimens were then cut along 0 and 45 direction s (2 specimen each). Specimen dimensions were selected based on the specimen shape factor and measurable elastic modulus limit chart for the instrument [122] [124] Resultant specimens were measured to be 40 mm long, 10 mm wide and 0.46 mm thick ( Figure 315) Testing Specimen Specimen holder PAGE 59 59 frequencies of 1,5,10, 20 and 50 Hz were used. Testing temperatu re was increased from 30 C to 200 C at a rate of 5C/min with the sampling time being 1 second. As a result storage modulus versus frequency and loss factor versus frequency data was available from DMA equipment, at various isothermals. Isothermals used in the present study were at 30C up to 180 C at 10 C intervals Figure 315. DMA test specimen : 0/90 specimen (left), 45 specimen (right). Data A nalysis From the DMA test data, if we analyze the 1 Hz frequency slice, it is possible to identify the glass transition temperature (Tg) of the test material. Figure 316 sho ws the corresponding plot of variation of the storage modulus and tan delta with respect to the temperature for both the test directions. The 0/90 orientation specimen shows almost twice the initial storage modulus than that of 45 orientation specimen, as expected. Table 3 2 lists the glass transition temperature observed for the test specimen based on different analysis methods. The glass transition temperature based on tan delta peak method is usually reported in the literature [ 121] Tg for the material is found to be about 120 126 C, very close to the curing temperature for the composite. The 0/90 specimen showed marginally higher Tg than the 45 orientation sp ecimen This might indicate the fiber orientation playing a small role in Tg as well. More repetitions of the test specimen would reveal if it is a chance occurrence or a systematic phenomenon. PAGE 60 60 Figure 316. DMA test data : 1 Hz frequency slice. Storage modulus and tan delta versus the test temperature. Table 3 2. Observed glass transition temperatures based on DMA test data Specimen T g C (Tan Delta peak) T g C (Storage modulus inflection) T g C (Storage modulus onset) 0/90 126.4 120.6 106.4 45/45 119.4 112.2 98.7 regression curves were then fit to this data for further analysis. At each isothermal curve, storage modulus and loss factor data w ere combined to get the frequency domain complex moduli (E*) [119] : *()'()"() '()[1()] EfEfiEf Efif (3 3) PAGE 61 61 Complex moduli at each isothermal were then converted to t ime domain relaxation moduli (E) or creep compliance ( J) by using an inverse Fourier t ransform and numerical integration, as follows [119] : 1 0 1 0(){[*()]}(0) (){[*()]}(0) 1 *() *() 1 (0) (0)t tEtFEfdtE JtFJfdtJ where Jf Ef J E A subroutine in Matlab was written to do inverse fast Fourier t ransform (IFFT) and the numerical integration by Simpsons 1/3 rd Rule. The program was validated by testing some known trial function s and their respective Fourier t ransforms, to get an excellent agreement. Relaxation moduli and creep compliance plots at v arious isothermals were combined using time temperature superposition technique [125] By the principle of TTSP, creep response is a function of temperature (T) an d time (t), (,) EETt (3 5) And the effect of temperature on the time dependant mechanical behavior is equivalent to a stretching (or shrinking) of the real time of the creep response for temperature (T) above (or below) the reference temperature (To) by a certain shift factor (aT). 0(,)(,) loglogTETtET t a (3 6) where, where, F 1 indicates inverse Fourier t ransform (3 4) -for all f -at t = 0 only PAGE 62 62 For the present study 30C was taken as the reference temperature and other curves were the n shifted horizontally on the log scale by the shift factors. The shift factors were chosen manually so that the isothermal curves overlap. Alternatively, the shift factors can be estimated from the activation energy of the glass transition relaxation [126] The data analysis detailed above was performed on the 45 orientation specimens as well as on the 0/90 orientation specimens. Figure 317 to Figure 320 show the creep compliance curves at various isothermal s as well as corresponding master curves achieved after horizontal manual shifting of the isothermal curves Figure 317. Creep compliance curves at different isothermals for 0/90 specimen. As we can see in Figure 317, with the increase in temperature the creep compliance increases, as expected The slope of the creep compliance curve also increases with increase in the isothermal temperature. The elevated temperature accelerates the viscoelastic response of the matrix material thus the composite becomes more compliant in nature. Near the glass transition temperature of the material, creep compliance changes by large amount with passage of time. PAGE 63 63 Figure 318. Master creep curve for 0/90 orientation specimen (Tref = 30C). Figure 319. Creep compliance curves at different isothermals for 45 specimen. PAGE 64 64 Figure 320. Master creep curve for 45 orientation specimen (Tref = 30C). As Figure 320 indicates, with DMA testing until a test temper ature of 100C, a master curve at 30C reference temperature can be drawn to have creep compliance predictions for up to ~ 30 years. The addition of test data for 110C and 120C temperatures stretches the master curve in time scale by two orders of magnit ude (up to 1000 years). This indicates the importance of testing at higher temperatures as well as the importance of using reliable TTSP shift factors. From the results obtained during this study, using the master curve, the creep compliance variation pred ictions can be made for up to >1000 years of storage at 30C. For understanding the effect of the fiber orientation on the creep, master curves for both the material orientations are normalized using their respective initial creep compliance values and the percent change from the initial values are reported on a graph as shown in Figure 321. PAGE 65 65 Figure 321. Comparison of normalized master creep curves for 45 and 0/90 specime n (Tref = 30C). Curves are normalized using their respective initial creep compliance values and show % change in the creep compliance values. The 45 orientation specimen creeps more than the 0/90 orientation specimen. This can be attributed to material property being dominated by matrix beha vior in case of 45 fiber orientation than the 0/90 direction The master curves can be approximated by suitable analytical models. The power law model developed by Findley [125] is one of the popular analytical models used for viscoelastic material modeling. A Prony series hereditary integral model [127] can be used to develop a viscoelastic material model. This model can further be used in a nonlinear FEA based analysis approach to develop a creep deformation prediction tool. Such a tool is expected to predict the fullfield b asis creep deformation of the bendable wing after the wing is stored at a stipulated temperature and for specified time duration. As noted earlier it is identified as a future work. PAGE 66 66 Experimental Characterization Conclusions The bendable load stiffen ed wing has a unique ability to load stiffen in the positive flight load direction while remaining compliant in the other (folding/packing) direction. The compliant nature is demonstrated experimentally using a visual image correlation ( VIC ) system. When a downward rolling moment is applied on the wing the root airfoil is shown to lose its camber and flattens. With the continuation of the applied rolling moment the wing is able to be rolled into a cylindrical shape. This enables compact storage of the benda ble wings inside a small diameter canister. The a ddition of quarter chord sweepback gives a load stiffening ability to the wing and increases its positive flight load carrying capacity. To verify and quantify the load stiffening effect, a three point bend test setup and a high resolution VIC system is used. Center of pressure locations on individual wing halves, as determined using the AVL panel code, are used as two support locations in the test and an increas ing downward force is applied at the center of gravity location of the aircraft. While a straight camber wing could support a maximum load of 9 N (~ 2 Gs load factor), the swept camber wing (load stiffening wing) supported 30.74 N central load (~ 7 Gs load factor). The leading edge of the load stiffe ning bendable wing is found to move down increasing its root airfoil camber and wing stiffness with increase in the central load. This gave higher load carrying capacity to the load stiffening wing. More sweepback could potentially further increase the load stiffening ability and the load carrying capacity of the wing. The locations of the fuselage mounting holes drilled on the wing at its root airfoil also play an important role in deciding the wing buckling load. A quick check shows that moving the front mounting hole more towards the leading edge helps to improve wing load carrying capacity. Wind tunnel tests performed at 7x104 Reynolds number show the addition of sweepback angle does not have significant effect on the wing aerodynamic s. Both the wings show similar CL values and the lift curve slopes with swept camber wing showing marginally higher CD at low PAGE 67 67 angles of attack. L/D ratios are similar for both the wings with straight camber wing showing highest L/D ratio of 8.4 versus 8.27 observed for the swept camber wing. Highest L/D ratios are observed to be at an angle of attack of 5. The sweepback also helps in improving the static stability (higher dCm/dCL derivative) of the wing. Since bendable wings might be stored inside a canister for a long dur ation before the MAV /UAV is deployed, VIC analysis is also used for the creep deformation measurement of the wings. S weepback introduced in the wing resulted in stable wing geometry with higher flexural stiffness than the wing with straight camber. The mag nitude of residual strains after storing the wing at 70 C for 24 hours is reduced for the wing with swept camber (load stiffening wing) than the wing with a straight camber. Permanent deformation caused by creep is thought to be with in acceptable limits. Thus with the addition of sweepback angle, the load stiffening wing (swept camber wing) has a clear advantage over straight camber wing. It offers stiffness improvement, provides load stiffening ability and reduces storage induced creep residual strains while maintaining the aerodynamic efficiency of the wing and improving the static stability margin In order to understand the effect of fiber direction on the creep deformations and to develop the creep master curves ( material characterization), a dynamic m echanical analysis testing technique was used along with a time temperature superposition (TTSP) technique to develop the master creep compliance curves for 0/90 and 45 fiber orientations at a reference temperature of 30C. Comparison of the master curves indicates 45 orientation specimen show matrix dominated behavior while undergoing higher percent change in the creep compliance. By virtue of the fibers oriented in the loading direction, the 0/90 specimen show s lower change in the creep compliance. PAGE 68 68 CH APTER 4 MULTIDISCILINARY SHA PE AND LAYUP OPTIMIZ ATION This chapter will discuss a multidisciplinary, multiobjective optimization effort for conceptual design of a bendable w ing used on a canister released micro air vehicle. The canister diameter (4.5 inch) limits the wing span to 24 inch due to presence of fuselage mounting pylons while the wing root chord is fixed at 7 inch due to the storage canister length limitations. This chapter will outline the conceptual design considerations as applicable to a bend able load stiffen ed wing, different wing modeling techniques used for aerodynamic and structural analysis, experimental validation of the analysis techniques, optimization framework used and the optimization results. The conceptual design of a bendable wing regardless of its size, must incorporate several disparate factors, necessitating a multi disciplinary, multiobjective optimization procedure [78] From a str uctural standpoint, the composite wing must be compliant enough and able to withstand being bent into the desired storage radius [79] without failing (fiber delam ination, matrix cracking, etc. [80] ). Conversely, the wing must be stiff and strong enough to handle a positive aerodynamic flight load without buckling or stress failure Higher wing loading is expected during some of the UAV flight regimes, for example, during pull up maneuvers and the wing should not buckle under such aggressive loads, causing the vehicle to become uncontrollable; possibly leading to a crash. Whi le these may seem two conflicting design requirements, the camber built into the wing provides a dissimilar stiffness in these two directions and helps to some extent The addition of quarter chord aft sweep is found to help increase the wings load carry ing capacity, as demonstrated in the previous section and work by Jagdale et al. [81] As discussed earlier, when a positive flight load is applied to the wing, the leading edge of the wing root deflects downward, increasing the wing centerline camber and its PAGE 69 69 moment of inertia. This results in a stable wing structure which may become stiffer as the positive load is increased. Such a wing geometry is not thought to si gnificantly remove the wings ability to roll into a canister, though does induce chordwise strains in the wing as the camber flattens out [5] From aerodynamic considerations, the wing must be able to produce enough lift to balance the weight of the UAV. Additionally the wing must be able to achieve longitudinal static stability in forward flight. Minimizing the storage volume requirement constrains the physical dimensions of the horizontal stabilizer present on the air vehicle and its chord wise position with respect to the wing. This limits the pitching moment neutralization offered by the horizontal stabilizer and requires the wing to have close to zero pitchin g moment at level flight; in essence we require a flying wing. Selection of wing airfoil with appropriate reverse camber or reflex towards the trailing edge and a wing sweepback would help in meeting this requirement, although presence of reflex and sweepb ack might reduce the aerodynamic efficiency of the wing [68] A w ing design having higher aerodynamic efficiency is desired in order to increase the air vehicle en durance. The various balancing acts that will govern the conceptual design of a bendable UAV wing then become evident: compliant wings are preferred in order to fold the wing into a canister, but stiff wings are needed to withstand aggressive flight loads. The wing sweep helps in the latter performance metric, though it may decrease lift, increase drag and decrease the aerodynamic efficiency through glide performance, fuel consumption, etc. A wing design that simultaneously maximizes its aerodynamic efficie