Fixed membrane wings for micro air vehicles: Experimental characterization, numerical modeling, and tailoring

Progress in Aerospace Sciences

Volumn 44, Issue 4, 2008, Pages 258-294

  Stanford, Bret ^a   Ifju, Peter ^a   Albertani, Roberto ^a   Shyy, Wei ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AERODYNAMICS; DRAG REDUCTION; OPTIMIZATION; REYNOLDS NUMBER;

FIXED MEMBRANE WINGS; MICRO AIR VEHICLES;

WINGS;

EID: 44249115774     PISSN: 03760421     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.paerosci.2008.03.001     Document Type: Review

References (147)

1. Ailinger K. US navy micro air vehicle development. In: International UAV conference, Bristol, UK, April 12-14, 1999.
2. Torres G, Mueller T. Micro aerial vehicle development: design, components, fabrication, and flight testing. In: AUVSI unmanned systems symposium and exhibition, Orlando, FL, July 11-13, 2000.
3. Grasmeyer J, Keenon M. Development of the black widow micro air vehicle. In: AIAA aerospace sciences meeting and exhibit, Reno, NV, January 8-11, 2001.
4. Ifju P, Jenkins D, Ettinger S, Lian Y, Shyy W, Waszak M. Flexible-wing-based micro air vehicles. In: Confederation of European aerospace societies aerodynamics conference, London, UK, June 10-12, 2003.
5. Shkarayev S, Null W, Wagner M. Development of micro air vehicle technology with in-flight adaptive-wing structure. NASA contractor report, CR-213271, 2004.
6. Sun D, Wu H, Zhu R, Hung L. Development of micro air vehicle based on aerodynamic modeling analysis in tunnel tests. In: IEEE international conference on robotics and automation, Barcelona, Spain, April 18-22, 2005.
7. Settles G. Fluid mechanics and homeland security. Annu Rev Fluid Mech 38 1 (2006) 87-110
8. Brewer K. High-Tech micro air vehicle will battle with soldiers. United States Department of Defense Transformation 〈http://www.defenselink.mil/transformation/articles/2005-11/ta110105c.html〉, November 2005.
9. Air Force Scientific Advisory Board. New world vistas: air and space power for the 21st century, summary volume. Washington, DC, 1995.
10. Nair M. Conceptual design, engineering modeling, and experimental validation of air sampling system for chemical sensor insertion into the US army research laboratory's silent operating aerial reconnaissance program. ARL technical report, TR 3105, 2004.
11. Grady M. UAVs Tested as fire spotters. AVweb 〈http://www.avweb.com/avwebflash/briefs/188894-1.html〉, January 2005.
12. Shyy W., Lian Y., Tang J., Viieru D., and Liu H. Aerodynamics of low Reynolds number flyers (2008), Cambridge University Press, New York, NY
13. Jenkins D, Ifju P, Abdulrahim M, Olipra, S. Assessment of the controllability of micro air vehicles. In: Bristol international RPV/UAV conference, Bristol, UK, April 2-4, 2001.
14. Abdulrahim M., Garcia H., and Lind R. Flight Characteristics of shaping the membrane wing of a micro air vehicle. J Aircraft 42 1 (2005) 131-137
15. Young A., and Horton H. Some results of investigation of separation bubbles. AGARD Conf Proc 4 (1966) 779-811
16. Torres G. Aerodynamics of low aspect ratio wings at low Reynolds numbers with applications to micro air vehicle design. PhD dissertation, Department of Aerospace and Mechanical Engineering, University of Notre Dame, South Bend, IN, 2002.
17. Shyy W., Ifju P., and Viieru D. Membrane wing-based micro air vehicles. Appl Mech Rev 58 4 (2005) 283-301
18. Hoerner S., and Borst H. Fluid-dynamic lift (1975), Hoerner Fluid Dynamics, Brick Town, NJ
19. Tang J., and Zhu K. Numerical and experimental study of flow structure of low-aspect ratio wing. J Aircraft 41 5 (2004) 1196-1201
20. Lian Y., and Shyy W. Laminar-turbulent transition of a low Reynolds number rigid or flexible airfoil. AIAA J 45 7 (2007)
21. Albertani R., Stanford B., Hubner J., and Ifju P. Aerodynamic coefficients and deformation measurements on flexible micro air vehicle wings. Exp Mech 47 5 (2007) 625-635
22. Shirk M., Hertz T., and Weisshaar T. Aeroelastic tailoring-theory, practice and promise. J Aircraft 23 1 (1986) 6-18
23. Griffin C. Pressure deflection behavior of candidate materials for a morphing wing. Masters thesis, Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV, 2007.
