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Buckling Analysis of a Bendable Composite Unmanned Air Vehicle Wing

Permanent Link: http://ufdc.ufl.edu/UFE0025037/00001

Material Information

Title: Buckling Analysis of a Bendable Composite Unmanned Air Vehicle Wing
Physical Description: 1 online resource (59 p.)
Language: english
Creator: Patil, Abhishek
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: abhishek, analysis, bendable, buckling, expermiental, ifju, mav, patil, predictor, stress, tool, uav, ufl
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The bendable UAV wing developed by researchers at the University of Florida has the ability to load stiffen in the positive load direction and at the same time is compliant in the opposite direction. Such a design of a UAV wing enables a UAV to be stored in smaller packing volumes. The UAV wing will snap through buckle when over-loaded with aggressive flight loads. It will lose its load carrying ability since the airfoil of the wing may flatten out under the loads. The objective of my research is to develop a buckling prediction tool that can predict maximum load carrying capacity of a bendable wing. My thesis covers development of a finite element routine for modeling the wing and predicting load carrying capacity using snap through buckling as a limit state. Limit flight load is calculated using an incremental arc length method algorithm available in Abaqus finite element software. For validating buckling prediction methodology, tests are performed on a range of un-swept singly curved shell structures and the predictions are compared with experimental results obtained by performing three point bend tests on the wings. Such a buckling prediction tool can be used for conveniently modeling and testing wings numerically to predict the buckling velocities of the wings.
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.
Statement of Responsibility: by Abhishek Patil.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Ifju, Peter.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0025037:00001

Permanent Link: http://ufdc.ufl.edu/UFE0025037/00001

Material Information

Title: Buckling Analysis of a Bendable Composite Unmanned Air Vehicle Wing
Physical Description: 1 online resource (59 p.)
Language: english
Creator: Patil, Abhishek
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: abhishek, analysis, bendable, buckling, expermiental, ifju, mav, patil, predictor, stress, tool, uav, ufl
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The bendable UAV wing developed by researchers at the University of Florida has the ability to load stiffen in the positive load direction and at the same time is compliant in the opposite direction. Such a design of a UAV wing enables a UAV to be stored in smaller packing volumes. The UAV wing will snap through buckle when over-loaded with aggressive flight loads. It will lose its load carrying ability since the airfoil of the wing may flatten out under the loads. The objective of my research is to develop a buckling prediction tool that can predict maximum load carrying capacity of a bendable wing. My thesis covers development of a finite element routine for modeling the wing and predicting load carrying capacity using snap through buckling as a limit state. Limit flight load is calculated using an incremental arc length method algorithm available in Abaqus finite element software. For validating buckling prediction methodology, tests are performed on a range of un-swept singly curved shell structures and the predictions are compared with experimental results obtained by performing three point bend tests on the wings. Such a buckling prediction tool can be used for conveniently modeling and testing wings numerically to predict the buckling velocities of the wings.
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.
Statement of Responsibility: by Abhishek Patil.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Ifju, Peter.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0025037:00001


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1 BUCKLING ANALYSIS OF A BENDABLE COMPOSITE UNMANNED AIR VEHICLE WING By ABHISHEK J. PATIL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M ASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009

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2 2009 Abhishek J. Patil

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3 To my Parents, my Lifelong Mentors

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4 ACKNOWLEDGMENTS I would like to thank my advisor Dr Peter Ifju for giving me the opportunity to work under his guidance at the E xperimental S tress A nalysis lab His constant support and guidance during my research and study at the University of Florida has shown me a path to nurture my creativity and stay f ocused. I would also like to thank my commi ttee members Dr Bhavani Sankar and Dr Nam Ho Kim for their invaluable inputs during the course of the research. I thank my P arents for their support and motivation throughout my study My thanks go to Vijay for constantly helping me with research ideas for helping me with the experiment and thesis completion and for being patient enough to answer all my stupid questions at any time of the hour to Kaustubh for helping me with my thesis completion, to Yogesh for being there for me and making this place a home away from home, to Samta for believing in me and motivating me, to Anurag for the numerous discussions we have had about my research. My thanks go to my best friends Asawari, Sourabh and Shalaka for all the encouragement, to my lab mates Mulugeta, Wei qi & Enoch for making lab a great working environment, to m y manager Mr James Hardemon at Software Licensing S ervices for being understanding and supportive, to the staff at software licensing services for covering up my shifts, to all my friends and coll eagues who have always encouraged and motivated me and have made this journey a memorable experience.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLE S ................................................................................................................................ 7 LIST OF FIGURES .............................................................................................................................. 8 ABSTRACT ........................................................................................................................................ 10 CHAPTER 1 INTRODUCTION ....................................................................................................................... 11 Introduction to Unmanned Air Vehicles .................................................................................... 11 Bendable Wing Unmanned Air Vehicle .................................................................................... 12 Design Parameters for UAV Wing ............................................................................................ 13 Load Carrying Capacity Predictor ............................................................................................. 17 Experimental Validation ............................................................................................................. 18 2 LOAD CARRYING CAPACITY PREDICTOR ...................................................................... 19 General Analysis Procedure in Abaqus ..................................................................................... 19 Explai ning the Input File ............................................................................................................ 20 Need of Input File. ...................................................................................................................... 22 Modeling of UAV Wing. ............................................................................................................ 22 Material Property ......................................................................................................................... 23 Boundary Conditions and Loading ............................................................................................ 24 Different Methodologies for Simulation .................................................................................... 25 Non -Linear Static Analysis ................................................................................................. 25 Non -Linear Eigenvalue Analysis. ....................................................................................... 26 Riks Analysis ....................................................................................................................... 27 Results and Discussion ............................................................................................................... 29 3 EXPERIMENTAL VALIDATION ........................................................................................... 36 Experimental S pecimens ............................................................................................................. 36 Experimental Apparatus ............................................................................................................. 38 Fixture Design ...................................................................................................................... 38 Visual I mage Correlation System ....................................................................................... 39 Load Cell .............................................................................................................................. 40 Experimental Setup ..................................................................................................................... 42 Ab aqus Modeling ........................................................................................................................ 43 Results and Discussion ............................................................................................................... 45

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6 4 CONCLUSIONS AND FUTURE WORK ................................................................................ 54 LIST OF REFERENCES ................................................................................................................... 56 BIOGRAPHICAL SKETCH ............................................................................................................. 58

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7 LIST OF TABLES Table page 2 1 Wing parameters [9] ............................................................................................................... 31 2 2 Buckling velocities for designs [9] ....................................................................................... 31 3 1 Maximum buckling loads of the specimens ......................................................................... 47 3 2 Material models used ............................................................................................................. 52

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8 LIST OF FIGURES Figure page 1 1 KZO surveillance UAV. [4] .................................................................................................. 12 1 2 UAV systems used currently [7]. .......................................................................................... 12 1 3 Bendable UAV wing concept. [8] .......................................................................................... 13 1 4 Planform parameters used to define the wing [9] ................................................................ 13 1 5 Root airfoil profile [9] ........................................................................................................... 14 1 6 Planform of a UAV wing ....................................................................................................... 16 1 7 Example of a snap through buckled wing ............................................................................. 16 1 8 Un -swept wing and swept wing. ........................................................................................... 16 2 1 A complete Abaqus analysis. ................................................................................................ 19 2 2 Meshed UAV wing, meshing refined near root airfoil. ....................................................... 23 2 3 Wing with bounda ry conditions and loads. .......................................................................... 24 2 4 Local chordwise buckling of a UAV wing ........................................................................... 27 2 5 Standard load displacement curve ......................................................................................... 28 2 6 Buckling analysis possible plots ........................................................................................... 29 2 7 Snap through buckled baseline wing: large stresses are developed at the root airfoil ....... 30 2 8 Plot of the baseline wing. ....................................................................................................... 33 2 9 Planforms of the wings in study. ........................................................................................... 34 2 10 Normalized camber vs bukling velocity (air speed) for design A. ..................................... 34 2 11 Load stiffened configuration for design A. .......................................................................... 35 3 1 Cured composite shell ............................................................................................................ 37 3 2 Specimens used for experimental validation. ....................................................................... 38 3 3 The fixture assembly .............................................................................................................. 40 3 4 Specimens with random speckle pattern ............................................................................... 41