ncy and flight load carrying capacity would be desired. No single wing design is thus expected to satisfy all the structural as well as aerodynamic performance requirements and a Pareto front tradeoff study between different competing performance requireme nts / objectives would be required, where no single PAGE 70 70 wing design is better than other design unless some additional criterion are specified, e.g. mission requirement on minimum endurance, maximum expected flying speed, built in requirement of additional pay load carrying capacity, etc. The literature pertaining to multidisciplinary design and optimization of micro and small unmanned air vehicles is fairly diverse and is detailed in the literature survey chapter 2. Aeroelastic optimization studies, which include both aerodynamic and structural objective functions and constraints, are generally defined as aeroelastic tailoring. Although aeroelastic tailoring is generally defined as the addition of directional stiffness into a wing structure so as to beneficiall y affect performance [82] this has traditionally meant the use of unbalanced composite plates/shells. Examples are given by Stanford et al. [75] for small micro air vehicles in forward flight, and by Weisshaar et al. [83] for the lateral control of larger unmanned air vehicles. Non tailoring examples of aeroelastic wing optimization would either include sizing or topological variables with a strong influence upon the aerodynamics of the wing. An example of the latter is given by Stanford and Ifju [84] who consider a bi material wing structure (carbon fiber composites and a flexible membrane skin). The topological distribution of the two materials along a MAV wing is located to optimize a variety of aerodynamic metrics. In the present work, the airfoil shape, wing taper ratio, wing geometric twist, and wing sweep will be considered as design variables, as well as the lay up scheme of the composite bendable wing. A custom wing airfoil geometry definition is used in the research and is detailed in a later section. Planform parameters are single valued variables which ar e cubically distributed from root airfoil to the tip airfoil to achieve smooth wing shapes. An aerodynamic analysis will compute the pressure distribution over the wing, as well as the concomitant lift, lift to drag ratio, pitching moment coefficient and t he static stability margin. Aerodynamic computations and PAGE 71 71 optimization is performed at a single point of 5 angle of attack. This AOA corresponds to the maximum L/D ratio point for the baseline wings studied and detailed earlier in Chapter 3. Since the obje ctive of optimization is to achieve designs better than the baseline wings, this single point design process is thought to be justified. Using the pressure distribution from aerodynamic analysis, a nonlinear finite element mode l will then calculate the for ward flight velocity at which snap through buckling will occur, while an analytical stress/strain analysis is used to monitor the failure of the laminate as the wing is bent into the desired storage diameter. A multiobjective analysis will be used to opti mize the lift to drag ratio and the maximum velocity the wing can withstand without in flight buckling or failing (laminate failure) under aggressive load induced stresses. While maximizing aerodynamic efficiency is desired for any MAV/UAV mission, the obj ective of maximizing failure (structural or material) velocity is peculiar to the bendable load stiffening wing design. Various canister released UAV mission and bendable wing design specific constraints are used on the wing static stability margin, cruise speed (minimum operating speed) wing pitching moment coefficient and laminate failure due to folding. A limit on static stability margin and wing pitching moment coefficient can be combined into one constrain, both are kept separate in the optimization p roblem as their specific bounds are MAV/UAV configuration dependant. For example limits on level flight pitching moment coefficient depend on the horizontal stabilizer size and its chord wise location with respect to the wing. This might result in one of t hese two constrains being active while other remaining inactive. Design points on the resultant Pareto optimal front [85] are compared with a baseline design to hi ghlight improvements expected in the wing performance. For the present optimization study, a bendable UAV with 7 inch root chord and 24 inch wing span is considered PAGE 72 72 as discussed earlier ; nevertheless, procedures outlined here are applicable to any rigid mo nolithic fixed bendable UAV wing design Wing Model Seven variables are used to define the geometry of the bendable wing. Four root airfoil and three wing planform definition variables. The airfoil at the root of the wing is completely defined by four vari ables (see Figure 41): the maximum positive camber towards the leading edge z1 the chord wise position of this control point x1 and similar information for the reflex towar ds the trailing edge, z2 and x2 A combination of three curves is used to define the airfoil shape. A quadratic curve from the leading edge to the maximum camber point (curve 1 in Figure 41), a 5th order polynomial in the middle (curve 2) and another quadratic curve from reflex point to the trailing edge (curve 3), can completely and uniquely define the root airfoil shape. Curvature continuity is ensured between the se three curves. Two quadratic equations have 3 coefficients each and the middle full quintic equation has 6 coefficients, thus we have a total of 12 unknowns These unknowns can be uniquely found by using geometric boundary conditions for the airfoil. Sta rting and end point co ordinates for three curves provide 6 point information We have 4 slope information : leading edge quadratic curve should have zero slope at maximum camber point, middle 5th order curve should have zero slope at maximum camber and max imum reflex point, whereas trailing edge quadratic curve should have zero slope at maximum reflex point. Additional 2 curvature continuity constraints ; leading edge quadratic curve and middle quintic curve should have H1 continuity at maximum camber point, while similar continuity is required between middle quintic curve and the trailing edge quadratic curve at maximum reflex point So these 12 geometric constraints can be used to find 12 airfoil defining polynomial curve coefficients Such a definition avoids any secondary reflection points as that was observed in previous study [86] on some of the wing designs. Such a formulation allows for a re flex in the PAGE 73 73 airfoil towards the trailing edge. The negative aerodynamic forces in this region can help offset the nose down forces of the remainder of the wing, and provide a certain measure of static stability for potential tailless flying wing configu rations Figure 41. Wing root airfoil control variables. The w ing chord and span are fixed for the current work, and thus three variables control the remainder of the wing shape: taper ratio (ratio of chord at tip by chord at root) wing geomet ric twist angle twist, and the wing sweep angle (defined at quarter chord location) All the metrics are cubically interpolated between the root and the tip to e nsure a kink free wing shape, as graphically seen in Figure 42. Since the wing thickness is very small (< 0.42 % of root chord) compared to its other dimensions (chord and span), the surface defined using seven variables appropriately represent the mid surface of the laminated composite wing shell. Figure 42. Wing planform shape control variables. PAGE 74 74 Wing Analysis Techniques While both aerodynamic and structural metrics are included in the wing design, the analyses are not explicitly coupled in an aeroelastic sense [82] [84] : stable deflections of the wing due to air loads are thought to be small, excess of which will lead to buckling failure. While buckling of the wing is associated with loosin g the wing root airfoil camber under aggressive flight loads, an aeroelastic behavior where an iterative and costly computational analysis scheme would be desired that solves for equilibrium wing shapes and pressure distributions over the wing at every step of the way un til buckling, for present study no aeroelasticity is considered. While the amount of lift generated will vary with change in camber, the amount of camber change that the wing undergoes before buckling is considered and experimentally (wind t unnel testing) observed to be small A s a result the pressure distribution over the wing is assumed to remain unchanged throughout the buckling analysis. The experimental validation of this technique is performed (detailed in later section) using wind tunn el testing to observe maximum flight velocity predictions by the model to be within acceptable limits. Aerodynamic Analysis For aerodynamic analysis, Athena Vortex Lattice (AVL) software developed by Harold Youngren and Mark Drela [76] is used. AVL employs an inviscid, extended vortex lattice model for the lifting surfaces and is useful for aerodynamic and flight dynamic analysis of rigid aircraft of arbitrary confi guration. In vortex lattice methods, as that of AVL, the continuous distribution of bound vorticity is approximated by discretizing the wing into a paneled grid, and placing a horseshoe vortex upon each panel. Each horseshoe vortex is comprised of a boun d vortex (which coincides with the quarter chord line of each panel), and two trailing vortices extending downstream. Each vortex filament creates a velocity whose magnitude is assumed to be governed by the Biot Savart law. Furthermore, a control point i s placed at the threequarter - PAGE 75 75 chord point of each panel. The tangency condition is applied (i.e., the wing becomes a streamline of the flow) by stipulating that the induced flow (from the horseshoe vortices) along the outward normal at each control point exactly cancels with that caused by the freestream velocity. Further details are given by Bertin and Smith [87] among many others. In the present study AVL is u sed to compute the aerodynamic pressure distribution over the wing. AVL is run within the Matlab environment using a code developed in house to automate the AVL input file generation for various optimization trials. Drag computations present a problem for such inviscid modeling techniques, which can only provide induced drag due to lift (the downwash of the finite span deflects the local velocity vector at each wing section downward, tilting the lift vector slightly backward to provide a small drag force): drag due to flow separation and viscous shear is unaccounted for. The latter terms are included by augmenting the drag with a non zero CDo, estimated from wind tunnel experimental data detailed in Chapter 3 to be 0.05, value also reported by Albertani [61] and Stanford [64] The viscous drag terms are not truly constant (fl ow separation generally increases with angle of attack, for example), and so the vortex lattice method is expected to under predict the overall drag. While these issues will become more problematic as the Reynolds number decreases (as is the case for smal l UAVs), successful MAV analysis studies with vortex lattice methods are evidenced in the work of Stanford and Ifju [84] and Abdulrahim and Lind [88] Based on the geometry variables (discussed in earlier section ) a structured wing grid is built. The coordinates of the wing mesh, as well as the angle of attack variable are f ed into AVL p, the coefficient of lift CL, the coefficient of drag CD, the coefficient of pitching moment Cm and the aerodynamic center of the wing Xac. PAGE 76 76 The cruisin g speed of the vehicle can then be computed: 0.5 CLV2.W/{S.C} (4 1) Furthermore, the static stability margin of the wing can be computed by [56] : naccgcgKXX/X (4 2) Where, Xcg is estimated from the wing geometry and mass properties, as well as a predetermined payload distribution throughout the airframe. Aerodynamic model convergence and validation study In aerodynamic analysis only half of the wing geometry is modeled, taking advantage of the wing symmetry. In vortex lattice methods accuracy of predictions depend on the number of panels as well as their spatial distribution used to represent the wing geometry Two types of distribution s are tried: 1) Chord wise and span wise equally spaced panels, (refer Figure 43, left) 2) Chord wise cosine spacing (bunching of panels near leading edge and trailing edge of the wing) and spanwise half sine spacing (closely spaced panels near tip of the wing). (refer Figure 43, right) Figure 43. Example of equally spaced panel distribution (left), same number of panels with chord wise cosine and span wise half sine spacing (right). PAGE 77 77 Different numbers of panels are t ried and the effect of the number of panels and panel spatial distribution on the wing aerodynamics (CL, CD, Cm and L/D ratio) is studied. The model predictions are compared with experimental wind tunnel results for straight and swept camber wings tested a t Re = 7 x 104 (detailed in Chapter 3). Comparing the results for the straight camber wing, predictions of model using equally spaced vortex lattice distribution are found to be sensitive to number of panels (refer Figure 44), whereas the results using cosine/sine distribution are found to be relatively insensitive to the number of panels used to model the wing geometry. CL and L/D ratio predictions are found to be sensitive wh ereas Cm predictions are found to be relatively insensitive to the number of panels. Figure 44. Change in aerodynamic coefficient predictions for straight camber wing with the inverse of the number of panels. PAGE 78 78 Model predictions using 14 chord wise panels (cosine distribution) and 24 semi span wise panels (half sine distribution) are found to strike the best balance between computational cost and prediction error (refer Figure 45). Computational cost reported here is normalized with respect to the minimum time it took for the most coarse panel distribution. Prediction error reported here is the root mean squared average er ror for CL and L/D ratio predictions at 5 AOA. Aerodynamic predictions for the straight camber wing using 14x24 cosine/half sine panel distribution is shown in Figure 46. As can be seen, the model predictions are in good agreement with the experimental observations in the low angle of attack region where the aerodynamics is more or less linear. Figure 45. Change in prediction error with the inverse of the number of panel s (left), Tradeoff between prediction error and computational cost (right). In the high angle of attack region aerodynamics is dominated by nonlinear effects, e.g. flow separation etc and model predicts higher lift and consequently higher L/D ratio. At 5 AOA (design point) the model predictions are in good agreement with the experimental results with less than 10% prediction error (refer Figure 45) The comparison of model pred ictions and experimental values for the