24. Pawlowski K., Belvin H., Raney D., Su J., Harrison J., and Siochi E. Electrospinning of a micro air vehicle wing. Polym Commun 44 4 (2003) 1309-1314
25. Xu Y., Jiang F., Newbern S., Huang A., Ho C., and Tai Y. Flexible shear-stress sensor skin and its application to unmanned aerial vehicles. Sensors Actuators 105 3 (2003) 321-329
26. Waszak M, Jenkins L, Ifju P. Stability and control properties of an aeroelastic fixed wing micro air vehicle. In: AIAA atmospheric flight mechanics conference and exhibit, Montreal, Canada, August 6-9, 2001.
27. Stanford B, Ifju P. Membrane micro air vehicles with adaptive aerodynamic twist: numerical modeling. In: AIAA structures, structural dynamics, and materials conference, Honolulu, HI, April 23-26, 2007.
28. Lin J., and Pauley L. Low-Reynolds-number separation on an airfoil. AIAA J 34 8 (1996) 1570-1577
29. Persson P, Peraire J, Bonet J. A high order discontinuous galerkin method for fluid-structure interaction. In: AIAA computational fluid dynamics conference, Miami, FL, June 25-28, 2007.
30. Lian Y., Shyy W., Viieru D., and Zhang B. Membrane wing mechanics for micro air vehicles. Prog Aerospace Sci 39 6 (2003) 425-465
31. Bisplinghoff R., Ashley H., and Halfman R. Aeroelasticity (1955), Dover, Mineola, NY
32. Ho S., Nassef H., Pornsinsirirak N., Tai Y., and Ho C. Unsteady aerodynamics and flow control for flapping wing flyers. Prog Aerospace Sci 39 8 (2003) 635-681
33. Ormiston R. Theoretical and experimental aerodynamics of the sail wing. J Aircraft 8 2 (1971) 77-84
34. Fitt A., and Pope M. The unsteady motion of two-dimensional flags with bending stiffness. J Eng Mech 40 3 (2001) 227-248
35. Alexander D., and Vogel S. Nature's flyers: birds, insects, and the biomechanics of flight (2002), John Hopkins University Press, Baltimore, MD
36. Wilkinson M. Sailing the skies: the improbable aeronautical success of the pterosaurs. J Exp Biol 210 10 (2007) 1663-1671
37. Greenhalgh S., Curtiss H., and Smith B. Aerodynamic properties of a two-dimensional inextensible flexible airfoil. AIAA J 22 7 (1984) 865-870
38. Mueller T. Aerodynamic measurements at low Reynolds numbers for fixed wing micro-air vehicles. In: RTO special course on the development and operation of UAVs for military and civil applications, Von Karman Institute, Belgium, September 13-17, 1999.
39. Burner A, Fleming G, Hoppe J. Comparison of three optical methods for measuring model deformation. In: AIAA aerospace sciences meeting and exhibit, Reno, NV, January 10-13, 2000.
40. Kaplan S., Altman A., and Ol M. Wake vorticity measurements for low aspect ratio wings at low Reynolds Numbers. J Aircraft 44 1 (2007) 241-251
41. Tamai M, Murphy J, Hu H. An experimental study of flexible membrane airfoils at low Reynolds numbers. In: AIAA aerospace sciences meeting and exhibit, January 7-10, Reno, NV, 2008.
42. Sytsma, M. Aerodynamic flow characterization of micro air vehicles utilizing flow visualization methods. Masters thesis, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 2006.
43. Pujara P., and Lardner T. Deformations of elastic membranes-effect of different constituitive relations. Z Angew Math Phys 29 2 (1978) 315-327
44. Sugimoto T. Analysis of circular elastic membrane wings. Trans Japanese Soc Aerodyn Space Sci 34 105 (1991) 154-166
45. Heppel P. Accuracy in sail simulation: wrinkling and growing fast sails. In: High performance yacht design conference, Auckland, New Zealand, December 4-6, 2002.