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9 3 5 Load cell ................................................................................................................................. 41 3 6 Experimental Setup on t he MTI machine ............................................................................. 42 3 6 continued ............................................................................................................................ 43 3 7 Singly curved wing with loading and boundary conditions ................................................ 44 3 8 Buckled shape of the singly curved wing predicted by the predictor tool .......................... 44 3 9 Change of airfoil as the load changes for a 75 degree wing. ............................................... 45 3 10 Plot of chord normalized camber vs applied load for a 90 degree wing for experiment and simulation ........................................................................................................................ 46 3 11 Comparison of experiment an d predictor tool results for the change in camber for 40, 45, 60 and 75 degree specimens. ........................................................................................... 47 3 12 Plot of applied load vs chord and initial camber normalized camber ................................. 48 3 13 Plot for peak normalized load vs chord and initial camber normalized camber. ............... 49 3 14 Maximum buckling load vs initial chord normalized camber ............................................. 49 3 15 Load vs chord normalized deflection at loading point. ........................................................ 50 3 16 Load vs chord normalized deflection at loading point for 75 and 60 degree wings. ......... 51 3 17 Load vs chord normalized deflection at loading point for 40 and 45 degree specimens using Model 1 ......................................................................................................................... 51 3 18 Plot of load vs chord normalized defle ction for a 40 degree specimen. ............................. 52

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10 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science BUCKLING ANALYSI S OF A BENDABLE COMPOSITE UNMANNED AIR VECHICLE WING By Abhishek J. Patil August 2009 Chair: P eter Ifju Major: Mechanical Engineering The bendable UAV wing developed by researchers at the University of F lorida has the ability to load stiffen in the positive load direction and at the same time is compliant in the opposite direction. Such a design of a UAV wing enables a UAV to be stored in smaller packing volumes. The UAV wing will snap through buckle when over loaded with aggressive flight loads. It will lose its load carrying ability since the airfoil of the wing may flatten out under the loads. The objective of my research is to develop a buckling prediction tool that can predict maximum load carrying ca pacity of a bendable wing. My thesis covers development of a finite element routine for modeling the wing and predicting load carrying capacity using snap through buckling as a limit state. Limit flight load is calculated using an incremental arc length m ethod algorithm available in Abaqus finite element software. For validating buckling prediction methodology, tests are performed on a range of un swept singly curved shell structures and the predictions are compared with experimental results obtained by pe r forming three point bend tests on the wings. Such a buckling prediction tool can be used for conveniently modeling and testing wings numerically to predict the buckling velocities of the wings.

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11 CHAPTER 1 INTRODUCTION Introduction to U nmanned A ir V ehicles Unmanned air vehicle or UAV is generally referred to an air vehicle that does not have a pilot on board. The vehicle maybe expendable or re usable. The idea of a UAV is a tested and proved to be reliable branch of aerospace development, rather than a new and revolutionary concept. However, advancements in structural materials, control systems and technological developments such as synthetic aperture radars, increasingly capable microprocessors, etc. have changed the way a UAV is used. Some of the applicati ons of the UAV are: Scientific Research : UAVs are preferred for applications dangerous to the piloted aircraft. Some of the applications include, hunting hurricanes and communicating real time information to scientists / meteorologists. The UAV can work ve ry close to the water's surface Improved intelligence, searching, and reconnaissance : Gaining current, accurate information about the terrain, weather and physical resources within a specified area of operations is an important aspect of surveillance. One of the UAVs used for this purpose is the KZO Surveillance and Reconnaissance UAV, Germany seen in Figure 1 1 Reducing risk to human lives: Employing a UAV for most hazardous missions is beneficial in saving the lives of pilots thus reducing the mission risk. Transport: Use of UAVs in transport is less common compared to other applications. They are usually to transport goods. The UAV is equipped with the payload to be delivered depending on its configuration. Figure 1 2 shows Global Hawk and P redator which are among the latest UAV systems used for surveillance. The work done by Cook [ 1 ] and Sullivan [ 2 ] explains the historical development of a UAV s ystem. They also explain how recent revolutionary concepts introduced miniature or micro aerial vehicle that improve s surveillance and stealth. At U niversity of Florida research is being conducted to develop a bendable UAV wing which can be rolled around t he fuselage and can be stored in small volumes. The UF team has the US patent for the bendable wing [ 5 ].

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12 Figure 1 1 KZO surveillance UAV. [ 4 ] A B Figure 1 2 UAV systems used currently A) Global hawk [ 5 ], B) Predator [ 7 ]. Bendable W ing Unmanned Air V ehicle A series of unmanned air vehicles (UAVs) have been developed at the Univer sity of Florida, equipped with a bendable wing configuration to reduce the packing volume. The UAV wings can be rolled around the fuselage of the vehicle, as seen in Figure 1 3 The concept is small and inexpensive platform that can be deployed from a host vehicle or larger UAV. This Bendable UAV wing concept can have a span size ranging fro m 6 to 30 inches and the bend ability enables the wing to be packed within volumes of 3 300 inch3. The UAV is stored inside a canister, which can be deployed from a manned vehicle or from a larger UAV. Once this UAV is released from the canister, the wings will spring back to the desired aerodynamic shape. Vehicles have been constructed in reduced storage space such that the canister with the UAV can

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13 be fitted into the cargo pocket of a soldiers uniform. This provides flexibility and ease to deploy the UAV for over the -hill surveillance capabilities. A B Figure 1 3 Bendable UAV wing concept. A) F light ready w ing, B) Folded for storage [8 ] Design Parameters f or UAV W ing The UAV wing shape is defined using the root airfoil and important planform parameters like Sweep, Taper Ratio and Twist angle. Figure 1 4 show these planform parameters. The parameters like camber & reflex are defined at the root airfoil. The root airfoil is the critical airfoil of the wing as it is subjected to maximum loads, Figure 1 5 shows the parame ters that are used to define the root airfoil of the wing a method developed and used by Jagdale et.al [9 ]. Root airfoil is the part of the wing which i s connected to the fuselage. The standard root airfoil of a UAV wing is as shown in Figure 1 5 Figure 1 4 Planform parameters used to define the wing [9 ]

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14 Figure 1 5 Root airfoil p rofile [9 ] The root airfoil has a complex shape, so it is defined usi ng combination of 3 curves. The first curve is a quadratic curve from the leading edge to the point of maximum camber, z1. The second curve is a 5th degree polynomial curve from point of max imum camber to the reflex point and the third is again a quadratic curve from reflex point to the trailing edge. The coordinates of the wing are defined such that, the chord location is along the x-axis; span location along the y axis and the elevation change is along the z axis. The Coordinate (x1,z1) corresponds to the camber location of the wing which is us ually near the quarter chord location. The camber is defined as the maximum Z distance of the structure from the imaginary horizontal line joining th e two end points in any configuration at the root airfoil. Coordinates (x2,z2) corresponds to the reflex location of the wing. The root airfoil profile is swept to get the wing shape. Figure 1 6 shows the planform of a UAV wing. T he UAV wing used for the study is a wing having 7 inch root chord length and 24 inch wing span. The wing is manufactured using a T300/934 bi directional plain weave carbon/epoxy prepreg. Layup used is a two layer of lamina havi ng 45 degree fiber directions [9 ]. It is observed that the [45]S layup is easier to roll and store inside a canister as the 0 or 90 degree layup would fail because of high bending stresses being developed in [0/90]T layup when we try to roll it in small di ameters [ 3 ]. Two layers of lamina provide sufficient flexibility to the wing to be rolled,

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15 as having higher number of la yers would make the wing rigid and difficult to roll into desired diameter without material failure. Bendable wing has beneficial compliant nature and load stiffening ability. W hen the wing sees aggressive flight loads, its leading edge at the root airfoil moves down, increasing the effective root camber and the moment of inertia of the wing at the root airfoil This makes the wing stiffer, improving its load carrying capacity. This phenomenon is known as load stiffening of the UAV wing. How ever if the flight loads keeps increasing th e wing will snap through buckle. T his is the state of the wing where the wing losses its load carrying capacity and the root airfoil flattens out and becomes almost straight. The wing design should have high load carrying capacity to generate enough lift to carry payload at the same time it should be easy to bend in other direction for storage. Figure 1 7 shows a n example of a snap through buckled wing. The initial g eneration of UAV wings had no sweep at the leading edge. However it was observed that if these wings are subjected to aggressive flight loads they experienced in -flight buckling. Leading edge sweep was added to avoid such occurrences which improved the load carrying capacity of the wings. The washout effect can be achieved by using the twist angle parameter. This ensures that the angle of attack r educes from the root airfoil to the tip, meaning the root airfoil would buckle before the tip. This prevents the wing from buckling completely at a time. The parameters discussed above are important from the structural design point of view of the UAV wing. There are also parameters which improve the aerodynamic performance of the wing. These parameters can be seen in t he work done by J agdale et al [ 9 ]. Figure 1 8 shows two wings, wing with straight quar ter chord is an example of easily buckled wing used in initial generations, and wing with 15 degree sweep is an example of current generation wing which has load stiffening ability.