swept camber wing show similar trends with errors being less than 10%. PAGE 79 79 Figure 46. Comparison of results from aerodynamic model and wind tunnel testing of straight camber wing at Re = 7x104. (Model uses 14x24 cos ine/half sine panel distribution). Structural Analysis Limit Flight Velocity Calculation As discussed earlier the structural portions of the wing design must incorporate two disparate analyses: the first is finding the maximum aerodynamic load and thus maximum flight velocity (termed limit flight velocity henceforth) that the wing can sustain without inflight buckling or experiencing laminate failure and the second is to find the safe rolling diameter to which the wing can be rolled and stored inside canister without composite material failure due to the rolling induced stresses. For the former, a nonlinear snap through buckling analysis is conducted within the ABAQUS family of finite element software. For the current work, snap thro ugh buckling of the wing is the state, where the root airfoil of the wing flattens out and the wing loses its load carrying capacity. Since the wing snap through buckling is inherently unstable structural behavior, t he modified Riks analysis procedure [89] a nonlinear arc length PAGE 80 80 method, implemented in ABAQUS [90] is used No nlinear eigenvalue analysis is deemed unsuitable due to the presence of the reflex in wing geometry. Depending on its design the wing will have multiple eigenmodes (flattening of the reflex is a local buckling mode) and it is difficult to identify the corr ect eigenmode that corresponds to the global span wise buckling, we are interested in. In the problem formulation t he modified Riks method treats the load magnitude as an additional unknown. This approach gives solutions regardless of whether the response is stable or unstable. T he analysis assumes aerodynamic loading to be proportional; all load magnitudes vary with a single scalar parameter. Additionally it is also assumed that the flight load wing deformation response is reasonably smooth and no sudde n bifurcations occur. These assumptions are found to be valid on simulating and testing some trial wings in ABAQUS. Half of the wing is analyzed in ABAQUS using Y symmetry boundary conditions and appropriate support conditions as are used on the actual air vehicle The w ing is mounted on the air vehicle through two mounting holes, where the leading hole is just aft of the maximum camber point, and the trailing hole is just forward of the maximum reflex point. Such a mounting arrangement maximizes the suppor t length at the root airfoil while maintaining the rolling/folding ability of the wing at the root airfoil. During the finite element analysis g eometrical nonlinearity is considered and the loads are made to follow nodes. T p distribution computed from AVL is used to compute normal flight aerodynamic loading on elements, given by : 2 eep,e cruiseFSC0.5(V) (4 3) w here Se is the area of the finite element. The value of Vcruise is used from Equation 41. This loading is then interpolated onto the finite element mesh, giving nodal forces. After interpolation it is made sure that the total flight load value is conserved. The analysis procedure then travels along the flight load wing deformation arc, in effect, increasing the wing loading from a fraction PAGE 81 81 ( e.g. 10%) of normal flight load to a higher reference load, in return, solving for the load proportionality factor, LF at each equilibrium analysis step. The pull up maneuvers are expected to introduce loads that are 3 to 4 times the normal flight loads. To take care of this and more, an arbitrary reference load of 20 times the normal flight load is used in the present study. Such a high value of reference load allows analysis to capture complete flight load wing deformation history to identify the correct limit flight velocity for the wing design. The number of increments in the ABAQUS analysis is limited to 40 in order to reduce the computational cost. The selected numbers of increments adequately cap ture the wing structural behavior until instability and beyond, for the design space considered during optimization. The flight velocity at each step then can be shown to be related to load proportionality factor and Vcruise by : 0.5 cruiseFlight_VelocityLF.20.V (4 4) The snap through buckling velocity is found by plotting flight velocity at each equilibrium step versus camber of the root airfoil at that particular step to find a point where the flight velocity starts reducing in magnitude (wing 2 in Figure 47) or a point when the graph reaches a minimum camber point (wing 1 in Figure 47); whic hever occurs first. If the wing continues to load stiffen (wing 3 in Figure 47), the flight velocity corresponding to a load proportionality factor of 1 (load 20 times the nor mal flight load ), will be returned to calculate the buckling velocity. Depending on the initial wing geometry different structural behaviors can be observed. The structural behavior (flight velocity versus normalized root airfoil camber) indicated by the wing 1, in Figure 47, shows an expected behavior typical for a wing which has a moderate camber, zero or close to zero sweepback and zero twist, for instance, which is expected to buckle even at moderate flight loads, without any load stiffening. The straight camber wing discussed earlier, in PAGE 82 82 Figure 39, is an example of a wing showi ng such structural behavior. The wing 2, in Figure 47, is an example of a wing with a moderate camber and a moderate amount of sweepback. Such a wing is expected to initially l oad stiffen with increased flight velocity (and thus flight load) and later buckle when it encounters higher flight loads. Swept camber wing structural behavior, as shown in Figure 39, can be found to fall in this category. The structural behavior indicated by wing 3, in Figure 47, is an example of a wing having aggressive positive camber, higher sweepback angle and high amount of washout. Such a wing is expected to continue to load stiffen (continue to increase its root airfoil camber) under increased flight loads, eventually may be buckling at very high loads. This wing design is expected to encounter mat erial failure first, due to high stresses at the root airfoil. Figure 47. Completely buckled shape of the baseline wing (left), buckling analysis possible wing structural behavior plots (right). The stresses induced in the wing are monitored througho ut the buckling analysis process, with the highest stresses expected to occur at the root airfoil and at the mounting locations Wing material failure (laminate failure) along the root due to excessive loading is monitored during the analysis using the Tsa i Wu composite failure criterion [91] with a factor of safety of 1.5. Flight velocity at which the first ply failure occurs is returned as material failure velocit y. The l imit flight velocity for the wing is then, the minimum of the snap through buckling flight velocity or PAGE 83 83 the stress induced material failure velocity. One of the objectives in optimization is to maximize thus found limit flight velocity. Limit flight velocity / load calculation model convergence and validation study From the ABAQUS family of shell elements S4R and S8R elements are tried for the present research since these elements are based on first order transverse shear flexible theory in which the transverse shear strain is assumed to be constant through the thickness of the shell Such elements are suitable for analysis of laminated composite shells [92] The full integration general purpose element S4 is also tried and compared with S4R and S8R elements. In the convergence study multimesh extrapolation technique is used [93] Different mesh sizes using h refinement are tried as listed in Table 4 1. The number of elements along the chord and span are selected so as to avoid excessive element elongation, skewness and warping (in the initial element shapes). Table 4 1. Multimesh extrapolation mesh sizes used Mesh number Total number of elements Elements along chord Elements along semi span Minimum element aspect ratio (near root airfoil) Maximum element aspect ratio (near tip airfoil for wing with taper ratio = 0.5 and sweep = 30) (1) 120 10 12 1.43 4.06 (2) 180 10 18 0.95 2.80 (3) 600 20 30 1.14 3.50 (4) 720 20 36 0.95 2.99 (5) 2880 40 72 0.96 3.13 Increasingly complex experimental testing is used for validation. First singly curved specimen s having 20 inch span and different initial chord and camber are tested in three point bend test mode ( Figure 48). These specimens are portions of a 4.5 inch diameter cylindrica l tube, manufactured using 2 layers of T300/934 composite prepreg, cut to have various included angles with the circle center (40, 45 and 60 deg). These specimens can be visualized as singly curved wings having zero sweep angles. Specimens are supported at their 1/4th and 3/4th span PAGE 84 84 locations while a central downward force is applied at the specimen mid span location. A visual image correlation technique is used to monitor the root airfoil shape change as the loading is increased from a zero load to the poi nt specimens are found to cross the limit point, when the load reaches its maximum and starts reducing, followed by negative structural stiffness region. Further details of the test can be found in the work of Patil et al. [94] Figure 48. Singly curved specimens: 45 deg and 60 deg (left) [94] and the three point bend test schematic (right). Such a testing mode and the specimen loading configuration capture the required structural behavior. The predictions of structural analysis mo del for 60 deg singly curved specimen using different element types and mesh sizes is shown in Figure 49. The error in limit load prediction is presented for each element type and mesh size in Figure 410. The tradeoff between percent prediction error ((model prediction experimental value) over model prediction times 100) and normalized computati onal cost (normalized by computational time of S4 element, mesh 10x12) is also shown in the Figure 410. As can be seen, results converge to the experimentally observed values The limit load prediction errors for all element types and mesh densities are less than 5%. PAGE 85 85 Figure 49. Comparison of experimental and model predictions for 60 deg singly curved specimen. Amongst the three element types tested in this study, element S8R matches the experimental results the best considering it closely follows the load root airfoil camber curve (refer Figure 49) and has minimum error for the given mesh de nsities (refer Figure 410). Within the S8R element, the 20x36 mesh provides a good balance between limit load prediction error and the computational cost while maintaining g ood element aspect ratios (refer Table 4 1). Element S4R also looks to perform well considering the lower computational cost for the same amount of error. But this element might give higher error when more complex specimen configurations and loading will be encountered (regular wing). PAGE 86 86 Figure 410. 60 deg singly curved specimen: tradeoff between prediction error and element size (left), tradeoff between prediction error and normalized computational cost (right). Comparison of experimental results and model predictions for 40 deg, 45 deg and 60 deg singly curved specimens is shown in Figure 411. Model predictions reported here are for S8R element with 20x36 mesh. As can be seen, the model could very well replicate the experimentally observed structural behavior for all specimens. Limit load predictions are within 5% of experimentally observed valu es. Figure 411. Comparison of experimental and model predictions for 40, 45 and 60 deg singly curved specimen three point bend test. PAGE 87 87 The model predictions are also compared with the three point bend tests of straight camber and swept camber wings (det ailed in Chapter 3). Figure 412 shows model predictions for 20x36 element mesh using different element types. As can be seen, S8R element provides the best predictions for s traight as well as swept camber wing. The S4 element is found to be little too stiff, while S4R element is found to be compliant than experimental observations for the swept camber wing. Figure 412. Comparison of experimental observations and model pr edictions (20x36 mesh) for straight and swept camber wing three point bend tests detailed in Chapter 3. Figure 413 shows tradeoff between prediction error and element size, as well as between prediction error and normalized computational cost for the straight camber wing. 20x36 mesh shows its superiority providing accurate results with reasonable computational cost. Similar observations are made for the swept camber wing. PAGE 88 88 Figure 413. Straight camber wing: tradeoff between prediction error and element size (left), tradeoff between prediction error and normalized computational cost (right). To increase the experimental complexity full fledged wind tunnel testing is performed. Both swept (15 sweepback) and straight camber wings (zero sweep) are fixed at relatively high angle of attack (16) to ensure wing buckling occurs at relatively low air speeds, from the wind tunnel working limit point of view The air speed is increased inside wind tunnel from zero to a velocity at which the wings snap through buckled. The root airfoil and its camber change are monitored during the wind tunnel test with a VIC technique. The structural analysis model predictions about the limit flight vel ocity are compared with the experimental observations, to find good agreement of results. As can be seen in Figure 414, the straight and swept camber wing results are predict ed quite well. The result s shown here are for three types of element (S4, S4R and S8R) using 20x36 mesh size. As noted earlier S8R element predictions are closer to experimental observations. The change in camber for the straight camber wing is perfectly predicted up to the limit point. During wind tunnel testing, the straight camber wing is found to snap through buckle beyond a velocity of 12 m/s, correctly predicted by the analysis model. The change in camber at different test air speeds is also predicted well by the model. In the wind tunnel tests, the swept camber wing is found to snap through buckle beyond a velocity of 18 m/s. PAGE 89 89 This is also predicted quite well by the model. S ince the wind tunnel testing was performed at a high angle of attack, the resultant limit velocities are lower. During normal flight with an angle of attack of 5 (typically used on UF MAVs), the flight speeds that will cause the wing to snap through buckle would be of higher magnitudes. The ratio of limit velocities for the swept camber and t he straight camber wings is also lower in wind tunnel testing than observed during the three point bend tests (explained in Chapter 3). This difference can be attributed to a distributed pressure load acting on the wings during the wind tunnel testing vers us the point loads experienced during