46. Pellettier A., and Mueller T. Low Reynolds number aerodynamics of low aspect ratio thin/flat/cambered-plate wings. J Aircraft 37 5 (2000) 825-832
47. Hunt R, Hornby G, Lohn J. Toward evolved flight. In: Genetic and evolutionary computation conference, Washington, DC, June 25-29, 2005.
48. Gili P., and Battipede M. Experimental validation of the wing dihedral effect using whirling arm equipment. J Aircraft 38 6 (2001) 1069-1075
49. Babinsky H, Cattafesta L, Abate G. Design considerations for a micro aerial vehicle aerodynamic characterization facility at the university of florida research and engineering education facility. In: AIAA aerodynamic measurement technology and ground testing conference, San Francisco, CA, June 5-8, 2006.
50. Carmichael B. Low Reynolds number airfoil survey. NASA contractor report, CR 165803, 1981.
51. Mueller T. The influence of laminar separation and transition on low Reynolds number airfoil hysteresis. J Aircraft 22 9 (1985) 763-770
52. Marchman J. Aerodynamic testing at low Reynolds numbers. J Aircraft 24 2 (1987) 107-114
53. Kochersberger K, Abe, C. A novel, low Reynolds number moment balance design for micro air vehicle research. In: AIAA fluid dynamics conference and exhibit, Toronto, Canada, June 6-9, 2005.
54. Suhariyono A., Kim J., Goo J., Park N., and Yoon K. Design of precision balance and aerodynamic characteristic measurement system for micro air vehicles. Aerospace Sci Technol 10 2 (2006) 92-99
55. Ifju P., Albertani R., Stanford B., Claxton D., and Sytsma M. Flexible-wing micro air vehicles. In: Mueller T., Kellogg J., Ifju P., and Shkarayev S. (Eds). Introduction to the design of fixed-wing micro air vehicles (2007), AIAA, Reston, VA [Chapter 5]
56. Recommended practice R-091-2003. Calibration and use of internal strain-gage balances with application to wind tunnel testing (2003), AIAA, Reston, VA
57. Moschetta J., and Thipyopas C. Aerodynamic performance of a biplane micro air vehicle. J Aircraft 44 1 (2007) 291-299
58. Albertani, R. Experimental aerodynamics and elastic deformation characterization of low aspect ratio flexible fixed wings applied to micro aerial vehicles. PhD dissertation, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 2005.
59. Newman B., and Low H. Two-dimensional impervious sails: experimental results compared with theory. J Fluid Mech 144 (1984) 445-462
60. Galvao R, Israeli E, Song A, Tian X, Bishop K, Swartz S, Breuer K. The aerodynamics of compliant membrane wings modeled on mammalian flight mechanics. In: AIAA fluid dynamics conference and exhibit, San Francisco, CA, June 5-8, 2006.
61. Shyy W., Jenkins D., and Smith R. Study of adaptive shape airfoils at low Reynolds number in oscillatory flows. AIAA J 35 9 (1996) 1545-1548
62. Kline S., and McClintock F. Describing uncertainties in single-sample experiments. Mech Eng 75 1 (1953) 3-8
63. Stanford B., Sytsma M., Albertani R., Viieru D., Shyy W., and Ifju P. Static aeroelastic model validation of membrane micro air vehicle wings. AIAA J 45 12 (2007) 2828-2837
64. Pankhurst R., and Holder D. Wind tunnel technique (1952), Sir Isaac Pitman and Sons, London, UK
65. Barlow J., Rae W., and Pope A. Low-speed wind tunnel testing (1999), Wiley, New York, NY
66. Fleming G, Bartram S, Waszak M, Jenkins L. Projection moiré interferometry measurements of micro air vehicle wings. SPIE paper 4448-16.
67. Sutton M., Turner J., Bruck H., and Chae T. Full field representation of the discretely sampled surface deformation for displacement and strain analysis. Exp Mech 31 2 (1991) 168-177
68. Orteu J. 3-D computer vision in experimental mechanics. Opt Lasers Eng, doi:10.1016/j.optlaseng.2007.11.009.
69. Schreier H., Braasch J., and Sutton M. Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39 11 (2000) 2915-2921
70. Sutton M., and McFadden C. Development of a methodology for non-contacting strain measurements in fluid environments using computer vision. Opt Lasers Eng 32 4 (2000) 367-377
71. Albertani R, Stanford B, Sytsma M, Ifju P. Unsteady mechanical aspects of flexible wings: an experimental investigation applied to biologically inspired MAVs. In: European micro air vehicle conference and flight competition, Toulouse, France, September 17-21, 2007.