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16 Figure 1 6 Planform of a UAV wing Figur e 1 7 Example of a snap through buckled w ing Figure 1 8 Un -swept wing and s wept wing.

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17 Load Carrying Capacity Predictor The wing is a geometrically non -linear thin shell structure having a cur vature. To find the load carrying capacity of the wing a snap through buckling analysis procedure is implemented. Snap through buckling analysis of curved shell structures like spherical, cylindrical or conical are commonly explored [ 11, 12, 13]. There are various algorithms that are used to solve the snap through buckling analysis. Crisfield has listed a use of Riks method that can be used to predict the no n linear structu ral behavior [ 14]. He explains how the load displacement curve for a nonlinear structure behaves and why the simple analysis fails to completely predict the load carrying capacity of a structure as it will terminate at a local limit point and not global. He has analyzed cylindrical shells subjected to transvers e point loads and uniform loads. T he analysis was done using Riks method first by keeping the incremental load step automatic and then keeping the step fixed. He conclude s that using a Riks method not only allows the limit points to be passed but also improves the convergence characteristics of such iterative procedure. The snap through buckling analysis can be done using experimental methods like the three point bend test where the supports are given to the wing by finding out the center of the pressure points and the load is applied at the root airfoil of the wing at the quarter chord. This is done in pr evious work by J agdale et al [ 10]. For the conceptual design of the wing, flexibility to change the wing design parameters and evaluate different wing shapes in a very quick and efficient way is imp ortant. This flexibility to evaluate wing with varying design parameters is achieved using a tool developed around the finite element software Abaqus This tool is used to predict the load carrying capa city of the wing. This predictive methodology is used in an optimization routine which will do structural analysis for wings with varying design parame ters [ 9 ]. The motivation behind this is, we need to test wings of various profile to check which profile provides maximum

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18 load carrying capacit y but at the same time satisfy other aerodynamic constraints. Chapter 2 will discuss the development of this predictor tool in detail. Experimental Validation The load carrying capacity of the wing obtained from the predictor tool was compared with the load carrying capacity of the wing obtaine d by doing a wind tunnel test [ 9 ]. To further validate the load carrying capacity predictor, three point bend tests of singly curved straight wings is carried out. The test specimen geometry and the test mode contain the required snap through buckling structural behavior. A UAV wing has a very complicated geometry with numerous parameters to be considered as discussed earlier Also the loading conditions on the wing are complicated. For the experimental validation of our procedure the geometry used is a sin gly curved composite shell. A three point bend test is performed; the loading is simulated on these curved shells on an experimental setup to find the load carrying capacity of these curved shells and comparing the results with the predictor results. To simulate flight lo ads, the wing is fixed at a selected location on each semi -wing, and a negative force is applied at the root. Chapter 3 will discuss the experimental setup and the specimen specification in detail.

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19 CHAPTER 2 LOAD CARRYING CAPACI TY PREDICTOR Non -Linear bu ckling analysis is done using ABAQUS family of finite element software. The predictor is implemented by performing a snap through buckling analysis. For the wing buckling is a state when the root aerofoil flattens out and the wing losses its load carrying capacity. General Analysis Procedure in Abaqus The structural analysis to predict the buckling behavior of the UAV wing is done using, Abaqus, a finite element analysis software In the Abaqus GUI modeling and analysis of a model is done step by step by fo llowing the ten basic modules. Once the model is ready and the job is submitted for analysis, the software writes an input file for the model which is a text file. The input file records all the information for the model like the nodes, elements, boundary conditions, nodes and element sets, loading, analysis type etc. This input file is analyzed by the Abaqus solver and the results like stresses, strains, displacements etc are saved in a data file which als o can be read as a text file. Figure 2 1 shows the procedure with three distinct stages: preprocessing, simulation and postprocessing. Figure 2 1 A complete Abaqus a nalysis.

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20 The input file can be written by the user instead of using the graphic user interface (GUI). However one disadvantage of using a n input file is that all the commands needs to be known. The standard input file defines: Nodes, that is, the discretized geometry of the model. (*Node). Type of elements and element connectivity. (*Elem ent). Material properties of the material used. (*Material). Loads (*Cload) being applied on the model and boundary conditions (*Boundary) required to simulate the model. Analysis type (*Step). In the step we define whether our analysis is linear or non-linear, static or dynamic analysis. Desired field output required for our model (*node print or *el print). For example when analyzing a frame structure stresses and strains induced in each member would be of interest. The keywords corresponding components are in the brackets. From above, the input file is made of modules and each keyword is started with a n followed by one or two data lines. Once all these keywords are defined in a n input file and the file is submitted, the solver checks if there are any errors in the file, and if the check for syntax errors is successful the solver processes the job. Explaining the Input File The UAV wing is a composite shell structure. The keywords necessary to define an input file for the composite structure are explai ned below with their syntax to be followed to define these keywords. The file is saved in a n .inp format, example, input.inp. *Heading: This option is used to define a title for the analysis. *Node: the syntax for the first line is: Node number First (X) coordinate of the node Second (Y) coordinate of the node Third (Z) coordinate of the node

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21 *Element: This option is used to define an element directly by specifying its nodes, the syntax for the first data line are: Element number First node number formin g the element Second node number forming the element Up to 15 node number in the first line. *Shell Section: This option is used to specify a shell cross -section. The syntax for the first data line for the use of composite material are: Layer thickness Nu mber of integration points to be used through the layer. This number must be an odd number. The default is one integration point. Name of the material forming this layer. Orientation angle Repeat this data line as often as necessary to define the properti es for each layer of the composite solid. *Material: This option is used to indicate the start of a material definition. *Elastic: This option is used to define linear elastic moduli. The composite model is defined under type lamina. The first date line i s defined as E1, E2, Nu12, G12, G13, G23. *Boundary: This option is used to prescribe boundary conditions at nodes. The boundary conditions can be applied at the nodes of the structure. The data line for boundary definition is: Node number or node set labe l First degree of freedom to be constrained. Last degree of freedom to be constrained. If non zero constraint then specify the value. *Step: This option is used to begin the step definition; the step definition is followed by analysis definition. The name of step, nonlinear constraint and no of increments are included in the data line. *Static: This option indicates that the step should be analyzed as a static load step. The data line definition for this step changes for different analysis. Riks method is used to perform analysis on the UAV wing. The data line used for the Riks analysis is explained below Initial increment in arc length Total arc length

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22 Minimum arc length Maximum arc length Maximum value of load proportionality factor *Cload: This option is used to specify a concentrated load at particular nodes. The data line definition is Node number or node set Degree of freedom Magnitude *Node Print: This option is a one of the field output command, nodal variables displacement, reaction forces are wr itten to the data file. In the data line give the identifying keys for the variables that are required in the data file for a particular node set. For example, to obtain displacements U1, U2, U3. The commands listed above are the ones required to completel y write the input file for the analysis of a UAV wing. Need of Input File. The snap through buckling analysis of the UAV wing is performed by defining the UAV wing model information in an input file named Riks analysis.inp. This predictor tool which impleme nts Riks methodology is used in the optimization routine to do the analysis. The input file is required so that the analysis can be automated. The optimization routine [9 ] is developed such that, a code in M atlab saves all the model information required in an input file an d loads this input file in the A baqus solver. This process is repeated for wings with different loading conditions and geometry. Modeling of UAV W ing. The UAV wing is symmetric along the span direction. Takin g advantage of this only one half of the wing is modeled in A baqus. The geometry of the wing is discretized into 10 panels along the chord length and 18 panels along the semi span length Discretized geometry is obtained from a program written by Jagdale e t al [ 9 ]. This discretized geometry is used to define