the three point bend tests. Upward pressure loads acting near the leading edge area are thought to reduce the amount of downward leading edge movement, resulting in reduction of the load stiffening effect. Figure 414. Comparison of wind tunnel test data and the results from analysis model. From the convergence and validation study, a finite element model using S8R elements with a mesh of 20 elements along the chord and 36 along the semispan is found to give the be st tradeoff between model accuracy (errors within 5%) and computational cost. The performance of PAGE 90 90 analysis model for wind tunnel testing validates both the aerodynamic model as well as the structural model. S torage Analysis Minimum Safe Storage Diameter C alculation In order to keep the computational cost low, to simulate the wing rolling/storage process a simpler analytical method based on laminate analysis using strain superposition is used Use of finite element method to accurately predict safe storage diameter involves a multi step approach which would be computationally costly. As a downward force is applied on the wing to begin the rolling process, the root of the wing experience s snap through buckling, in the opposite direction of that discussed in the earlier section and the airfoil flatten s out. This happens very quickly, long before the wings are actually folded into the final shape. As such, the chord wise strains induced by this airfoil flattening are assumed to be constant during the further ro lling process. The definition of the root airfoil used in the study allows for the calculation of the curvatures along the root airfoil and so the chord wise strains introduced by loosing this curvature can be calculated. Additional span wise strains will be introduced by the incremental folding of the wing, un til it achieves the final desired storage diameter. The r oot airfoil is treated as the critical section of the wing during the folding process and thus analysis is performed at this section. By using the strain superposition and the plane stress reduced stiffness matrix, stresses can be computed at each point along the root airfoil. These stresses act in conjunction with a span wise curvature induced stresses, computed from the rolling diameter. The s tresses in each ply, at every location along the root airfoil are continually monitored and assessed with the Tsai Wu composite failure criteria, with a factor of safety of 1.5 If the rolling diameter that initiates the first ply failure is larger than t he desired diameter of the packed volume, the design is unacceptable. For the T300/934 bi directional prepreg carbon composite used for wing manufacturing, the following material properties are considered during the limit flight velocity PAGE 91 91 and safe storage diameter calculation analysis procedures: Elastic properties, E1 = E2 = 34.8 GPa, 12 = 0.05, G12 = 2.34 GPa and correspondingly failure strengths [95] F1t = 324 MPa, F1c = 338 MPa, F2t = 314 MPa, F2c = 320 MPa, F6 = 41 MPa. Strain superposition analysis experimental validation The storage analysis is based on the assumption of strain superposition, i.e. chord wise strains and span wise strains can be t reated independent of each other during the folding process. In order to validate this assumption, three rectangular strain rosettes CEA 06250UR 350, available from Vishay Micro Measurements, are mounted on the underside of the swept camber wing root airf oil as can be seen in the schematic shown in Figure 415. The chord wise and span wise strains are noted while wing is rolled around different tubes of diameter 9, 6.24, 4. 74 and 3.24. Strain rosette G1 is in the middle of the leading edge portion (between leading edge and the maximum camber line) of the root airfoil which has constant curvature, rosette G2 is in the middle portion of the airfoil, which is almost flat in w ing deployed condition, while rosette G3 is mounted in the middle of the trailing edge portion (between maximum reflex line and the trailing edge) of the airfoil which also uses constant curvature definition. Figure 415. Rectangular strain rosettes G 1, G2 and G3 are mounted on the underside of the swept camber wing PAGE 92 92 The strain predictions using strain superposition method are compared with the measured strains in Figure 416. The difference in model prediction and measured value as a fraction of model prediction is reported as percent strain prediction error in Figure 417. Chord wise strains are predicted with less that 10% error, while span wise strain predictions are within 15% of the measured values A s expected span wise strain is observed to vary inversely proportional to the folding diameter (refer Figure 416, right) as a result similar amount of error is expected to occur in the safe diameter predictions Figure 416. Predicted and measured chord wise strains for different folding diameters (left), similar measurements for span wise strains (right). For span wise strains, error in strain predictions goes up as the folding diameter becomes smaller and smaller ( Figure 417, right). For chord wise strains, error in compressive strain predictions is found to reduce as folding diam e ter becomes smaller (gage G 3, Figure 417, left) whereas for tensile strains (gage G1) error is found to go up as the folding diameter becomes smaller and smaller. PAGE 93 93 Figure 417. Model percent prediction error in chord wise strains for different folding diameters (left), similar measurements for span wise strains (right). From an error calculation point of view, the measured chord wise strain in gage G2 (~ 140 considerably different than predicted value of 258 as such; it is not shown in Figure 417. In practical wing geometries, due to presence of initial curvatures, areas near the leading edge and trailing edge would be more critical than the straighter airfoil middle portion. The assumption of chord wise strain rema ins constant throughout the rolling is observed to be reasonable with very minimal change in chord wise strains at various locations of the airfoil for different rolled diameters (refer Figure 416, left). Strain predictions are conservative (prediction errors are positive), which will result in prediction of failure to occur before would be actually observed In all strain superposition method utilized here gives acceptable r esults at very low computational cost Wing Manufacturing Layup Orientation and Optimization Considerations The requirement of storing the wing inside a canister of 4.5 inch poses the constraint on number of layers that can be used to manufacture the wing as well as the layup orientation that can be utilized. For increasing load carrying capacity of the wing one of the choice would be to increase the number of layers used in the wing laminate, but that would also increase the strains PAGE 94 94 introduced in the wing root airfoil section, when the wing is rolled into a cylindrical shape for storage. This might cause bending stress induced failure (first ply failure) of the wing laminate. From storage related consideration, the operator of the MAV/UAV should be able to bend the wing for storage with average human effort. For storing into a canister of 4.5 inch diameter, the wing needs to be rolled to a smaller diameter (e.g. 4 inch) so that it provides enough clearance between the canister and wing to work with and the wing can be inserted into the canister. Typically the operator is expected to apply a downward force on the individual wing halves, generating a bending moment, causing the wing to lose i ts camber at the root airfoil. When we consider a grip strength norm (maximum grip force generated for a short duration of time) of 330 N for an average adult as noted in NASAs Man Systems Integration Standards [96] and using a human efficiency of 21% (for prolonged gripping force, grip strength may be reduced corresponding to human efficiency, which should give conservative results), the MAV/UAV operator can exert a gripping force of ~ 70 N (termed Flimit) during the process of folding the wing and storing it in the canister. The ease of bending requirement thus poses a limit on the resulting bending moment that can be applied by an average human being. Consequently this limits the number of layers and the layup orientation that can be used to manufacture the wing. By using the strain superposition (root airfoil flattening causes chord wise strains + cylindrical span wise rolling causes span wise strains) and laminat e analysis discussed in an earlier section, it is possible to calculate, for a particular wing geometry and laminate layup sequence, the required in plane moment resultant Mx [97] that needs to be applied in order to roll the wing in cylindrical shape for storage. By considering a moment arm of 12 inches (assuming operator folds the wing by holding it at respective wing halves), we can calculate the required force ( Frequired) that needs to be exerted by the MAV/UAV operator. A constraint then can be PAGE 95 95 posed on Frequired so as to limit it to be less than Flimit. This constraint will not be required if we find that laminate failure occurs during bending well before we ex ceed the human effort limit on applying the bending force. From a wing manufacturing point of view we want a symmetric and balanced laminate that would not warp during the manufacturing curing process. Due to the nature of the bi directional weave of the p repreg used for wing manufacturing, a balanced laminate condition is automatically satisfied. The layup symmetry condition needs to be considered during the candidate layup selection. From an air vehicle control point of view, the wing deformation due to a erodynamic loading should be symmetric about the root airfoil section. Any unsymmetrical wing deformation would introduce rolling or yawing of the air vehicle. This symmetric wing deformation condition thus requires the laminate layup to be symmetric about the root airfoil section and considering the bi directional nature of the composite prepreg being used, th us constrains the possible layup orientations to be either 45 or 0/90, defined with respect to the root airfoil section. The requirement of the l ayup to be symmetric about laminate midplane then constrains the candidate layups to be as listed in Table 4 2. Here, single 45 layer is referred as 45 orientation and single 0/90 layer is referred as 0 orientation. Table 4 2. Candidate layups that can be used for wing manufacturing No of layers in laminate Candidate Layups Corresponding layup number 1 [45] or [0] 1, 2 2 [45] s or [0] s 3, 4 3 [45 3 ] or [45/0/45] or [0/45/0] or [0 3 ] 5, 6, 7, 8 4 [45 2 ] s or [45/0] s or [0/45] s or [0 2 ] s 9, 10, 11, 12 For limiting the number of layers to be considered during optimization, preliminary laminate analysis [97] of a flat plate wing is carried out. A flat plate wing, being more compliant than usual cambered wings, should provide an upper limit on the number of layers that can be PAGE 96 96 considered during the optimization study. As can be seen in Figure 418, left, none of the layups considered (listed in Table 4 2) exceed the bending force limit that can be exerted by average human. Whereas, Figure 418, right, shows that flat plate wings with one and two layer layups could be folded to 4 inch diameter as well as the layups [453] and [45/0/45], but other stiffer layups resulted in bending stress induced failure before the wing could be rolled to 4 inch diameter. Thus the bending stress induced failure limit is found to be active well before the bending force limit is exceeded. The layups considered during the present optimization study are given in Table 4 3. Figure 418. Bending force required for flat plate wing laminate layups (left) and diameter to which wings can be folded without bending stress induced failure (right). Table 4 3. Candidate layups considered during the wing optimization study No of layers in laminate Candidate Layups Corresp onding layup number 1 [45] or [0] 1, 2 2 [45] s or [0] s 3, 4 3 [45 3 ] or [45/0/45] 5, 6 PAGE 97 97 Optimization Problem Formulation The w ing geometry can be defined completely using seven design variables, as discussed in the earlier wing model section. The remaining design variable constitutes the layup schedule of the graphite/epoxy wing. Each layer extends uniformly throughout the semi wing. Due to manufacturing constraints and to ensure symmetric deformation of the two wing halves under aerodynamic loading, as discussed earlier, only 45 or 0/90 layup orientations are allowed. Between one and three layers of bi directional plain weave laminates are permissible, with fiber orientations as listed in Table 4 3. Wing geometry variables are continuous whereas the layup scheme is a discrete variable, which can be handled by genetic algorithm, described in a later section. The analysis procedures used in this research will study only one semi wing, with the appropriate symmetric and support boundary conditions at the root, as discussed earlier. The de sign variables can then be summarized as X = (z1, x1, z2, x2twist layup number ), and the design optimization problem is formally given as: M aximize f( X ) = L/D and M aximize g( X ) = Vlimit such that: cruising speed Vcruise CL > 0 Kn rolled diameter at first ply failure, Dmin < desired diameter (4 inch) 0.05 m L (4 5) Since we are simultaneously trying to optimize two objectives: maximize the lift to drag ratio and maximize the buckling velocity, it is not expected that a single design will simultaneously perform best in both aerodynamic and structural metrics, and so a trade off curve (Pareto optimal front) between the two metrics is required. The first constraint reflects the fact that cruising speeds for such a vehicle in urban environment flying settings should be less t han PAGE 98 98 20 m/s. This limit is also required for air vehicles flown by remote pilot. T he second constraint is added because the airfoil formulation seen in Figure 41 with planform shape as shown in Figure 42, using design bounds as listed in Table 4 4, can easily provide a wing wi th negative lift at the candidate angle of attack of 5. The third constraint ensures the static stability of the wing, while the fourth allows the wing to roll into the desired packing diameter without laminate failure. As the bendable wing UAVs are desi gned to be stored inside a canister, there are limitations on the size of the horizontal stabilizer control surface and its chord wise position with respect to the wing. These size limits are imposed by the inside diameter and the length of the storage can ister. In such cases there is a limitation on the pitching moment neutralization that can be offered by the control surface and the wing needs to be almost a flying wing with close to zero pitching moment at design flying AOA. For a single flat plate hor izontal stabilizer, with an aspect ratio of 1 and area of 16 square inch, located close to wing root trailing edge, pitching moment neutralization offered for level flight configuration (horizontal stabilizer mounted at 0 to 12 AOA) is estimated [40] The fifth constraint poses this limit on the pitching moment coefficient of the wing. The side constraints are given in Table 4 4. In the optimization algorithm utilized in this research the design variables are discretized into a number of intervals as noted in the table. Table 4 4. Side constraints for design variables z 1 x 1 z 2 x 2 twist Layup number Lower Bound 1% 15% 10% 65% 0.5 10 0 1 Upper Bound 10% 35% 0 % 85% 1 0 30 6 Number of intervals 19 5 21 5 6 11 16 6 The wing is mounted on the fuselage through two mounting holes at the root airfoil, as mentioned earlier. The clamping hole towards the root airfoil leading edge is usually 8 to 10 mm behind the maximum camber point, whereas the clamping hole towards the r oot airfoil trailing PAGE 99 99 edge is in front of the maximum reflex point by the same amount. In practice this is found to ensure wing can be folded into a cylindrical shape. In limit flight velocity structural analysis the support boundary conditions reflect this clamping arrangement. The upper bound on the chord wise location of maximum camber point, x1 and the lower bound on the control point x2 are chosen so as to have some minimum support length between these two mounting holes. The bounds on the z1 and z2 ensure we have airfoil designs with positive camber and zero or some reflex (negative camber). Geometric twist ( twist) side constraints make wing designs with wash out possible, wing designs with washin are not considered. This gives some measure on the wing stalling characteristics (not explicitly studied here). A large amount of sweepback adversely affects the longitudinal stability of the wings near stall, as indicated by Shortal and Maggin [46] Near stall, at high angles of attacks, flow separation at the tips and loss of lift over parts of the wing behind the CG of wing results in a nose up pitching moment, creating longitudinal stability problems. For the w ing with aspect ratio of 4.6 a sweepback angle of less than 30 is suggested [46] in keep ing away from the longitudinal instability problem near stall. This is reflected in the upper bound selected for sweep angle ( ). Fixing twist angle to be zero Wing geometric twist angle is one of the important design variables. It affects the wing pitching moment, wing stall characteristics (not explicitly studied here) and is a lso expected to influence the wing load carrying capacity. In the optimization study the effect of fixing geometric twist angle to zero on the Pareto optimal front designs is investigated. Optimization Algorithm The above optimization problem will be solv ed with an elitist nondominated sorting genetic algorithm: NSGA II [98] This algorithm is implemented in Matlab. As such, the design variable X given above is now considered a chromosome. Each of the continuous design PAGE 100 100 variables given above is discretized into a finite number of intervals ( refer Table 4 4) between the lower and upper bo unds Genetic algorithms are particularly well suited to laminate design [99] : each laminate scheme of interest ( listed in Table 4 3) is converted into an integer from 1 to 6. NSGA II ranks designs, not based explicitly upon aerodynamic or structural performance (f(X) and g(X) stated above) but by non domination [98] If for example, design A has a L/D ratio of 8.5 and a maximum Vlimit of 30 m/s, design B has a L/D ratio of 9.5 and a buckling velocity of 40 m/s, and design C has a L/D rat io of 8.8 and a buckling velocity of 50 m/s, then design A is dominated by both B and C (and thus undesirable), but B and C are non dominated with respect to one another (and thus Pareto optimal). The proposed design problem is not expected to have a glob ally dominating design, as discussed above. For a given set of designs, the Pareto front is rank 1, the next layer is rank 2, etc. Low rank designs (best designs) are given the greatest probability of being selected to reproduce, and crossover and mutatio n functions can then be used to create the child population. The child and parent populations are combined, and elitism (selection of the lowest ranking designs) and niching (a parameter based upon crowding distance, where designs which provide the greates t spread along the Pareto front are favored) techniques create the next generation. Constraints can be handled with constraint domination ideas. If two designs are both feasible, the standard non domination techniques given above apply. If one design is feasible and the other is not, the former is obviously favored. If both designs are infeasible, the design with a smaller overall constraint violation is favored [98] PAGE 101 101 Results and Discussion Results are discussed as comparison between various Pareto optimal front designs. Pareto front for problem as defined in Equation 45 Figure 419 shows the Pareto optimal front giving tradeoff between limit flight velocity (Vlimit) and L/D ratio for the problem formulation as defined in Equation 45. Table 4 5 details the objective function and constraint values for design points A, B, C D and E as well as a baseline wing design (swept camber wing studied in Chapter 3). As can be seen the baseline wing has highe r Cm about air vehicle CG location than permitted in current study, while all the designs on the Pa reto front are found to satisfy the Cm constraint. Table 4 6 provides respective design variable values for the wings. Wing root airfoil shapes, curvatures along the root airfoil and planform shapes of some of the selected designs are shown in Figure 420. Figure 419. Pareto optimal front : tradeoff between Limit flight velocity and L/D ratio PAGE 102 102 While most of the designs on the P areto front can withstand higher flight velocities and in that sense are stiffer that the baseline wing, designs high lightened in the gray box also have higher aerodynamic efficiencies at 5 AOA and thus are better designs in both the objectives than the baseline wing. Table 4 5. Objective function and constraint values for designs noted in Figure 419 Wing L/D ratio f(X) V limit (m/s) g(X) V cruise C L K n D min C m Design (m/s) (inch) Baseline 9.50 27.1 12.2 0.58 0.46 2.70 0.062 A 6.98 54.9 13.7 0.41 0.26 3.95 0.040 B 7.89 49.4 13.4 0.48 0.27 3.95 0.048 C 9.55 48.0 11.5 0.63 0.30 3.05 0.048 D 10.65 39.3 10.3 0.76 0.29 2.93 0.049 E 11.67 24.5 9.0 1.03 0.20 2.65 0.048 Wing designs on the Pareto optimal front are found to use [45, 0, 45] or [45, 45] layups. The layups numbered 1 and 2, as identified in Table 4 3 using single layer of 45 and 90 orientation respectively, are found to be too compliant from aggressive flight load carrying capacity point of view, whereas cambered wings using layup [0, 0] are too stiff to be rolled into desired storage diameter of 4 inches. Low camber wing designs which might use [0, 0] layup are not as aerodynamically efficient and are thus dominated by other wing designs which have high camber (thus higher CL and L/D ratio) a nd use [45, 45] layups. Wing designs using [45, 45, 45] orientation are found to be dominated by similar wing geometries (thus same L/D ratio) using [45, 0, 45] layup orientation (being more stiff). Multiple wings between design A and B use three layer co mposite layup with orientations [45, 0, 45] defined with respect to the root airfoil section (due to bi direction nature of composite prepreg and it being a plain weave, layup orientations can be equivalently specified about span wise direction as well) T hree layer layups are stiffer which results in the s torage diameter PAGE 103 103 constraint being active for these des igns (refer Table 4 5) which limits the maximum camber (4.5% located at q uarter chord) and the curvatures along the wing root airfoil s (refer Figure 420) Wings between design A and B are found to use lower positive camber towards the leading edg e and shallower curvatures than other two layer designs on the P areto front, including the baseline wing design. Although three layer wing designs are stiffer (have high Vlimit) than the baseline wing due to lower camber and high wash out, their L/D ratio is lower than the baseline design. All of the wing designs which are better in both of the objectives than the baseline design, use two layer composite laminate with [45]s layup. Wing designs using [45]s layup can accommodate higher curvatures along the root airfoil and thus use higher camber (10%). Use of higher camber for these wings (designs in gray shaded box) results in higher CL and correspondingly higher L/D ratio. Table 4 6. Variable values for P areto front designs and the baseline wing noted in Figure 419 Wing Root airfoil (chord normalized) Taper ratio Twist Sweep Layup Design z 1 x 1 z 2 x 2 twist () Baseline 0.06 0.22 0.02 0.83 0.43 0 15 [45]s A 0.045 0.25 0 0.7 0.9 10 14 [45,0,45] B 0.045 0.25 0 0.7 0.6 9 12 [45,0,45] C 0.1 0.25 0 0.65 0.5 9 10 [45]s D 0.1 0.25 0 0.7 0.6 5 10 [45]s E 0.1 0.3 0 0.85 0.5 0 6 [45]s Stiffer wing designs (three or two layer layups) also use higher geometric twist (wash out) As the wash out is reduced CL and L/D ratio increases whereas limit flight velocity is found to reduce. Wing aerodynamic loading has to undo the twist before global span wise snap through buckling of wing can occur. PAGE 104 104 Higher sweepback increases wing stiffness and benefits the wing load carrying capacity as experimentally demonstrated in Chapter 3. But wings with higher sweepback will result in higher negative coefficient of pitching moment about the air vehicle CG location. The requirement o f limiting Cm to be within 0.05 and 0 is found to restrict the wing sweepback to less than 14. Figure 420. Root airfoil shapes (top), curvatures along root airfoils (left) and planforms of semiwings for designs A, B, C, D, E and baseline wing. All wing designs use zero reflex. Reflexed wings have lower CL and hence lower L/D ratio and thus are not preferred. Cm requirement is mostly satisfied by adjusting the wing sweepback angle, wing wash out and taper ratio. While satisfying the Cm constraint wing sweepback is observed to be high when washout is high and taper ratio is high. Wing sweepback reduces when washout reduces as well as when taper ratio reduces. This reduction also results in the PAGE 105 105 reduction in limit flight velocity and increase in L /D ratio. Higher taper ratio wing designs have marginally lower CL and hence lower L/D ratio. Higher taper ratio designs also have comparatively lower static stability margin and less negative Cm. The structural behavior of selected P areto front designs under flight loads leading to Vlimit is shown in Figure 421. Designs A and B have higher sweepback angle and wash out, but these designs use low maximum camber towards leading edge. As a result these wings are observed to load stiffen but eventually snap through buckle (example of structural behavior of wing 2 noted in Figure 47). The p resence of sweepback and wash out gives them load stiffening ability, while due to the use of three layer laminate the maximum flight velocity that these wings can sustain before structural snap through buckling occurs is likely to be higher than a wing with the same geometry using only a two layer laminate. The laminate failure (material failure) occurring at the onset of snap through buckling is observed to limit the flight velocity for these wings. Figure 421. Wing flight load analysis for the baseline design and P areto front designs A, B, C, D and E. PAGE 106 106 Wing designs C and D use higher positive camber along with moderate sweepback and high washout, hence theses wings are observed to exhibit continued load stiffeni ng ability (an example of structural behavior of wing 3 as noted in Figure 47). The limiting flight velocity is observed to be governed by laminate failure for these wings. Wing design E has high camber (10%) but it uses low sweepback (6) and zero geometric twist, hence it load stiffens initially but eventually experiences snap through buckl ing Thus when layup is not a factor (two layer layups), stiffer wing designs in gener al use high camber, high negative geometric twist and high sweepback angle. While high L/D wing designs use aftward located large camber, zero aftward located reflex, zero washout and lower taper ratio. Pareto front Layup fixed at [45]s and Geometric twi st fixed at 0 In the earlier study detailed above, wing designs using three layer laminate were found to use lower camber due to storage diameter constraint, which resulted in lower CL and consequently lower L/D ratio than the baseline wing, whereas the w ing designs having two layer laminate were found to use wing geometries that performed better than the baseline wing in both the objectives. Additional optimization runs are performed by fixing the layup to two layers of [45]s orientation. To study effect of wing geometric twist angle, another optimization study is performed by fixing it to zero. The resultant P areto fronts are shown in Figure 422 and root airfoil and planform shapes for selected designs are shown in Figure 423. The P areto front with layup = [45]s and pitching moment constraint (points marked in black diamond) replicates the desig ns of the earlier study. Most of the wing designs use 10% maximum camber located at 25% chord and zero reflex located at 65% or 70% chord, with taper ratio of 0.5 or 0.6. Most aerodynamically efficient design (wing design 2, as noted in F igure 422, T able 4 7 and Figure PAGE 107 107 423) uses 10% camber located at 35% chord and zero reflex at 85% chord, with lower taper ratio of 0.5, zero twist. Additional use of lower sweepback angle also limits the flight velocity of this wing to 21.7 m/s. Spread across the P areto front is mainly g overned by twist and sweepback angle. Figure 422. Pareto optimal front: Effect of fixing layup and geometric twist angle = 0 When the twist angle is fixed at zero (design 1 versus design 1 in Figure 422 and Figure 423), the wing CL improves which results in improvement of L/D ratio. Washout was also found to help in increasing load carrying capacity of the wing, as noted in earlier study, hence when twist angle was fixed at zero, it reduced the limit flight velocity (design 1 compared with design 1 in Figure 422). The range of L/D ratio as well as Vlimit reduces as a result of fixing twist angle to zero. The spread across the P areto front is now mainly governed by sweepback angle and taper ratio. The Cm constraint limits the sweepback angle, which in turn limits the load carrying capacity of the wings. PAGE 108 108 T able 4 7. Design variable and objective function values for the Pareto design points noted in Figure 422 Wing Root airfoil (chord normalized) Taper ratio Twist Sweep Layup L/D ratio V limit Design z 1 x 1 z 2 x 2 twist () (m/s) Baseline 0.06 0.22 0.02 0.83 0.43 0 15 [45] s 9.50 27.1 1 0.1 0.25 0 0.65 0.7 8 10 [45] s 9.58 45.9 1' 0.1 0.25 0 0.65 0.7 0 10 [45] s 11.14 33.8 2 0.1 0.35 0 0.85 0.5 0 4 [45] s 11.65 21.7 3 0.1 0.25 0 0.65 0.9 0 12 [45] s 10.76 34.6 Figure 423. Root