72. Rojratsirikul P, Wang Z, Gursul I. Unsteady aerodynamics of membrane airfoils. In: AIAA aerospace sciences meeting and exhibit, Reno, NV, January 7-10, 2008.
73. Lorillu O., Weber R., and Hureau J. Numerical and experimental analysis of two-dimensional separated flows over a flexible sail. J Fluid Mech 466 (2002) 319-341
74. Parks H. Three-component velocity measurements in the tip vortex of a micro air vehicle. Masters thesis, School of Engineering and Management, Air Force Institute of Technology, Wright Patterson Air Force Base, OH, 2006.
75. Gamble B, Reeder M. Experimental analysis of propeller interactions with a flexible wing micro air vehicle. In: AIAA fluid dynamics conference and exhibit, San Francisco, CA, June 5-8, 2006.
76. Argentina M., and Mahadevan L. Fluid-flow-induced flutter of a flag. Proc Natl Acad Sci: Appl Math 102 6 (2005) 1829-1834
77. Voelz K. Profil und Auftrieb Eines Segels. Z Angew Math Mech 30 (1950) 301-317
78. Thwaites B. The aerodynamic theory of sails. Proc R Soc London 261 1306 (1961) 402-422
79. Nielsen J. Theory of flexible aerodynamic surfaces. J Appl Mech 30 3 (1963) 435-442
80. Haselgrove M, Tuck E. Stability properties of the two-dimensional sail model. In: Society of naval architects and marine engineers New England sailing yacht symposium, New London, CN, January 24, 1976.
81. Jackson P. A simple model for elastic two-dimensional sails. AIAA J 21 1 (1983) 153-155
82. Sneyd A., Bundock M., and Reid D. Possible effects of wing flexibility on the aerodynamics of pteranodon. Am Nat 120 4 (1982) 455-477
83. Greenhalgh S., Curtiss H., and Smith J. Aerodynamic properties of a two-dimensional inextensible flexible airfoil. AIAA J 22 7 (1984) 865-870
84. Boudreault R. 3-D program predicting the flexible membrane wings aerodynamic properties. J Wind Eng Ind Aerodyn 19 1 (1985) 277-283
85. Holla V., Rao K., Arokkiaswamy A., and Asthana C. Aerodynamic characteristics of pretensioned elastic membrane rectangular sailwings. Comput Methods Appl Mech Eng 44 1 (1984) 1-16
86. Murai H., and Murayama S. Theoretical investigation of sailwing airfoils taking account of elasticities. J Aircraft 19 5 (1982) 385-389
87. Jackson P., and Christie G. Numerical analysis of three-dimensional elastic membrane wings. AIAA J 25 5 (1987) 676-682
88. Smith R., and Shyy W. Incremental potential flow based membrane wing element. AIAA J 35 5 (1997) 782-788
89. Schoop H., Bessert N., and Taenzer L. On the elastic membrane in a potential flow. Int J Numer Methods Eng 41 2 (1998) 271-291
90. Smith R., and Shyy W. Computational model of flexible membrane wings in steady laminar flow. AIAA J 33 10 (1995) 1769-1777
91. Cyr S., and Newman B. Flow past two-dimensional membrane aerofoils with rear separation. J Wind Eng Ind Aerodyn 63 1 (1996) 1-16
92. Smith W, Shyy W. Coupled computations of a flexible membrane wing in unsteady viscous flow. In: AIAA fluid dynamics conference, San Diego, CA, June 19-22, 1995.
93. Levin O., and Shyy W. Optimization of a low Reynolds number airfoil with flexible membrane. Comput Modeling Eng Sci 2 4 (2001) 523-536
94. Gordnier R. High fidelity computational simulation of a membrane wing airfoil. In: AIAA aerospace sciences meeting and exhibit, Reno, NV, January 7-10, 2008.
95. Viieru D. Flapping and fixed wing aerodynamics of low Reynolds number flight vehicles. PhD dissertation, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 2006.