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23 the nodal coordinates. The optimization code developed in Matlab calls a function get r iks inp .m writes the co -ordinates for the nodes in the input file. When the input file i s loaded in the Abaqus solver the wing model seen in GUI is shown in Figure 2 2 Meshing in the form of a paneled grid can be seen in Figure 2 2 the meshing is further refined near the root airfoil as hi gh stresses would be developed at this location when the wing initially load stiffens and eventually buckles. For mesh refinement affect study wing with 20 panels along the chord and 30 panels along the span was evaluated for the predictor tool However th e analysis was computationally expensive and the difference in results was less than 5%. Shell elements are used for the analysis. Initially analysis was done using S4R5 shell element but these elements have linear interpolation. To account for geometric nonlin earity, second order S8R5 shell elements having quadratic interpolation are implemented. Figure 2 2 Meshed UAV wing meshing refined near root airfoil Material Property A T300/934 bi -directional carbon epoxy composite prepreg is used as the material. Following elastic properties are considered in Abaqus : E1= E212= 0.05, G12= 2.34 GPa. This material model is obtained from the work done by J agdale et al. [ 9 ]. The fiber orientation used is + 45 as discussed in the previous chapter.

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24 Boundary Conditions and Loading The wing is fixed at the root airfoil location to the fuselage at two points one at 40% chord loca tion and the other at 60% chord location. Due to the way wing is supported and mounted on the fuselage, the wing portion between the supports remains almost straight during application of any flight load. To simulate this all the nodes between 40% and 60% chord location are fixed. The corresponding nodes in the model are fixed for all rotations and translations. All the nodes on the root airfoil are specified a Y -symme tric boundary condition as only one half of the wing is modeled. Pressure loads or flight loads on the wing are obtained using Athena Vortex Lattice (AVL) software developed by Ha rold Youngren and Mark Drela [ 15]. The flight lo ad acting on the wing is a function of the cruise velocity Vc, differential pressure coefficient on each panel pp distribution computed from AVL is used to compute the normal flight aerodynamic load on the element given by: Fee*(Vc)2 p (2 1) Where Fe is the force on each e the air density, Se is the area of finite element. The cruising speed VC of the vehicle can be computed using VCL})1/2 (2 2) Where W is the weight of the vehicl e, S is the planform area and CL is the coefficient of lift. CL for complet e flight geometry is obtained from AVL. The pressure loading is then Figure 2 3 Wing with boundary conditions and loads.

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25 interpolated onto the finite element mesh to give nodal forces. Figure 2 3 s hows the wing with the normal flight loads and boundary conditions. Different Methodologies for Simulation The UAV wing is modeled and appropriate loading and boundary conditions are applied to the wing, we then perform the buckling analysis on the wing to find the maximum load the structure can withstand before it becomes i nstable and buckles This section will discuss the different analysis types implemented to perform the buckling analysis. Non -Linear Static Analysis The wing is defined as a geometrical ly nonlinear structure. The non -linear static analysis assumes the wing to be a stable structure. When the pressure loading obtained from AVL is discretized and applied at the nodes, this analysis can predict the configuration of the wing by predicting th e out -of -plane deflection of the wing. U sing a static linear perturbation step the out of -plane t ip displacement is monitored. I f the tip displacement crosses a certain specified value it is assumed that the wing is buckled. The time step of 1 is specifie d for this analysis with a min imum time step increment of 1x105. The analysis of one wing geometry is performed in about 7 8 seconds. This analysis can predict the deflection for normal ized flight loads. However for actual flight loads it was seen that th e analysis would terminate midway due to stress concentration near the fixed nodes. Limitation was placed on the analysis due to insufficient refinement of mesh. For aggressive flight loads the structure becomes in stable and buckles. Large displacements ar e associated with buckling. T his analysis fails to capture this deflection behavior. This is because buckling is re lated to structural instability and this analysis assumes the structure to be stable When the wing buckles the root airfoil flattens out and while doing so the tip of the wing is

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26 raised out of the plane as seen in Figure 1 7 For the assumptions associated with this analysis, other options should be explored to find the load carrying capacity of the wing. Non -Linear Eigenvalue Analysis. The eigenvalue analysis is used to estimate the critical load of stiff structures. It uses a linear perturbation procedure. To define geometric nonlinearity of the structure we define a dummy step before the eigenvalue calculation ste p. The eigenvalue step considers the previous step in the analysis as the base step to run the analysis. A classical eigenvalue problem is defined with zero load, but in our case we will provide the initial flight load at cruise speed, PN. The eigenvalue a nalysis uses a load perturbation methodology which after each step perturbs the load (QN) to find the load at which the model stiffness matrix becomes singular. When the analysis is complete we will have a n i and the corresponding load at which the structure buckles is given by Critical buckling load = PNi*QN (2 3) Where i is the ith eigenvalue. O ne of the dr awback observed about this analysis is, it fails to capture the load displaceme nt curve for a nonlinear structure completely In our case where the reflex wing is one of the possible wing design configuration, local chord wise buckling can easily be observed. Buckling eigenvalue analysis will predict all the local buckling plus globa l buckling modes. There is no easy way of predicting which eigenvalue corresponds to global spanwise buckling that we are looking for Figure 2 4 shows the eigenmode shape of the wing at local buckling predicted by the eigenvalue analysis. The eigenvalue buckling analysis is done usually for stiff structures. A n example is an Euler column which has a very stiff response to the compressive axial load until a critical load is reached when the column bends suddenly causing it to buckl e. The UAV wing is large

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27 deformation structure, while the large deformation can be included in the step prior to the buckling analysis step as the final shape would be the base state for the eigenvalue analysis, the eigenvalue analysis relies on very littl e geometric change due to the perturbed load QN. Figure 2 4 Local chordwise buckling of a UAV wing Riks Analysis Riks analysis also known as arc length method is efficient in predicting the behavior of unstable structures ha ving large deformation. We employ Riks method to determine the load carrying capacity of the wing in the predictor tool. The response of a geometrically nonlinear static problem involving buckling where load -displacement curve shows a negative stiffness ca n be found using Riks method. The Riks method considers the load as an unknown in addition to the displacement and solves simultaneously for both. The Riks analysis can be in continuation to a previ ous step. A load applied to the structure in the previous step is considered as a dead load, P0 by Riks analysis. The load specified in the Riks analysis step is considered as the reference load. During the analysis the load is ramped proportionally from the initial dead load to the reference load, while doing s o the load t otal, is given by Pt otal= P0 ref P0) (2 4)

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28 To measure the progress of the solution, arc length is used. For example consider the nonlinear load dis pla cement curve shown in Figure 2 5 The Riks analysis will follow the curve to find the load proportionality factor and displacement at each increment. The increment size for the first step is defined by the user, by specifying t he initial arc length, lin. The initial arc length is also the first load proportionality constant, if the total arc length scale factor, lperiod, is set to 1, the initial load proportionality constant is found by using in = lin/lperiod (2 5) maximum and minimum arc length increment can be controlled, so when the analysis passing across a linear part of the curve, for ex ample before point A in Figure 2 5 the analysis will have a larger arc length but as it approaches the peak the arc length will reduce for better control. As a result the analysis will have a faster convergence. The analysis can also be performed with a fixed arc length, however this would increase the number of iterations required to reach the maximum load. Figure 2 5 Standard load displacement curve For the uav wing it is also assumed that the lo ad vs wing deformation response is reasonably smooth and no sudden bifurcations occur. These assumptions are found to be valid on simulating and testing some trial wings in Abaqus