airfoil shapes (left) and planforms of semi wings for designs 1, 1, 2, 3 and baseline wing noted in Figure 422. Pareto front Pitching moment coefficient constraint removed Constraint on Cm was found to restrict the sweepback angle in an earlier study and hence the load carrying capacity of the wings. I n order to study effect of Cm constraint an additional optimization run is performed by removing this constraint. The resultant P areto front is compared with earlier fronts in Figure 424. PAGE 109 109 Figure 424. Pareto optimal fronts: effect of Cm constraint. After removing Cm constraint most of the P areto front designs (red star points in Figure 424) are found to use the highest possible sweepback angle. Increased sweepback moves the aerodynamic center aft and is found to increase negative pitching moment about the air vehicle CG location (refer Table 4 8) All of the P areto front designs now have high negative Cm ( 0.15 to 0.23). As the sweepback is found to help in increasing load carrying capacity of the wings, there is an associated increase in the limit flight velocity for the wings. In the absence of Cm constraint, the maximum camber location also moves afterward for all the designs which is found to improve L/D ratio of the wings. All of the designs on the P a reto front use minimum allowed taper ratio of 0.5. Most of the designs use zero reflex located at 70% chord. Spread across the P areto front is mainly governed by geometric twist (wash out) angle. PAGE 110 110 Table 4 8. Design variable and function values for the Paret o design points noted in Figure 424 Wing Root airfoil (chord normalized) Taper ratio Twist Sweep L/D ratio V limit C m Design z 1 x 1 z 2 x 2 twist () (m/s) Baseline 0.06 0.22 0.02 0.83 0.43 0 15 9.50 27.1 0.062 4 0.09 0.35 0 0.7 0.5 10 30 9.32 50.8 0.176 5 0.1 0.35 0 0.7 0.5 5 28 11.17 45.9 0.178 6 0.1 0.35 0 0.85 0.5 0 30 11.92 34.9 0.225 7 0.085 0.3 0.01 0.65 0.5 0 30 11.18 43.6 0.182 Figure 425. Root airfoil shapes (left) and planforms of semi wings for designs 4, 5, 6, 7 and baseline wing noted in Figure 424. Additionally fixing the twist angle to zero is found to improve the aerodynamic efficiency while the load carrying capacity of the wings is found to decrease, as discussed earlier. PAGE 111 111 C HAPTER 5 DESIGN OF BENDABLE WING UNDER UNCERTAINTY In deterministic optimization usually an experience based factor of safety is considered in the design process and t he optimization process pushes the designs to the boundaries of the constraints. The effe ct of uncertaint ies in the design variables (wing shape parameters and the composite layup in this study ) and random design parameters (lamina thickness, material stiffness and strengths) on the performance metrics and the constraints is of interest. Deter ministically optimized designs are usually sensitive to variable uncertainties and thus have unknown actual safety levels. In this sense deterministically optimized designs are not optimal in performance as well as safety. The uncertainties in design vari ables and parameters can be quantified with the knowledge of manufacturing methods and the experimental measurement techniques used There are uncertainties related to modeling and analysis techniques as well, quantification of which involves experimentati on and/or experience. In the present study design variable uncertainties are estimated using experimental observations while the random parameter uncertainties are used from a mix of experimental measurements and literature review. Uncertainties associated with modeling techniques are calculated from the convergence studies performed in chapter 4 When all of these uncertainty sources are considered, the deterministically optimized wing shapes may result in high probability of failure designs and the design variables (mean values) need to be adjusted so as to obtain the wing designs with acceptable failure rate. In probabilistic optimization, no factor of safety is considered; actual variable uncertainties and their underlying random distributions are modeled. M onte Carlo simulation (MCS) techniques are typically used to study uncertainty propagation where mult iple failure modes are present (violation of any of the constraint is termed failure here). T o give an accurate estimate of PAGE 112 112 the probability of failure or reliability, MCS requires a large number of samples. T o alleviate the computational burden surrogate m odels are used for the objectives and constraints. Xueyong Qu et al. [100] used reliability based optimization with constraint on probability of failure for optimiz ation of composite laminate for cryogenic environment. Use of multiple surrogates for optimization have been reported in the literature [101] [102] which involves fitting multiple surrogates and performing optimization multiple times with multiple surrogates [101] The u se of weighted average surrogate (WAS) [103] [104] is also reported in the literature in which the weights associated with each surrogate model are determined based on the global cross validation error measure, predicted error sum of squares (PRESS) B ut the use of WAS does not always guarantee better results [105] In the current study, instead of a single surrogate per objective and constraint, multiple surrogates are fitted ( including kriging [106] [107] polynomial response surface [108] [109] radial basis neural network [110] [111] and support vector regression [112] ) and one surrogate; best surrogate is picked based either on cross validation [113] [105] or test points based root mean square error ( RMSE ) Simultaneous use of multiple surrogate s to identify richer Pareto optimal front [105] is not found to benefit in the current study. The Pareto optimal front design predictions from the best surrogate are found to dominate the Pareto front designs achieved using other relatively inferior surrogates Th e remain der of th is chapter is organized as follows. Uncertainty propagation analysis is performed by using the original computational model simulations and the probability of failure is estimate d for some of the Pareto front designs using Monte Carlo samp ling technique A l ater s ection discusses the probabilistic problem formulation and response surface modeling. The effect of using different target probability of failure on Pareto front designs is studied. The f inal section c loses the chapter recapitulati ng salient points and concluding remarks. PAGE 113 113 Uncertainty Quantification and Propagation Three sources of uncertainties are considered in the study; uncertainties from the random design variables, from the random parameters (which are not design variabl es) and the modeling uncertainties Uncertainties from random variables and random parameters are estimated from the experimental observations and literature, while the modeling uncertaint ies are calculated based on the computational model convergence studied Th e bendable wing shape variables and manufacturing layup orientations have uncertaint ies associated with them arising from systematic as well as random sources. This uncertainty when propagated to constraints will make current feasible deterministic designs fail (violate constraints). Table 51 details uncertaint ies in design variables considered in the present work The wing shape parameters will be affected by the manufacturing t ooling in accuracy as well as the spring back (more correctly spring in) of thin composite shells [114] Since spring in is shown to be related to the initial bend in the composite structures [115] the uncertainty in the root airfoil definition parameters is considered to be proportional to their set values (mean values). The geometric twist angle being defined as the angle tip chord line makes with the root airfoil chord line, equal proportional amount of springin of both the cross sections is assumed to result in almost no change in twist angle. Thus it can be treated as a d eterministic variable. The taper ratio and the sweep angle are also considered as deterministic variables in the present study. Wings having two layers of 45 composite layup are considered in the study. Since the wings are manufactured using hand prepreg layup and curing under vacuum bagging, the layup orientation is susceptible to human error as well as shift during vacuum bagging application and curing process; associated uncertainty is considered in the study. PAGE 114 114 Table 51. Uncertaint ies in random desi gn variables Variable Root a irfoil Planform Layup orientations z 1 x 1 z 2 x 2 twist 1 2 Uncertainty 10 % of set value Distribution Normal distribution Normal distribution Random Deterministic Random Lamina thickness, material stiffness and strength parameters also have uncertainties associated with them due to the manufacturing as well as underlying testing process and representative uncertainty values for them are considered in the present study ( Table 5 2). Table 5 2. Uncertaint ies in random parameters Parameter Material properties Lamina thickness (mm) Material s trength v alues (MPa) ** E 1 (GPa) E 2 (GPa) 12 G 12 (GPa) F1t F1c F2t F2c F6 Mean value 34.80 34.80 0.05 2.34 0.254 324 338 314 321 41 10 % 20 % Distribution Normal distribution Normal distribution *Material stiffness properties and lamina thickness have 10% uncertainty **Material strength values have 20% uncertainty The computational model uncertainties / error are selected based on the model convergence studies in chapter 4. Aerodynamic analysis is performed using medium fidelity 3D panel method. A predict ion error of 15% ( Table 53) is considered in the study. Limiting flight velocity is predicted using high fidelity A BAQUS modeling and a lower prediction error of 10% is found to be justified based on convergence study results (chapter 4) For calculating rolling diameter at first ply failure, an analytical method; a classical laminate plate theory and strain superposition based approach is used. The experimental strain measurement s on wing showed the prediction errors are well within 20% PAGE 115 115 Table 53. Computational m odel u ncertainties Variable Aerodynamic measures Structura l measures CL Cm L/D Kn Vcruise Vlimit Dmin Uncertainty ( 15% 10% 20% Distribution uniform uniform *Aerodynamic measures have 15% modeling error To check the effect of the design variable and parameter uncertaint ies on the Pareto optimal design s, representative design points a1, a2 and a3 marked in Figure 51, are selected and uncertainty propagation as well as probability of failure (Pf) calculations is performed for each of the selected design s Figure 51. Selected Pareto optimal design points a1, a2 and a3 for uncertainty propagation and probability of failure study. Design of experiments (DOE) is performed at each of the three points using Monte Carlo simulation with 1000 Latin Hypercube Sampling (LHS) points normally distributed about the design point under consideration. Violation of any of the design constraints, as listed in Equation 45, is considered as a failure. Probability of failure is simply a ratio of number of LHS points that violated constraint boundaries (Nf) over total number of LHS point (N=1000). Although 1000 points is a moderate number for direct probability of failure calculations, better accuracy PAGE 116 116 predictions can be achieved by using mean and standard deviation information from the simulation to calculate reliability index (how many standard deviations away the mean value is from the constraint boundary) and predicting probability of failure based on the reliability index. Moreover, we are interested in the indicative values rather than exact values. Table 54 shows the results of the uncertainty propagation study. Uncertainty (three standard deviation) and coefficient of variation (CV) values reported here are the maximum amongst the three design points considered. Aerodynamic performance metrics are observed to have lower propagated uncert ainties than the structural performance metrics Aerodynamic performances are functions of wing geometry alone whereas structural performances are additionally affect ed by wing composite layup, lamina thickness and material elastic as well as strength properties. The uncertainties associated with these parameters results in high coefficient of variation for Vlimit and Dmin values. Table 54. Uncertaint ies for the deterministic Pareto front designs noted in Figure 51 Performance Metric CV (%) Objectives L/D ratio 0.27 0.9% Vlimit (m/s) 10.4 8.1% Constraint parameters Vcruise (m/s) 0.26 0.7% CL 0.03 1.5% K n 0.001 0.1% D min (inch) 2.08 19.9% Cm 0.005 3.1% Table 55 shows probability of failure for the deterministic Pareto front design points with and without considering modeling uncertainties As can be seen, the current probability of failure for the Pareto optimal design points, when all sources of uncertainties are considered in the design process, is quite high. This is somewhat expected as deterministic optimization pushes designs to the constraint boundaries. Pf distribution does not seem to follow any particular trend across the Pareto front ( three point data is insufficient to conclude anything). Lower limit on the PAGE 117 117 pitching moment coefficient and the storage diameter constraint is noted to govern the probabi lity of failure values. After adding the modeling uncertaint ies the failure rate becomes unacceptable. It is desire d to find out optimal designs that satisfy certain target probability of failure requirement while including all the uncertainty sources and thus there is a need to perform design of the bendable wing under uncertainty Table 55. Current probability of failure for Pareto optimal designs noted in Figure 51 Pareto f ront design point P f (with variable uncertainty alone) P f (with addition of modeling uncertainty) a1 0.08 6 0.31 1 a2 0.316 0.41 8 a3 0.256 0.41 1 Reliability Based Design Optimization (RBDO) of Bendable Wing Design Space Reduction and RBDO Problem Formulation By observing the Pareto optimal designs achieved during deterministic optimization work, it is possible to tighten the box constraints for z1 z2, taper ratio and sweepback angle. All of the Pareto optimal designs that perform better than the baseline wing design, are observed to use two layers of 45 laminate layup orientation. During simulations the single layer wing wa s found to possess lower stiffness and a laminate with more higher than two layers was found to be either too stiff to roll inside a canister without laminate failure due to rolling strains or had lower L/D ratio than the baseline wing because of lower leading edge curvature and hence camber limited by storage constraint Two layers of 0/90 layup was also too stiff to roll. Thus wing manufacturing layup is fixed at [45]s and to account for uncertainty in layup orientation it is treated as random design parameter. The revised design variables, their side constraints and associated uncertainties are detailed in Ta ble 56. PAGE 118 118 Table 56. RBDO : s ide constraints for the design