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«By VIJAY NARAYAN JAGDALE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR ...»

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EXPERIMENTAL CHARACTERIZATION AND MULTIDISCIPLINARY CONCEPTUAL

DESIGN OPTIMIZATION OF A BENDABLE LOAD STIFFENED UNMANNED AIR

VEHICLE WING

By

VIJAY NARAYAN JAGDALE

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2010 1 © 2010 Vijay Narayan Jagdale 2 To my idol and inspiring father, Late Narayan L Jagdale; my caring mother, Kaushalya N.

Jagdale; my loving wife, Ujwala; my supportive sister, Balika and her family; and my brother, Shridhar and his family 3

ACKNOWLEDGMENTS

I would like to thank my adviser Dr. Peter Ifju, for his support, guidance and motivation throughout my PhD studies. I would also like to thank him for his patience and allowing me to work with freedom, injecting ideas at appropriate stages. I would like to thank my committee co- chair Dr. Bhavani Sankar for serving on my committee and advising me on the research. Many thanks to Dr. Raphael Haftka for supporting me, serving on my committee and providing me with invaluable inputs and guidance during my research. Thank you to Dr. Anthony Brennan for serving on my committee, for his valuable inputs and to allow me to use his lab facilities.

I would also like to acknowledge Dr. Nam-Ho Kim for his useful inputs. Thanks to Dr.

Bret Stanford for his valuable inputs, discussions and help in the research. Thank you to Dr.

Roberto Albertani for his help and allowing me to use the wind tunnel facility at REEF.

Many thanks to my past and present lab-mates in the Experimental Stress Analysis Lab for their help and making the lab fun and exciting workplace. Thank you to Abhishek Patil, Dr.

Weiqi Yin, Dr. Enoch Chen, Dr. Mulugeta Haile, Yaakov Abudaram and other graduate students in the department: Dr. Felipe Viana, Anurag Sharma and Dr. Prasanna Thiyagasundaram.

Thanks to my many wonderful, to be lifelong friends that I made during my stay at Gainesville. Finally many thanks to my loved family members who constantly encouraged me during my studies and for their patience and support.

4

TABLE OF CONTENTS

page ACKNOWLEDGMENTS

LIST OF TABLES

LIST OF FIGURES

Abstract

CHAPTER 1 INTRODUCTION

Bendable UAV Wing Design

Problem Statement

Approach

2 LITERATURE REVIEW

UAV Wing Designs to Reduce Storage Volume

Compliant Wings

Mechanically Deployable Wings

Inflatable Wings

Low Aspect Ratio (LAR), Low Reynolds Number (LRN) Aerodynamics

Low Aspect Ratio Studies

Low Reynolds Number Studies

LAR and LRN Combined Studies

Wing Airfoil and Planform Parameters Affecting Aerodynamics

Wing Optimization Studies

University of Florida Flexible Wing MAV

3 EXPERIMENTAL CHARACTERIZATION

Design and Manufacturing of Experimental Wings

Visual Image Correlation (VIC)

Wing Compliance in the Folding Direction

Wing Load Stiffening Ability in Positive Flight Load Direction

Wind Tunnel Aerodynamic Measurements

Storage-Induced Creep Deformation Measurement

Material Creep Characterization

Experimental Setup

Data Analysis

Experimental Characterization - Conclusions

54 MULTIDISCILINARY SHAPE AND LAYUP OPTIMIZATION

Wing Model

Wing Analysis Techniques

Aerodynamic Analysis

Structural Analysis – Limit Flight Velocity Calculation

Storage Analysis – Minimum Safe Storage Diameter Calculation

Wing Manufacturing Layup Orientation and Optimization Considerations

Optimization Problem Formulation

Optimization Algorithm

Results and Discussion

5 DESIGN OF BENDABLE WING UNDER UNCERTAINTY

Uncertainty Quantification and Propagation

Reliability Based Design Optimization (RBDO) of Bendable Wing

Design Space Reduction and RBDO Problem Formulation

Response Surface Approximations

Results and Discussion

6 CONCLUSIONS AND FUTURE WORK

LIST OF REFERENCES

BIOGRAPHICAL SKETCH

–  –  –

3-1 Spanwise strain measurements during the creep study

3-2 Observed glass transition temperatures based on DMA test data

4-1 Multimesh extrapolation mesh sizes used

4-2 Candidate layups that can be used for wing manufacturing

4-3 Candidate layups considered during the wing optimization study

4-4 Side constraints for design variables.