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29 The analysis procedure then travels along the load -wing deforma tion arc. I n effect, increasing the wing loading from the normal flight load to a reference load (20 times normal buckling flight velocity then can be shown to be relat ed to load proportionality factor and Vc by: Vbuckle1/2 Vc (2 6) The snap through buckling velocity is found by plotting Vbuckle versus camber at the root airfoil to find a point where the Vbuckle starts reducing in magnitude (wing 1) or a point when graph reaches a minimum camber point (wing 2); whichever occurs first. If the wing continues to load stiffen (wing 3), the maximum flight load corresponding to 20 times the normal flight load will be returned to calculate Vbuckle. An Example is shown in Figure 2 6 The analysis of one wing geometry is performed in about 2 3 minutes. Figure 2 6 Buckling analysis possible plots Results and Discussion Riks analysis predicts the snap throu g h buckling behavior of the UAV wing completely. The load and displacement values are recorded for the root airfoil in a data file. These values are then monitored for the maximum camber of the root airfo il at each increment. Figure 2 6 shows

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30 the different possible plots depending on the structur al stability of the wing. Wing 1 is a example of a wing which initially load stiffens as the flight load increases, and then a point is reached after which the wing snap through buckles. Win g 2 is a n example of a wing which is not a very stiff s tructure and as the flight load increases the camber reduces to a point where is becomes zero at which the buckling velocity of the wing is maximum. Wing 3 is a n example of a wing which continues to load stiffen even at aggressive flight loads, unti l the buckling velocity corresponds to the reference load, 20 times the a ctually flight load. Figure 2 -7 shows the snap through buckling shape of a baseline wing where the root airfo il flattens out and the tip undergoes a large displacement. The structural paramete rs for the baseline wing are listed in Table 2 1 When the wing snap through buckles large stresses are expected to be induced at the root airfoil as it flattens out. A small subroutine is developed by Jagdale et al. [9] which checks for the failure in the structure along the material co -ordinate system using the Tasi -Wu failure criteria. A n optimization routine is used to test the wings with varying parameters, Table 2 1 [9] shows the parameters of a few wings tested using this technique. All the wings tested have a span of 24 inches and a root chord length of 7 inches. Figure 2 7 Snap through buckled baseline wing: large stresses are developed at the root airfoil

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31 Table 2 1 Wing parameters [9 ] Design point z 1 x 1 z 2 x 2 Sweep Angle Taper Ratio Twist Angle E 7 % 20 % 0.5 % 80 % 30 0.6 7 D 7 % 20 % 1 % 65 % 30 0.5 3 C 7 % 20 % 0.5 % 65 % 28 0.5 2 B 8.5 % 35 % 0 % 70 % 30 0.5 1 A 10 % 35 % 0 % 85 % 30 0.5 0 Baseline wing 6 % 25 % 1 % 75 % 15 0.5 0 The camber value s are observed to vary from 6% 10% of t he root chord length while the maximum reflex for the wings is 1% of the chord length. The camber is located either at 20% chord location or at 35% chord location, in case of the baseline wing the camber is located at the quarter chord location. Sweep back angle helps the wing to perform better aerodynamically and also increases the wing stiffness and load st iffening ability [ 9 ]. Taper ratio is 0.5 for all the wings except it is 0.6 for design E. The twist angle values are obser ved to vary from 0 degree to 7 degree s Figure 2 8 shows a plot of chord normalized camber verses air speed for baseline wing with 15 degree sweep plot of. Point A on the plot is the max imum buckling speed of the wing The wing b uckles at a velocity of 29 m/s, h owever a wing with same parameters but with a zero sweep back angle buckles at a velocity of 12 m/s. So the sweep back improves the load carrying capacity of the wing. Table 2 2 shows the buckling velocities of the wing with design parameters in Table 2 1 Table 2 2 Buckling velocities for designs [9 ] Design point V buckle (m/s) E 74.30 D 69.43 C 64.62 B 55.54 A 43.32 Baseline wing 29.14

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32 All the designs have a higher buckling velocity as compared with the baseline design. It is observed that even though de signs A and B have a high camber and a swept back angle of 30 degrees they have lower buckling velocitie s as compared to other designs It is also observed that the bendable wings with higher twist angle have a higher load carrying capacity. Design E has the highest buckling velocity and also hi ghest twist angle of 7 degrees. So it can be concluded that the washout effect added by the twist angle improves the structural performance of the wing It is seen that the change in reflex is very minimal, so the reflex has little to no effect on improving the buckling velocity of the bendable wing. The plan forms of a ll the de signs can be seen in Figure 2 9 Design A is further analyzed in detail to understand how the predictor tool works. Design A has 10% camber located at 35% root chord length with a 30 degree sweep angle and 0 twist angle. Figure 2 10 shows the plot of chord normalized camber verses the air speed for design A. For design A the dis cretized geometry is saved in the input file, this pre processing step is performed by a function (getriksinp.m) developed in Matlab Once the input file is ready with all the model details, another function (runriks) developed in Matlab calls Abaqus solver offline to perform the analysis for design A The analysis is done using Riks method. As the analysis progresses at each increment it finds a load proportionality factor by considering the load and displacement as unknown s Load at each step is found by multiplying this load proportionality factor with the reference load. Reference load used is 20 times the actual flight load For design A, initially the wing starts to load stiffen, that is the camber increases as the load increases However due to high percentage of the camber, which provides high lift to the wing, the wing structure continues to load stiffen till the analysis reaches the reference load. Figure 2 11 shows the load stiffened configuration for design A.

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33 For postprocessing the load proportionality factor and the nodal displacement at the root airfoil and are saved in a data file. The data file content s are extracted by using function (getriksdisp.m) developed in Matlab This Matlab function plots the F igure 2 10. The buckling velocity returned for Design A is 43.32 m/s. It can be concluded that t he numerical procedure to predict the snap through buckling behavior of the bendable UAV w ing was developed. T he design of the UAV wings was done successfully as continually load stiffening wings are desired. This predictor tool was used as a part of optimization effort on conceptual design of bendable wing along with other tools developed by J agdale et al [ 9 ]. Further research can be done to study the sensitivity analysis. This will provide a idea of how sensitive the buckling velocity is, to the changes in parameters like camber, sweep angle, twist angle etc. Fig ure 2 8 Plot of the baseline wing.

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34 Figure 2 9 Planforms of the wings in study. Figure 2 10. Normalized camber vs bukling velocity (air speed) for design A.

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35 Fig ure 2 11. Load stiffened configuration for design A.

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36 CHAPTER 3 EXPERIMENTAL VALIDAT ION The wing geometry of a UAV wing as discussed in the previous chapters is complicated. A lot of parameters are to be considered to design th e wing and tweaking a certain parameter would entirely change the results obtained. For example increasing the sweep angle would increase the load carrying capacity but at the same time if the camber is reduced then the load carrying capacity of the wing r educes. The motivation to do the validation is to test the predictor for simple geometry to gain confidence in the predictor methodology. The idea is to experimentally test a structure having a simple geometry to find the load carrying capacity of the stru cture and then compare the experimental results with the results obtained from the predictor tool. To find the load carrying capacity of the specimen a 3 point bend test is performed on a MTI tensile test machine. A three point bend test is performed on t he specimen as a snap through buckling behavior can be captured using this technique. Experimental Specimens To gain confidence on the load carrying capacity predictor we test the predictor tool by using a simple geometry like a singly curved composite she ll. The layup of the specimens is done using a two layer 45 degree orientation bi -directional carbon epoxy prepreg The layup is done by cutting two prepreg sheets having a 45 degree orientation of 20 inches length and width equal to the development length corresponding to 270 degrees that is 10.6 inches. The layup is done on a Teflon covered pipe having a outside diameter of 4.5 inches. The entire lay up is covered with Teflon peel -ply, this allows the extra resin to pull out of the carbon fiber. A breat her material is placed on top of that layup to make sure vacuum would be applied uniformly. This pipe is placed inside a standard vacuum bag & the oven curing under vacuum is done.