variables Variable Root a irfoil Planform z1 x1 z2 x2 twist Lower bound 6% 15% 2% 65% 0.5 10 0 Upper bound 10% 35% 0% 85% 0.9 0 20 10 % Distribution Normal distribution Random Deterministic *Root airfoil parameters have 10 % uncertainty The design variables are thus X = (z1, x1, z2, x2 twist, all of the deterministic constraints are converted in to reliability constraints where we want to achieve a certain target reliability index t (also function of probability of failure Pf t) for each of the Pareto optimal front designs. Combining all the constraints into a single reliability index constraint is found to give an inferior reliability index surrogate with high prediction errors and hence this approach is not utilized in the study. To perform optimization under uncertainty, RBDO problem is formulated as below : M aximize f( X ) = L/D and M aximize g( X ) = Vlimit such that: i t i = 1 to number of deterministic constraints L ( 51) R espo nse Surface Approximations The cost of evaluating designs is high in the case of nonlinear snap through buckling analysis (Vlimit) which involves ABAQUS procedure and the aerodynamic analysis using AVL. These we re also limiting factors for the population size and the number of gener ations that we re used during the earlier deterministic optimization study using NSGA II algorithm. Furthermore, it is desirable to have a large number of Monte Carlo sampling points if we want to predict probability of failure with reasonable accuracy The coefficient of variation of the computed PAGE 119 119 failure probability is given by, f/ Pf] (1 Pf)/Pf.N) In the present study 100,000 sampling points are used. The mean and standard deviation predictions from these large numbers of sampling points are then us ed to compute and construct the reliability index surrogates for individual deterministic constraints. Thus using direct analysis methods for objective and constraint evaluation s become infeasible while performing reliability based design optimization. Di fferent types of response surface approximations are fitted and use of either the best performing surrogate or combination of best two surrogates is explored in the optimization study. For fitting response surface to objectives: L/D ratio and Vlimit in terms of seven design variables, a design of experiment (DOE) of 300 points is used. The DOE utilized is combination of face centered central composite design (CC F ) filled with Latin hypercube sample points Vlimit values are without considering factor of safety. The earlier deterministic Pareto front designs are used as test points (30 points) and the best performing surrogate s based on combination of lowest PRESSRMS and lowest RMSE are used in the optimization. PR ESSRMS is given by [105] : = ( 52) where, n = no of points in DOE vector of cross validation errors. The k fold strategy [105] is used to reduce the computational cost of evaluating PRESSRMS. Instead of regular leaveone out strategy where one point is removed at a time and the surrogate is fitted to remaining data set, in kfold strategy n/k data point s are removed from the total DOE data set at a time and the surrogate is fitted to the remaining data while using the removed data points as test points. The process is repeated k times. Such an approach with k=10 (10% of data points removed at a time) is found to reduce computational cost while maintaining accuracy in the PRESSRMS calculation [105] PAGE 120 120 S urrogate model s are also developed for reliability index estimation. Since reliability index calculation involves high computation cost in terms of high number of sampling point e valuations, surrogate models are develop ed for each of the constr aint performance metric A second level sampling on these surrogates is used to construct reliability index surrogates. Aerodynamic performance metrics are functions of wing shape alone ( seven geometric design variables) and hence a DOE (combination of CC F and LHS filling) of 300 points, as used for objective function surrogate evaluations, is utilized. Structural constraint Dmin is a function of wing geometry as well as wing laminate layup, lamina thickness and material properties. Taking into account 7 design variables (4 random and 3 deterministic) and 12 more random parameters (hence total 1 9 variables), a DOE of 700 points is used to find the surrogate model for Dmin constraint. Latin hypercube sampling is utilized The statistical measure used to ch eck the quality of surrogates for the constraints is PRESSRMS [105] The best performing surrogate for each of the constraints is later used to find the reliability index surrogate for individual deterministic constraint. The surrogate model for each constr aint is in terms of 7 original design variables and hence a DOE of 300 points is used (same DOE as that for objectives) and at each of these 300 points, a second level DOE of 100,000 normally distributed points (using Matlab native function lhsnorm) is used to estimate the mean and standard deviation s of constraint performances and later reliability index Modeling uncertainty /error in constraint performances are added while performing the above said second level DOE. A simpler approach is utilized to achieve this. The m odeling error is assumed to have uniform distribution. A random number is generated within the error bound values of the individual deterministic optimization constraint and the respective surrogate prediction is multiplied by this random number. These modified values are then passed on to calculate the mean and standard deviation and later reliability index PAGE 121 121 of each constraint. The m odeling error in Vlimit prediction is also incorporated in its surrogate whereas L/D ratio surrogate is found to deteriorate (high PRESSRMS value) with addition of the modeling error and hence the modeling error is left out while constructing the L/D ratio surrogate. Hence while considering L/D ratio predictions a 15% error should be associated with the surrogat e predictions. The best two surrogates for each performance metric and their corresponding PRESSRMS values and PRESSRMS (%) values (PRESSRMS % = PRESSRMS / range of estimated output) are detailed in Table 57. The best surrogate with minimum PRESSRMS is utilized in the present study. KRG0 KRG1 and KRG2 stand for kriging model s using zero first and second order polynomial regression model s, respectivel y and all using Gaussian correlation model while PRS2 stands for second order polynomial response surface (full model is used) PRS3 (full third order polynomial response surface) was also tried The reliability index surrogates for coefficient of pitching moment constraint showed unacceptable PRESSRMS values (refer Table 57) ; hence a more straight forward approach is used. Surrogates are constructed to predict the mean and standard deviation for Cm as a function of design variables and the reliability index is calculated for each trial design during optimization based on these surrogates and respective Cm constraint boundaries. The d esign of a bendable wing under uncertainty is performed using an elitist nondominated sorting genetic algorithm: NSGA II [98] used in the earlier deterministic optimization study. The p opulation size is 30 at each generation and such 2000 generations are tried taking advantage of the minimal computational cost of evaluating the surrogates. Also the design variables are now discretized more densely. PAGE 122 122 Table 57. Surrogate models with associated PRESSRMS and PRESSRMS (%) Surrogate for Surrogate PRESS RMS PRESS RMS (%) Objective functions L/D ratio KRG1 0.034 0.47 KRG2 0.031 0.42 V limit (m/s) KRG2 3.65 10.40 PRS2 3.58 10.18 Reliability index constraints cruise < 20) KRG1 0.058 0.44 KRG2 0.045 0.34 L > 0) KRG1 0.051 3.15 KRG2 0.039 2.40 n > 0.1) KRG0 0.051 0.49 KRG1 0.037 0.36 min < 4) KRG1 0.042 0.59 KRG2 0.037 0.52 m > 0.1) KRG0 0.37 2.00 KRG2 0.48 2.55 m > 0.05) KRG0 0.66 3.75 KRG1 1.30 7.42 m < 0) KRG0 0.22 2.50 KRG1 0.34 3.82 C m ** C mmean KRG0 3.16E 04 0.17 KRG2 2.41E 04 0.13 C mstd KRG0 1.42E 04 1.14 KRG2 7.72E 05 0.62 Surrogate PRESS RMS is found to be high ** Surrogates are fit to Cm mean and Cm standard deviation estimation Results and Discussion Figure 52 shows the Pareto optimal fronts achieved with two levels of target reliability index when the limit on coefficient of pitching moment is 0.05 The uncertainty i n Vlimit prediction is 3. 6 m/s ( its surrogate includes the modeling error) while er r or in L/D ratio reported in the text below is 15% (modeling error is not included in the L/D ratio surrogate ). The design variable values for the Pareto optimal front points marked on the Figure 52 are tabulated in Table 5 8. The aerodynamic and structural performance parameter values are PAGE 123 123 provided in Table 5 9 for reference. Root airfoil and planform shapes for selected wing designs are shown in Figure 53 for easy visualization. The RBDO design Vlimit values are without considering factor of safety and hence depending on the structural behavior of the wing (refer Figure 47), those should be in general higher than deterministic optimization design values for the same wing shapes. The requirement of higher reliability however restricts the Vlimit improvement. During t he earlier deterministic optimization study (detailed in chapter 4) coefficient of pitching moment constraint was observed to be the most influential constraint limiting permissible sweepback angle for the wing designs. With increase in reliability require ment this constraint further restricts the possible sweepback angle range to 4 to 9 for reliability index limit corresponding to Pft = 13 and to 6 to 8 for Pft = 16. With such small reduction in sweepback angle there is associated marginal loss in wing stiffness. Figure 52. Pareto optimal front s: Deterministic designs compared with RBDO designs of different levels of reliability index constraint. Since the pitching moment co efficient constraint was critical and n o factor of safety was considered on th is constraint dur ing deterministic optimization, when the uncertainties were considered in the design process ; deterministic ally optimized designs showed higher PAGE 124 124 pr obabilities of failure (refer Table 55). During probabilistic optimization it was discovered that adding safety in pitching moment coefficient constraint in terms of reliability requirement did not cost much in terms of objectives. Probabilistic Pareto fronts with reliability index corresponding to Pft = 13 and Pft = 16, almost fall on top of each other and lay close to deterministically optimized Pareto front. A s mall reduction in sweepback angle is found to satisfy the increased stringent reliability requirement and hence the Pareto front does not move much when the reliability index limit is changed corresponding to Pft = 13 to Pft = 16 (refer Figure 52i), a lower limit on Cm is found to be the most critical constraint followed by constraint on storage d iameter (Dmin) and static stability margin (Kn). The probabilistically optimized designs with higher Vlimit (design set S1 in Figure 52, right) showed actual factor of safety of 1.41 in the storage diameter constraint. Thus a factor of safety of 1.5, for minimum storage diameter constraint, considered during deterministic optimization is found to be sufficient. Table 5 8. Design variab le and objective function values for the Pareto design points noted in Figure 52 Wing Root airfoil (chord normalized) Taper ratio Twist Sweep Layup L/D ratio V limit Design z 1 x 1 z 2 x 2 twist () (m/s) Baseline 0.06 0.22 0.02 0.83 0.43 0 15 [45]s 9.50 27.1 ** R1 0.1 0.2 0 0.65 0.5 8 9 [45] s 9.82 45.3 R2 0.1 0.2 0 0.81 0.5 0 7 [45] s 11.59 36.9 R3 0.1 0.25 0 0.82 0.5 0 6 [45] s 11.63 29.2 V limit values are without considerin g factor of safety ** Baseline wing V limit value is with factor of safety All the designs on both of the Pareto fronts are found to use 10% maximum camber, zero reflex and taper ratio of 0.5. The spread across Pareto fronts is governed by remaining design variables. The RBDO Pareto front can be divided in two linear looking regi ons: design set S1 PAGE 125 125 (refer Figure 52) shows gradual reduction in Vlimit value but improvement in L/D ratio is at higher rate, while design set S2 shows almost same L/D ratio when Vlimit value is found to reduce at high rate. Table 5 9. Design variable and objective function values for the Pareto design points noted in Figure 52 Wi ng V cruise C L K n D min C m Design (m/s) (inch) Baseline 12.2 0.58 0.46 2.7 ** 0.062 R1 11.3 0.65 0.27 1.98 0.037 R2 9.4 0.94 0.23 1.98 0.034 R3 9.2 0.99 0.20 1.75 0.039 Values are calculated without considering factor of safety ** Baseline wing D min value is with factor of safety Figure 53. Root airfoil shapes (left) and planforms of semi wings for designs R1, R2, R3 and baseline wing noted in Figure 52. For the Pareto front designs corresponding to design set S1, as we move from designs with higher Vlimit and lower L/D ratio (e.g. design R1) to designs with relatively lower Vlimit and higher L/D ratio (e.g. design R2) negative geometric twist (wash out ) is found to reduce from 10 to 0, zero reflex location moves aft ward (0.65 to 0.85) and sweepback is found to reduce by 2 The m aximum camber location does not change and remains fixed at 0.2. Reduction in wash out (negative geometric twist) has asso ciated reduction in Vlimit and improvement in L/D ratio, as is discussed earlier. For the design set S2 as we move from designs with relatively PAGE 126 126 higher Vlimit (e.g. design R2) to designs with lower Vlimit (e.g. design R3), maximum camber location is found to move aft (0.2 to 0.3) zero reflex location moves slightly aft ward (0.8 to 0.85) and sweepback reduces by additional 1 to 2 degree. With the same maximum camber (10%) by moving its location aft ward the leading edge curvature reduces which in turn red uces win g stiffness at its root airfoil T his coupled with reduction in wing sweepback angle results in the reduction of Vlimit value. To check the effect of wing coefficient of pitching moment constraint its lower limit is reduced from 0.05 to 0.1. This corresponds to the 4x4 inch flat plate horizontal stabilizer initial AOA being changed from 12 degrees to 20 degrees. Even with such a change the horizontal stabilizer should have operating range of 10 de grees before horizontal stabilizer might experience stall at increased negative AOA [1] Figure 54 shows the Pareto fronts corresponding to this change with keeping the reliability index constraint at same level (corresponding to Pft = 16) Table 5 10 and Table 5 11 give the design variable and performance parameter values for selected wing designs as noted in Figure 54. The root airfoil and planform shapes for these selected designs are shown in Figure 55 for ready visualization As more negative Cm is allowed, designs with higher sweepback are selected (refer Table 510). There is an associated increase in the wing stiffness and he nce the Vlimit. The Pareto front is thus