96. Smith R., and Shyy W. Computation of aerodynamic coefficients for a flexible membrane airfoil in turbulent flow: a comparison with classical theory. Phys Fluids 8 12 (1996) 3346-3353
97. Chakrabarti S., and Brebbia C. A two-dimensional sail in turbulent flow. Adv Fluid Mech 30 16 (2001) 245-254
98. Scott R, Bartels R, Kandil O. An aeroelastic analysis of a thin flexible membrane. In: AIAA structures, structural dynamics, and materials conference, Honolulu, HI, April 23-26, 2007.
99. Lian Y, Shyy W, Ifju P, Verron E. A computational model for coupled membrane-fluid dynamics. In: AIAA fluid dynamics conference and exhibit, St. Louis, MO, June 24-26, 2002.
100. Alben S., Shelley M., and Zhang J. How flexibility induces streamlining in a two-dimensional flow. Phys Fluids 16 5 (2004) 1694-1713
101. Stanford B., Albertani R., and Ifju P. Static finite element validation of a flexible micro air vehicle. Exp Mech 47 2 (2007) 283-294
102. Ferguson L, Seshaiyer P, Gordnier R, Attar P. Computational Modeling of coupled membrane-beam flexible wings for micro air vehicles. In: AIAA structures, structural dynamics, and materials conference, Honolulu, HI, April 23-26, 2007.
103. Batoz J., Bathe K., and Ho L. A study of three-node triangular plate bending elements. Int J Numer Methods Eng 15 12 (1980) 1771-1812
104. Cook R., Malkus D., Plesha M., and Witt R. Concepts and applications of finite element analysis (2002), Wiley, New York, NY
105. Reaves M, Horta L, Waszak M, Morgan B. Model update of a micro air vehicle (MAV) flexible wing frame with uncertainty quantification. NASA technical memorandum, TM 213232, 2004.
106. Isenberg C. The science of soap films and soap bubbles (1992), Dover, New York, NY
107. Taylor R., Onate E., and Ubach P. Finite element analysis of membrane structures. In: Onate E., and Kröplin B. (Eds). Textile composites and inflatable structures (2005), Springer, Dordrecht, The Netherlands
108. Pauletti R, Guirardi D, Deifeld T. Argyris' natural finite element revisited. In: International conference on textile composites and inflatable structures, Stuttgart, Germany, October 2-5, 2005.
109. Wu B., Du X., and Tan H. A three-dimensional FE nonlinear analysis of membranes. Comput Struct 59 4 (1996) 601-605
110. Campbell J. On the theory of initially tensioned circular membranes subjected to uniform pressure. Q J Mech Appl Math 9 1 (1956) 84-93
111. Mooney M. A theory of large elastic deformation. J Appl Phys 11 (1940) 582-592
112. Oden J., and Sato T. Finite strains and displacements of elastic membranes by the finite element method. Int J Solids Struct 3 (1967) 471-488
113. Mase G., and Mase G. Continuum mechanics for engineers (1999), CRC Press, Boca Raton, FL
114. Stanford B, Boria F, Ifju P. The validity range of pressurized membrane models with varying fidelity. In: Society for Experimental Mechanics International Congress, Springfield, MA, June 4-6, 2007.
115. Ramamurti R, Sandberg W, Löhner R. Simulation of the dynamics of micro air vehicles. In: AIAA aerospace sciences meeting and exhibit, Reno, NV, January 10-13, 2000.
116. Gad-el-Hak M. Micro-air-vehicles: can they be controlled better?. J Aircraft 38 3 (2001) 419-429
117. Viieru D., Albertani R., Shyy W., and Ifju P. Effect of tip vortex on wing aerodynamics of micro air vehicles. J Aircraft 42 6 (2005) 1530-1536
118. Kunz P., and Kroo I. Analysis and design of airfoils for use at ultra-low Reynolds numbers. In: Mueller T. (Ed). Fixed and flapping wing aerodynamics for micro air vehicle applications (2002), AIAA, Reston, VA [Chapter 3]
119. Baragona M., Bijl H., and Van Tooren M. Bubble bursting and laminar separation unsteadiness on a multi-element high lift configuration. Flow Turbulence Combust 71 2 (2003) 279-296
120. Tannehill J., Anderson D., and Pletcher R. Computational fluid mechanics and heat transfer (1997), Taylor & Francis, Philadelphia, PA
121. Shyy W. Computational modeling for fluid flow and interfacial transport (1994), Elsevier, Amsterdam, The Netherlands
122. Thakur S., Wright J., and Shyy W. STREAM: A computational fluid dynamics and heat transfer Navier-Stokes solver: theory and applications (2002), Streamline Numerics, Inc., Gainesville, FL
123. Krumbein A. Automatic transition prediction and application to three-dimensional high-lift configurations. J Aircraft 44 3 (2007) 918-926
124. Roberts S., and Yaras M. Large-eddy simulation of transition in a separation bubble. J Fluids Eng 128 2 (2006) 232-238
125. Shan H, Jiang L, Liu C, Love M, Maines B. Numerical study of passive and active flow separation control over a NACA0012 airfoil. Comput Fluids, doi:10.1016/j.compfluid.2007.10.010.