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37 When the curing cycle is complete, the pipe is removed from the vaccum bag T he specimen is carefully removed from the pipe. Smoothing of the edges is done by using medium gritted sandpaper. Figure 3 1 shows the composite shell curved having a n included angle of 270 degrees. The layup is done using fibe r direction of 45 degree s orientation and two layers to be consistent with the layup properties used for the wing. By keeping the span of the specimens close to the span of the wing it can be assume d that these specimens are singly curved wings having a ro ot airfoil which has camber located at 50% chord location, no reflex and zero sweep angle. The singly curved wings are cut from this shell according to the different included angles required for the experiment. The edges of the specimens cut should be stra ight and parallel to each other. Specimens with included angle of 40, 45, 60, 75 and 90 degrees are used for the experiment. Figure 3 1 Cured composite s hell The only parameter s associated with the des ign of the singly curve d wing are the camber and the root chord. The camber is defined as the maximum Y distance of the structure from the imaginary horizontal line joining the two end points at any given configuration at the root airfoil. The imaginary horizontal line is the ch ord length The radius of curvature of the wing is fixed to 2.25 inches. Figure 3 2 shows different wings used for the experiment along with the camber location. It can be observed that as the included angle increases the camber of the wings increases.

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38 Figure 3 2 Specimens used for experimental validation. Experimental Apparatus The singly curved wings are supported at two points and point loads acting at the center of the specimen are used to buckle the specimen unti l the root airfoil flattens out. The deflection of the specimen is recorded using a high resolution visual im age correlation (VIC) system [16]. Figure 3 3 shows the experimental appar atus Fixture Design To perform the bend test a fixture is developed on which the specimens can be supported. The support points are located such that they are at quarter span distances (5 inches) from t he point load on both the sides The fixture assembly is as follows: The Base Plate : The Base plate is fixed onto the MTI machine with 4 bolts and also the fixture on which t he VIC cameras are attached to the base plate The Top Plate : The Top plate has the two support points which are 10 inches apart from each other. The support is a rod having 0.5 inch diameter. At each support the specimen will in contact with two points. One point support will cause the wing to twist while applying the load.

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39 The distance between the top plate and the base plate is to ensure the VIC cameras field of view ca n completely capture the out -of -plane deflection of the root air foil. Figure 3 3 shows the fixture assembly with the base plate, the top plate and the two supports, also the Figure shows the 2 VIC cameras used to record the deflection of the wing Visual Image Correlation System High resolution visual image correlation is used to study the behavior of the specimens under the point load. The stereo triangulation technique is used by the VIC sys tem which recovers 3 D struc ture by using imaging sensors [ 10]. The imaging sensors are two high resolution cameras that obtain accurate 3 D measurements of a surface having low luster and random speckle pattern. The two camera s are connected to a PC via an IEEE 1394 firewire cable, and a special unit is used to synchronize the camera triggers to enable capturing simultaneous images from both the camera. These VIC cameras are initially focused on the specimen so that the cameras can easily recognize the speckle pattern. The next fundamental step is to calibrate the two cameras to determine the pixel spacing. The calibration is done by taking images of a known grid of white dots over a black paper. The spacing between the dots ran ge from 1.5 to 3.0 mm. The closer your specimen is to the camera, the smal ler dot spacing should be used. Once the calibration is done a reference image is taken (no load applied) Once the reference state is set the system can measure both in -plane and out of -plane measurements by comparing the deformed state with the reference state. Figure 3 4 shows the specimens with random speckle pattern near the root airfoil area. The root airfoil for whic h the deflection is recorded is highl ighted in Figure 3 4 Random speckling is done by first painting the area white which is near the root airfoil ; then by slightly enlarging the nozzle of the black spray can speckle the specimen [16, 17]. The results obtained from the VIC system c onsist of geometry in discrete X, Y and Z coordinates.

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40 Load Cell The load cell having a resolution of 1000 lbs is used for load measurement. Before the experiment was performed the load cell was checked for calibration by hanging known dead weights and cross checking the out put given by the load cell. LabVIEW 8.6 is used to record the load by using a code developed in house. The mechanical load is converted into volts by the load ce ll and the voltage is converted ba ck to load in Newton by using E quation 3 1 N = 420067.8446 V (3 1) A bolt having 0.5 inch diameter is attached to the load cell. To maintain a point contact with the specimen the head of this bolt is grinded on the grinding machine in the machine shop. Figure 3 5 shows the load cell with the bolt attached to it. Figure 3 3 The fixture assembly

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41 Figure 3 4 Specimens with random speckle pattern Figure 3 5 Load c ell

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42 Experimental Setup The fixture is mounted on the MTI machine with the base plate fixed to the machine. Four bolts are used to fix the base plate to the MTI machine. Using a spirit leve l it is ensured that the fixture is horizontal and the supports points are at same level. Figure 3 6 shows the singly curved wing supported on the support points. The load is applied on the center section of the specimen. Before t he experiment is perform ed it is checked if the 2 support points and the loading point are in a straight line. If not in a straight line it will cause off center loading of the wi ng that can twist the wing. The two VIC cameras are mounted on a fixture whic h has two horizontal arms This fixture is fi xed with the base plate using C clamps The experiment is displacement controlled movement of the loading point The displacement is given in small increments, at each increment the load is recorded from the l oad cell output and the VIC system is used to record the deflection images. The displacement is controlled unti l the root airfoil flattens o ut. A t this configuration the wing is considered to be buckled. As the root flattens out it causes the tip to underg o a large displacement as shown in Figure 3 6 A Figure 3 6 Experimental Setup on the MTI machine A) Initial Wing Shape. B) Buckled Wing Shape

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43 B Figure 3 6. continued Abaqus M odeling The singly curved wing is tested using the predictor tool developed in C hapter 2 For the simulation only semi -span of the wing is modeled. The coordinate system used is X axis along the chord length, Y axis along the camber change, and Z axis is along the span direc tion. Appropriate point loading is applied at the center node on the root airfoil section. Meshing is done such that the two nodes at the support are 0.5 inch apart from each other. A ppropriate boundary conditions are applied to the s pecimen, Z -symmetry is applied for all the nodes on the root airfoil and the two nodes at the support are free to rotate about X axis and have a free translation along Y axis Riks analysis is performed to predict the buckling load for the wings. For 40 and 45 degree specimens reference load used is 10 N and for all the other specimens reference load used is 50 N. Figure 3 7 shows a 90 degree specimen modeled with the loading and boundary conditions. Figure 3 8 shows the snap through buckled shape of the 90 degree wing.

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44 Figure 3 7 S ingly curved wing with loading and boundary conditions Figure 3 8 Buckled shape of the singly curved wing predicted by the predictor t ool

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45 Results and Discussion Specimens or the singly curved wings having different included angles thus having different camber values are tested to find the maximum load which it can sustain before it buckles. The motivation is to compare these experimenta l values with the values obtained by using the buckling predictor tool in Abaqus by doing this comparison the accuracy of the predictor tool is validated. The comparison of these values is discussed in this section. Load is applied at the center section of the singly curved wings. This cross section at which the load is applied will be referred to as the root airfoil. When the load is applied the shape change of the root airfoil is recorded using a VIC technique. As a point load is used to buckle the wing the root airfoil doesnt flatten out completely. Using a distributed load might completely flatten the airfoil. Figure 3 9 shows how the root airfoil changes shape and eventually almost flattens out for a specimen having 75 degr ee included angle. A similar trend is recorded by the predictor tool as shown in Figure 3 9 So it is concluded that predictor tool can predict the change in the airfoil of the specimen to predict the buckling behavior. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 X-axis, Normalized ChordNormalized Root Camber Increasing Load 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 X-axis, Normalized ChordNormalized Root Camber Increasing Load Figure 3 9 Change of airfoil as the load changes for a 75 degree wing. It is expected that the singly curved wings having high camber would load stiffen under actual flight load. We say the camber is high because 10% camber is the m aximum allowed for