found to move up (refer Figure 54). Similar to observations made earlier, the Pareto front can be divided in two linear regions and relation of design variables and resulting performance parameters is observed to be the same as di scussed in earlier paragraphs. PAGE 127 127 Figure 54. Pareto optimal front s: Deterministic designs compared with RBDO designs of different levels of reliability index constraint. Table 5 10. Design variable and objective function values for the Pareto design points noted in Figure 54 Wing Root airfoil (chord normalized) Taper ratio Twist Sweep Layup L/D ratio V limit Design z 1 x 1 z 2 x 2 twist () (m/s) Baseline 0.06 0.22 0.02 0.83 0.43 0 15 [45]s 9.50 27.1 ** R4 0.1 0.2 0 0.65 0.5 9 15 [45] s 9.56 47.6 R5 0.1 0.2 0 0.65 0.5 5 14 [45] s 10.87 42.7 R6 0.1 0.2 0 0.85 0.5 0 12 [45] s 11.67 39.0 R7 0.1 0.27 0 0.85 0.5 0 10 [45] s 11.72 28.4 V limit values are without considerin g factor of safety ** Baseline wing V limit value is with factor of safety PAGE 128 128 Table 5 11. Design variable and objective function values for the Pareto design points noted in Figure 54 Wing V cruise C L K n D min C m Design (m/s) (inch) Baseline 12.2 0.58 0.46 2.7 ** 0.062 R4 11.7 0.61 0.44 1.98 0.071 R5 10.5 0.75 0.42 1.98 0.07 R6 9.4 0.94 0.37 1.98 0.067 R7 9.1 1.01 0.31 1.7 0.07 Values are calculated without considering factor of safety ** Baseline wing D min value is with factor of safety Figure 55. Root airfoil shapes (left) and planforms of semi wings for designs R4, R5, R6, R7 and baseline wing noted in Figure 54. When considering the entire Pareto front designs some general observations can be made. RBDO could identify stiffer and aerodynamically efficient designs than the deterministically optimized wing designs. Stiff (high Vlimit) wing designs use maximum camber toward the leading edge (high curvatures), high wash out ( negative geometric twist angl e) and high sweepback angle whereas e fficient (high L/D ratio ) wing designs use aft ward located maximum camber zero reflex, zero geometric twist and lower sweepback angle. We can obtain wing designs that can fly faster if we allow relatively high er prob ability of failure By better quality control PAGE 129 129 (reducing uncertainty bounds on random variables and random parameters) we can get improv ed designs that are superior to the baseline wing in both the objectives while maintaining acceptable target probability of failure. PAGE 130 130 CHAPTER 6 CONCLUSIONS AND FUTURE WORK The bendable load stiffen ed wing has a unique ability to load stiffen in the positive flight load direction while remaining compliant in the other (folding/packing) direction. The compliant nature is demonstrated experimentally using a visual image correlation ( VIC ) system. When a downward rolling moment is applied on the wing the root airfoil is shown to los e its camber and flattens. With the continuation of the applied rolling moment the wing is able to be rolled into a cylindrical shape. This enables compact storage of the bendable wings inside a small diameter canister. The a ddition of quarter chord sweepb ack gives a load stiffening ability to the wing and increases its positive flight load carrying capacity. To verify and quantify the load stiffening effect, a three point bend test setup and a high resolution VIC system is used. Center of pressure location s on individual wing halves, as determined using the aerodynamic 3D panel code, are used as two support locations in the test and an increas ing downward force is applied at the center of gravity location of the aircraft. While a straight camber wing having zero quarter chord sweepback could support a maximum load of 9 N (~ 2 Gs load factor), the swept camber wing (load stiffen ed wing) having 15 quarter chord sweepback supported 30.74 N central load (~ 7 Gs load factor). The leading edge of the load stiffen ing bendable wing is found to move down increasing its root airfoil camber and wing stiffness with increase in the central load. This gave higher load carrying capacity to the load stiffening wing. More sweepback could potentially further increase the load stiffening ability and the load carrying capacity of the wing. The locations of the fuselage mounting holes drilled on the wing at its root airfoil also play an important role in deciding the wing buckling load. A quick check shows that moving the front mounting hole more towards the leading edge helps to improve wing loa d carrying capacity. PAGE 131 131 Wind tunnel tests performed at 7x104 Reynolds number show that the addition of sweepback angle does not have significant effect on the wing aerodynamics. Both the wings show ed similar CL values and the lift curve slopes The swept camber wing show ed marginally higher CD at low angles of attack. The L/D ratios are similar for both of the wings with the straight camber wing showing the highest L/D ratio of 8.4 versus 8.27 observed for the swept camber wing. The h ighest L/D ratios are obser ved to be at an angle of attack of 5. S weepback also helps in improving the static stability (higher dCm/dCL derivative) of the wing. Since the bendable wings might be stored inside a canister for a long duration before the MAV /UAV is deployed, VIC analysis is also used for the creep deformation measurement of the wings. S weepback introduced in the wing resulted in stable wing geometry with higher flexural stiffness than the wing with straight camber. The magnitude of residual s trains after storing the wing at 70 C for 24 hours is reduced for the wing with swept camber (load stiffening wing) than the wing with a straight camber. Permanent deformation caused by creep is thought to be with in acceptable limits. Thus with the additi on of sweepback angle, the load stiffening wing (swept camber wing) has a clear advantage over straight camber wing. It offers stiffness improvement, provides load stiffening ability and reduces storage induced creep residual strains while maintaining the aerodynamic efficiency of the wing and improving the static stability margin In order to understand the effect of fiber direction on the creep deformations and to develop the creep master curves ( material characterization), a dynamic mechanical analysis t esting technique was used along with a time temperature superposition (TTSP) technique to develop the master creep compliance curves for 0/90 and 45 fiber orientations at a reference temperature of 30C. Comparison of the master curves indicates 45 orien tation specimen show matrix dominated behavior while undergoing higher percent change in the creep compliance. By PAGE 132 132 virtue of the fibers oriented in the loading direction, the 0/90 specimen show lower change in the creep compliance. A multidisciplinary approach is used to perform a conceptual design study to optimize the aerodynamic efficiency of the wing while simultaneously maximizing its positive flight load carrying capacity Air vehicle wing aerodynamics, wing structural performance under aggressiv e flight loads and stresses developed in the wing during the rolling process are observed using appropriate numerical and analytical tools. Aerodynamics is studied using an inviscid, extended vortex lattice model based Athena Vortex Lattice ( AVL ) program, while, wing nonlinear snap through buckling under higher flight loads is studied using a modified Riks analysis based FEA routine in ABAQUS. The m aximum velocity (termed limit flight velocity) at which the air vehicle can fly, without wing structural fail ure or material failure, is calculated. Wind tunnel test results are utilized to validate the aerodynamic model predictions, while increasingly complex testing is performed to validate the limit flight velocity predictions of the nonlinear FEA routine. Lim it load predictions from numerical model for a singly curved as well as regular wings tested in the three point bend test mode were in good agreement with the experimental observations. Prediction errors were less than 5%. Numerical buckling predictions are fur ther validated by testing two wings inside the wind tunnel Buckling velocit y predict ions match ed very well with the wind tunnel results. An a nalytical approach based on strain superposition principle and laminate theory is used to calculate the strains and the stresses developed in the composite wing during the rolling process and Tsai Wu failure criterion with appropriate safety factor is used to predict the first ply failure of the composite laminate wing while it is rolled for storage PAGE 133 133 C onceptual des ign of a 24 inch span and 7 inch root chord bendable wing is performed using an elitist nondominated sorting genetic algorithm: NSGA II. The w ing is designed to maximize L/D ratio, an aerodynamic performance metric and to maximize wing limit flight veloci ty a structural performance metric. The designs on the Pareto optimal front are compared with a baseline design to identify numerous designs with improved performance H igher maximum camber and zero reflex both located aft ward, zero wash out and lower taper ratio are found to help increase wing aerodynamic efficiency. Higher wing washout and high sweepback angle is found to help increase wing flight load carrying capacity. Higher maximum camber located forward results in higher leading edge curvature w hich was found to help in increas i ng the wing flight load carrying capacity. Due to smaller storage volume requirement and resulting limitations on air vehicle horizontal stabilizer dimensions and its chord wise location with respect to the wing, a limit on wi ng pitching moment coefficient was placed. This limit as well as the storage diameter constraint was found to be critical during the optimization study. During the optimization process wing designs that continue to load stiffen (increase root airfoil cambe r) were discovered. Such wing designs were found to use higher maximum camber high washout and high sweepback angle. When uncertainties in modeling, design variables and random parameters are taken into account, deterministic ally optimiz ed designs show ed high probabil ity of failure. Reliability based design optimization (RBDO) methodology is utilized. Accurate surrogate models are constructed for wing aerodynamic as well as structural performance metrics predict ion Reliability index surrogates are constructed for each of the constrain t s Best surrogate models based on PRESSRMS value are selected for optimization. The d esign space is reduced by using the results of the deterministic optimization study. As the demand on reliability increased, wing designs with PAGE 134 134 reduced sweepback angle are used. A l ower limit on Cm is found to be the most critical constraint followed by constraint on storage diameter (Dmin) and static stability margin (Kn). When the lower limit on Cm is relaxed, wing designs with higher sweepback are selected, which resulted in wing limit flight v e l o c i ty improvement. RBDO could identify stiffer and aerodynamically efficient designs than the deterministically optimized wing designs. In general, s tiff (high Vlimit) wing de signs use maximum camber toward the leading edge (high curvatures), high wash out ( negative geometric twist angle) and high sweepback angle, whereas e fficient (high L/D ratio ) wing designs use aft ward located maximum camber zero reflex, zero geometric tw ist and lower sweepback angle. We can obtain wing designs that can fly faster if we allow relatively higher probability of failure Suggested future work While validated aerodynamic and structural models were utilized in the optimization study, to ascertain the superiority of the optimized designs selected wing designs can be manufactured and tested to evaluate their aerodynamic as well as structural performance. Potential wing designs (deterministically optimized) that can be tested have been identified i n Table 4 6, T able 47 and Table 4 8. Potential candid ates for wing designs that are optimized under uncertainty have been identified in Table 5 8 and Table 5 10. The master curves developed in the current study and detailed in chapter 3 can be approximated by suitable analytical models. The power law model developed by Findley [125] is one of the popular analytical models used for viscoelastic material modeling. A Prony series hereditary integral model [127] can be used to develop a viscoelastic material model. This model can further be used in a nonlinear FEA based analysis approach to develop a creep deformation prediction tool. Such a tool should be able to predict the full field basis creep deformation of the PAGE 135 135 bendable wi ng after the wing is stored at a stipulated temperature and for specified time duration. Such predictions can be advantageously used to design wings that will experience lower creep deformations making them suitable for long term storage or to redesign the wings and the wing manufacturing molds so as to have the required wing geometry and the wing performance even after experiencing long term storage induced creep deformations. Stiff wing designs (high Vlimit) identified in the current study when flying at high flight velocities might experience flutter. The periodic unsteady vortex shedding at the trailing edge (forcing function) can interact with the inbuilt wing natural frequency (function of the wing stiffness and the wing mass distribution) to create undesirable vibrations that might result in wing buckli ng or catastrophic failure of wing laminate. This might become limitation especially at high flight speeds, even before snap through buckling of the wing occurs due to assumed steady state aerodynamic loads This aspect of the bendable wing design can be explored further by utilizing topology optimization If the flutter is found critical, the wing stiffness distribution can be changed by adding additional partial layers in the original layup. With the current research focus moving towards flapping wing concepts and Nano air vehicles [2] [3] the b endable wing design conce pt can be used to develop bendable flapping wings that work on the lines of ladybug wings. Ladybug folds its wings when not in use and deploys them just before its flying venture. The compliant nature of the bendable wing concept can be utilized to store t he high aspect ratio wings in compact volumes which can be deployed when needed. 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After joining Dr. Ifjus lab, Vijay briefly worked on manatee skin testing before his dissert ation work on the Bendable MAV w ing project. While performing his research tasks, Vijay also enjoyed being active in the student and local Gainesville community H e took up leadership roles in the student community initially as Treasurer of Indian Student Association G rad A ffairs and later as Graduate Student Senator of UF Student Government representing, advocating and working on graduate student problems on UF campus. Vijay complet ed the requirements for his Doctor of Philosophy degree in mechanical engineering in December 2010. |