126. Guruswamy G. A review of numerical fluids/structures interface methods for computations using high-fidelity equations. Comput Struct 80 1 (2002) 31-41
127. Lewis W. Tension structures: form and behavior (2003), Thomas Telford Ltd., London, UK
128. Kamakoti R., Lian Y., Regisford S., Kurdila A., and Shyy W. Computational aeroelasticity using a pressure-based solver. Comput Methods Eng Sci 3 6 (2002) 773-790
129. Fink M. Full-scale investigation of the aerodynamic characteristics of a model employing a sailwing concept. NASA technical report, TR 4062, 1967.
130. Katz J., and Plotkin A. Low-speed aerodynamics (2001), Cambridge University Press, Cambridge, UK
131. Hepperle M. Aerodynamics of spar and rib structures. MH AeroTools online database 〈http://www.mh-aerotools.de/airfoils/ribs.htm〉, March 2007.
132. Ifju P, Ettinger S, Jenkins D, Martinez L. Composite materials for micro air vehicles. In: Society for the advancement of material and process engineering annual conference, Long Beach, CA, May 6-10, 2001.
133. Allen M, Maute K. Probabilistic structural design of UAVs under aeroelastic loading. In: AIAA "unmanned unlimited" conference, San Diego, September 15-18, 2003.
134. Weisshaar T, Nam C, Batista-Rodriguez A. Aeroelastic tailoring for improved UAV performance. In: AIAA structures, structural dynamics, and materials conference, Long Beach, CA, April 20-23, 1998.
135. Frampton K, Goldfarb M, Monopoly D, Cveticanin D. Passive aeroelastic tailoring for optimal flapping wings. In: Proceedings of conference on fixed, flapping, and rotary wing vehicles at very low Reynolds numbers, South Bend, IN, June 5-7, 2000.
136. Snyder R, Beran P, Parker G, Blair M. A design optimization strategy for micro air vehicles. In: AIAA structures, structural dynamics, and materials conference, Honolulu, HI, April 23-26, 2007.
137. Garrett R. The symmetry of sailing: the physics of sailing for yachtsmen (1996), Adlard Coles, Dobbs Ferry, NY
138. Eden M. The magnificent book of kites: explorations in design, construction, enjoyment, and flight (2002), Sterling Publishing, New York, NY
139. Templin R, Chatterjee S. Posture, locomotion, and paleoecology of pterosaurs. Geological Society of America Special Paper 376, 2004.
140. Swartz S., Groves M., Kim H., and Walsh W. Mechanical properties of bat wing membrane skin. J Zool 239 (1996) 357-378
141. Norberg U. Bat wing structures important for aerodynamics and rigidity. Zoomorphology 73 1 (1972) 45-61
142. Stanford B., Abdulrahim M., Lind R., and Ifju P. Investigation of membrane actuation for roll control of a micro air vehicles. J Aircraft 44 3 (2007) 741-749
143. Maute K., and Allen M. Conceptual design of aeroelastic structures by topology optimization. Struct Multidisciplinary Optim 27 1 (2004) 27-42
144. Stanford B. Aeroelastic analysis and optimization of membrane micro air vehicle wings. PhD dissertation, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 2008.
145. Antony J. Design of experiments for engineers and scientists (2003), Butterworth-Heinemann, Boston, MA
146. Gürdal Z., Haftka R., and Hajela P. Design and optimization of laminated composites materials (1999), Wiley, New York, NY
147. Sloan J, Shyy W, Haftka R. Airfoil and wing planform optimization for micro air vehicles. In: Symposium of RTO applied vehicle technology panel, Ottawa, Canada, October 19-21, 1999.