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46 the UAV wing, as for the singly curved wings the 40 degree wing has 10% camber and the 90 degree wing has 20% camb er. It is observed that when a three point bend test is performed, the wings show a different behavior. As the load is incr eased instead of load stiffening the camber reduces gradually unti l the maximum loading point is reached. Beyond this point the structure becomes unstable and is considered to be buckled. Figure 3 10 shows the experimental plot th at records this behavior of the wing having a 90 degree included angle. This wing has a maximum load carrying capacity of 28.2 N. Figure 3 10 shows the buckling behavior predicted by the predictor tool. The simulation predicts the maximum buckling load of the specimen to be 29.98 N. T he experiment and the simulation plot matches pretty well, confirming that the predictor tool can predict the behavior of the structure. The difference in the result is less than 5 % for all the specim ens. Table 3 1 shows maximum buckling loads from the experiment and the loads predicted by the simulation. Figure 3 11 depicts the plots of all the specimens comparing the experimental and simulation values of change in camber against the applied load. 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 5 10 15 20 25 Chord Normalised Camber (z/c)Applied Load (N) Predictor 90 Experiment 90 Figure 3 10. Plot of chord normalized camber vs applied load for a 90 degree wing for experiment and simulation

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47 Table 3 1 Maximum buckling loads o f the specimens Included angle Degrees Maximum Load (N) Simulation Maximum Load (N) Experiment % Difference 90 29.5 28.6 3.15 75 21.9 22 0.45 60 13.1 12.7 3.15 45 6.2 6.6 6.06 40 4.6 5.3 13.21 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Chord Normalised Camber (z/c)Applied Load (N) Predictor 40 Experiment 40 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 1 2 3 4 5 6 Chord Normalised Camber (z/c)Applied Load (N) Predictor 45 Experiment 45 0.06 0.08 0.1 0.12 0.14 0.16 0 2 4 6 8 10 12 14 16 18 20 22 Chord Normalised Camber (z/c)Applied Load (N) Predictor 75 Experiment 75 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0 2 4 6 8 10 12 Chord Normalised Camber (z/c)Applied Load (N) Predictor 60 Experiment 60 Figure 3 11. Compariso n of experiment and predictor tool results for the change in camber for 40, 45, 60 and 75 degree specimens From the plots in Figure 3 10 & Figure 3 11 it is concluded that the predictor tool can predict the maximum buckling load sustained by the singly curved wings. Our motivation was to check if the predictor tool can predict the buckling values for the singly curved wings obtained from the experiment. The predictor tool provides results very close to th e experiment with the difference of 5% which is acceptable. This methodology can be applied to a compl ex geometry

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48 structure like a UAV wing to find the load carrying capacity with the error being minimal. Thus even before a wing is manufactured or actually tested this predictor tool methodology would give accurate results and insight into how a wing with the given set of parameters and loading conditions would behave structurally. While doing the validation is was observed that as wings with increasing camb er values showed a higher buckling load. Figure 3 12 shows the plot comparing the change of chord normalized camber vs applied load for all the specimens. Figure 3 13 shows the plot of double normalized c hord first with the chord then with the initial camber value vs the normalized load. It is interesting to see that all the wings show the same behavior. Figure 3 14 shows the plot of max load vs the initial chord normalized camber 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 Chord and Initial Camber Normalized Camber (z/c,inicamb) Applied Load (N) 90 Degree Experiment 90 Degree Predictor 75 Degree Experiment 75 Degree Predictor 60 Degree Experiment 60 Degree Predictor 45 Degree Experiment 45 Degree Predictor 40 Degree Experiment 40 Degree Predictor Figure 3 12. Plot of applied load vs c hord and initial camber normalized camber

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49 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 Chord and Initial Camber Nomarlized Camber (z/c,inicamb)Peak Nomarlized Applied Load (N) 90 Degree Experiment 90 Degree Predictor 75 Degree Experiment 75 Degree Predictor 60 Degree Experiment 60 Degree Predictor 45 Degree Experiment 45 Degree Predictor 40 Degree Experiment 40 Degree Predictor Figure 3 13. Plot for peak normalized load vs c hord and initial camber normalized camber. Figure 3 14. Maximum buckling load vs initial chord normalized c amber The deflection of the point on the root airfoil at which the load is acting can be recorded to plot the load vs deflection response. The load deflection plot helps to predict t he configuration of

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50 the wing at the particular flight load. This plot is important from the aeroelastic analysis point of view. In case of a aeroelastic problem the pressure distribution obtained from AVL (and aerodynamic software) by doing a aerodynamic a nalysis will be applied to the structure to find the deflection (configuration), if the distribution changes the shape of the wing then that means the pressure distribution has changed, so this deflected configuration of the wing is loaded in Abaqus to fin d the new pressure dis tribution. It is important for A baqus to predict the deflection accurately, so that the pressure distribution on the wing could be predicted accurately by AVL. For the 90 degree wing we plot the l oad vs deflection for the point at wh ich of load application on the root airfoil. Figure 3 15 shows the plot. Here again it is observed that for the 90 degree wing the predictor tool captures the deflection 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 25 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 90 Experiment 90 Figure 3 15. Load vs chord n ormalized d eflection at loading point.

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51 It is also seen that the predictor tool captures the deflection for 75 and 60 degree wings shown in Figure 3 16. However for 45 and 40 degree specimens the predictor and the experiment values are off by a factor of 2 as shown in Figure 3 17. The possible reasons why the deviation might be present is discussed later in this section. 0 0.02 0.04 0.06 0.08 0.1 0.12 0 2 4 6 8 10 12 14 16 18 20 22 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 75 Experiment 75 0 0.05 0.1 0.15 0 2 4 6 8 10 12 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 60 Experiment 60 Figure 3 16. Load vs chord normalized d eflection at loa ding point for 75 and 60 degree wings. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 40 Experiment 40 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 1 2 3 4 5 6 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 45 Experiment 45 Figure 3 17. Load vs c hord normalized d eflection at loading point for 40 and 45 degree specimens using Model 1 From p lots in Figure 3 16 and Figure 3 17 it is observed that the experimental specimen s show a higher stiffness value as compared to the predictor. So simulations were done by changing the material model to see how the change in material model affects the prediction.

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52 There are 3 different material model used as shown in Table 3 2 Model 1 is the material model used for analyzing the UAV wing [9 ]. Model 2 is the material model obtained from previous work done by Stanford [ 19]. Whereas Model 3 is the material model obtained from theory manual [ 18]. Table 3 2 Material models used Property Name Model 1 Model 2 Model 3 E1=E2 (GPa) 34.8 34.8 64.81 Nu12 0.05 0.41 0.05 G12 (GPa) 2.34 2.34 4.68 When model 2 was used for a 40 degree specimen it was observed that the stiffness for the experiment and the simulation match perfectly but the load at which the wing buckles increases. So it is seen that the buckling load is proportional to the material model. Figure 3 18 shows the plot using model 2 and model 3. A 0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 4 5 6 7 8 9 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 40 Experiment 40 B 0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 4 5 6 7 Chord Normalised Deflection (w/c)Applied Load (N) Predictor 40 Experiment 40 Figure 3 18. Plot of load vs chord normalized defl ection for a 40 degree spec imen. A) U sing Model 2, B) Using Model 3 It is observed that if we increase the poisons ratio and keep the stiffness values similar to model 1 then the buckling load reduces but the factor of 2 is retained between the Abaqus

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53 prediction and t he experiment v alues. From the results it is understood that the material model is a very important to predict the deflection of the structure as well as the buckling load. The experiment has the higher stiffness as compared to the predicted results from model 1 and mode l 3. Assuming our material model is accurate for the predictor tool, it can be thought that when the composi te is cured, it could undergo spring back This will reduce the radius of curvature making the singly curved wings stiffer. It can also be argued th at the thickness of the wings is not uniform at the root airfoil section which makes the wing stiff. The fiber orientation is also a n important parameter which affects the stiffness of the experimental specimen. As a part of f urther investigation sensitiv ity analysis can be performed. This will explain the sensitivity of the experiment to these parameters. If above parameters are within the acceptable range, f urther investigation i s required to tweak the material properties and find the material model for which the prediction will match the experimental results A tensile test of the material can also be performed using the ASTM standards to find the material properties. Although it is difficult to capture the deflection results using the predictor tool, ou r motive was to find out the buckling load prediction accuracy of the predictor tool. Accordingly in the load deflection plots desirable predictions were obtained for the buckling load s

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54 CHAPTER 4 CONCLUSIONS AND FUTURE WORK To conceptually design the ben dable UAV wing, a numerical procedure was developed. This numerical procedure was developed around an FEA software, Abaqus. The numerical tool was referred to as the load carrying capacity predictor tool. Preprocessing and post processing for this to ol was done using functions in M atlab. The actual analysis was done using the Abaqus solver. The load carrying capacity tool can predict the snap through buckling behavior for the bendable wing. The analysis methodology has evolved by using 3 different analysis techniques. Initially the predictor tool used a non -linear static analysis, this analysis used to terminate midway due to stress concentration effects and coarse meshing. More work is required in this area to further refine the mesh and check if the analy sis can work properly. Next, the analysis was done using a non -linear eigenvalue analysis. However this analysis cannot predict the large displacement effects. The eigenvalue analysis relies on very less geometric changes due to the perturbed load. The an alysis predicts all the local and global buckling modes. However there is no way of predicting which buckling mode corresponds to the global spanwise buckling. If the refined mesh provides appropriate results for the non-linear static analysis then the eig envalue analysis can be the following step in the model to predict the eigenmode and eigenvalue of the structure. Further, the analysis was done using a modified Riks method. This method could accurately capture the snap through buckling behavior of the wi ng. For the conceptual design study, the predictor tool by predicting the snap through buckling behavior was used as part of the optimization effort along with other codes. The optimization effort is done on a wing having 24 inch span and 7 inch r oot chord length. However this p redictor tool can be used to predict the behavior of wings having different parameter values.

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55 Also a sensitivity analysis can be done, to understand how sensitive the buckling load is to the changes in wing parameters. Although the predictor captures the results for the wing, to gain confidence in the analysis an experimental validation was done to check the accuracy to the predictor tool. A three point bend test was performed on singly curved wings to capture the experimental behavi or. The predictor tool managed to be within a difference of 5% to predict the buckling loads. However the deflection predictions show the stiffness is lower for the predictor tool results Further investigation is required to check the material model for t he predictor tool. A tension test can be done on the composite materials using ASTM standards to find the material properties. Accuracy of the parameters like thickness, radius of curvature and fiber orientation in the singly curved wing specimens play a n important role in capturing the experimental result. A sensitivity analysis can also be done for these parameters to find the how sensitive the predictions are to change in these parameter values.

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56 LIST OF REFERENCES 1 Cook, Kendra L. B. The silent force multiplier: The history and role of UAVs in warfare, IEEE Aerospace Conference, March 2007. 2 Sullivan J. Revolution or Evolution? The Rise of the UAVs, Technology and Society, 2005. Weapons and Wires: Prevention and Safety in a Time of Fear. ISTAS 2005P roceedings, June 2005. 3 Johnson B., Claxton D., Stanford B., Jagdale V., Ifju P. Development of a Composite Bendable Wing Micro AirVehicle, 45th AIAA Aerospace Sciences Meeting and Exhibit, Nevada, January 2007. 4 KZO Reconnaissance and target detection d rone Site. July, 6th 2009 Rheinmetall Defence. < http://www.rheinmetalldefence.com/index.php?fid=1599&lang=3&pdb=1> 5 Ifju P. Bendable wing for micro air vehicle, U.S. Patent Ap plication Docket No. 60/431,92, Dec. 2002. 6 Aerspace systems Site. 25 June 2009. Northrop Grumman. 26 June 2009 < http://www.as.northropgrumman.com/products/ghrq4a/index.html > 7 Preda tor Site 25 June 2009. General Atomics Aeronautical. 26 June 2009 < http://www.ga asi.com/products/aircraft/predator.php > 8 Jagdale V., Stanford B., Patil A., Ifju P. Multidisciplinary Shape and Layup Optimization of a Bendable Composite UAV Wing, 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL January 2009. 9 Jagdale V., Patil A., Stanford B., Ifju P. Conceptual Design of a Bendable UAV Wing Considering Aerodyna mic and Structu ral Performance, 50th Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA May 2009. 10. Ja gdale V., Stanford B., Claxton D., Johnson B., Lee K., Sankar B., Ifju P. Experimental Characterization of a Load Stiffening Wing for a Small U AV Society for Experimental Mechanics Annual Conference Springfield, MA June 2007. 11. Huang N C. Unsymmetrical Buckling of thin shallow spherical shells, ASME J Mech 1964; 31:44757. 12. Hunt G.W., Lord G.J., Peletier M.A. Cylindrical Shell Buckling: A C haracterization of Localization and Periodicity, Discrete and Continuous Dynamic Systems Series -B November 2003. 13. Akkas N., Bauld N.R. Buckling and Post Buckling of spherical caps, ASCE J Engng Mech Div 1971; 97:72739.

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57 14. Crisfield M.A. A Fast Incremental /Iterative Solution Procedure That Handles Snap Through, Composited & Structures 1980; 13:55 62. 15. D rela M. and Youngren H. AVL Aerodynamic Analysis, Trim Calculation, Dynamic Stability Analysis, Aircraft Configuration Development Athena Vortex Lattice 2006; 3 :26. < http://web.mit.edu/drela/Public/web/avl/ > 16. Sutton M., Cheng M., Peters W., Chao Y., McNeill S. Application of an Optimized Digital Image Correlation Method to Planar Analysis Image and Vision Computing, 1986; 4 :143 151. 17. Helm J. D., McNeill S. R., Sutton M. A. Improved 3 D Image Correlation for Surface Displacement Measurement, Optical Engineering, 1996; 35(7) : 19111920. 18. Department of Defense Handbook, MIL -HDBK -17-2F, Composite Materi als Handbook Volume 2. 17 June 2002 19. Stanford B., Ifju P., Albertani R., Shyy W. Fixed membrane wings for micro air vehicles: Experimental characterization, numerical modeling, and tailoring, Progress in Aerospace Sciences 2008; 44:258 294.

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58 BIOGRAPHI CAL SKETCH Abhishek Patil was born in Pune, India. He did is schooling in St. Xaviers High School, Mumbai, India. A s a single child to his parents and the sole centre of their attention, he longed for friends and play -mates in his co -students at the school. But for a short period of struggle to adjust to the new environment, he did well in his schooling including participation in extracurricular activities and eventually achieved a rank within the top 3% students in his school. With a desk top computer as his past time play -mate since secondary grades, he chose specialization in computer science in S.K.Somaiya Junior College, Mumbai. He made this decision considering two aspects; firstly, keeping with a contemporary trend and thinking that it is his interes t and secondly to skip learning biology while being focused at engineering as a choice of career. The two years at the junior college led him to the revelation that his interests really are in the area of mechanical sciences. Having done scholastically well with a silver medal for the junior college, he pursued a Bachelors degree in Mechanical Enginee ring at K.J.Somaiya College of Engineering and graduated with bachelor of engineering in May 2006. He honed his leadership skills through participation in a wide variety of professional and extracurricular activities spanning membership of S ociety of A utom otive E ngineers Student Chapter, Mechanical Engineers Students Association, and organizing cultural events and industrial visits, and many more. He did Summer internship at Larsen & Toubro Ltd, Mumbai and had opportunity to be entrusted with design of a special machine for stretch stabilization of thick Aluminum plates for Aerospace applications. He also pursued his degree project at Larsen & Toubro Ltd, Mumbai where he worked on design of eccentric shaft high reduction ratio gearbox. This project brought a ccolades to be adjudged as the best project in the mechanical engineering discipline in the institute wide competition in 2006.

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59 He chose the University of Florida in Fall 2007 to pursue Master of Science in e ngineering, after c ompleting a diploma in 2007 in computer aided design modeling and finite element analysis softwares The small town of Gainesville became Abhisheks home throughout his Master s Program. During this time, he got involved in a lot of extra -curricular activities and made numerous life long friends. He started working at Experimental Stress Analysis (ESA) lab under t he guidance of Dr. Ifju at the D epartment of Mechanical and Aersospace Engineering, where he was blessed with an opportunity to work with a dedicated group of researchers. He expects that the work he has pursued at ESA lab helps other researchers who are or will be part of this lab, directly or indirectly. Abhishek plans to be an industry professional for a couple of years where he expects to contribute in solving real life problems with the competence gained at ESA while continuing to learn and apply his knowledge. In addition to this, he is willing to do a M aster of Business A dministration from a reputed business school which will surely add credits to his academic future.