4-5 Objective function and constraint values for designs noted in Figure 4-19................... 102 4-6 Variable values for pareto front designs and the baseline wing noted in Figure 4-19.... 103 4-7 Design variable and objective function values for the Pareto design points noted in Figure 4-22





4-8 Design variable and function values for the Pareto design points noted in Figure 4-24. 110 5-1 Uncertainties in random design variables

5-2 Uncertainties in random parameters

5-3 Computational Model Uncertainties

5-4 Uncertainties for the deterministic Pareto front designs noted in Figure 5-1................. 116 5-5 Current probability of failure for Pareto optimal designs noted in Figure 5-1............... 117 5-6 RBDO: side constraints for the design variables

5-7 Surrogate models with associated PRESSRMS and PRESSRMS (%)

5-8 Design variable and objective function values for the Pareto design points noted in Figure 5-2

5-9 Design variable and objective function values for the Pareto design points noted in Figure 5-2

5-10 Design variable and objective function values for the Pareto design points noted in Figure 5-4

–  –  –

1-1 Typical NACA 4 digit airfoil (top), Example of a thin airfoil utilized in present research (bottom).

1-2 Applied Research Associates Inc. Nighthawk MAV [128] incorporates a bendablewing (left) that can be folded for compact storage (right).

1-3 Addition of curvature and sweep provides dissimilar bending stiffness. Beams are bendable / foldable in ‘low’ bending stiffness direction

1-4 Pocket MAV (left): 13 inch span bendable wing rolled and stored in a parallelepiped container (inset). UF’s 2006 IMAVC endurance MAV (right): 6 inch span wing rolled into 1 inch diameter.

1-5 Major concerns for bendable wing design: a) Initial rolling for storage induced stress failure, b) Creep due to storage inside a canister, c) In-flight buckling due to aggressive flight loads.

2-1 BYU’s IRIS UAV segmented rolling wing concept (Landon [11]). Wing laid flat (left), one side rolled under (center), both sides rolled under (right).

2-2 Advanced Ceramics Research Coyote UAV [19] utilizes scissor wing concept.............. 26 2-3 ILC Dover Inflatable UAV Wing [28] : Wing in deployed condition (left), wing packed in the fuselage (center), wing construction (right).

3-1 Bendable wing. The chord-wise shape of the airfoil can be seen with respect to the straight edge (left). Once bent, the airfoil shape becomes completely flat (right)............ 37 3-2 Straight and swept camber wing molds (top) and the wing planforms (bottom).............. 40 3-3 Speckled straight camber wing (left) viewed from top. Folded wing (right)................... 44 3-4 Compliant nature of bendable wings. Upon folding root airfoil flattens out in straight cambered wing (left) and in swept cambered wing (right).

3-5 ΔCp distribution on semi wings – output from AVL program. ΔCp distribution on straight camber wing (left) and on swept camber wing (right).

3-6 Three point bend test. Test schematic (top), test setup (left), supports are positioned at the center of pressure for each wing half (right).

3-7 Chord-normalized (z/c) shape of straight wing: initial shape (left) and buckled shape (right).

–  –  –

3-9 Chord Normalized camber (left), and normalized displacement at the loading point (right).

3-10 Graphical depiction of the root airfoil camber. The exaggerated camber for both straight camber (left) and swept camber (right) wings throughout the range of loading.

3-11 Lift coefficient vs AOA (left) and Drag coefficient vs Lift coefficient (right) at Re = 7x104

3-12 L/D ratio vs Lift coefficient (left) and Pitching moment coefficient vs Lift coefficient (right) at Re = 7x104

3-13 Measured out-of-plane creep deformation of the straight camber wing (top) and swept camber wing (bottom) after being stored at 70° C for 24 hour (picture 1 hr after unfolding).

3-14 DMS 110U equipment used in the study (left), composite specimen inside the sample holder (right).

3-15 DMA test specimen : 0/90 specimen (left), ±45 specimen (right).

3-16 DMA test data : 1 Hz frequency slice. Storage modulus and tan delta versus the test temperature

3-17 Creep compliance curves at different isothermals for 0/90 specimen.

3-18 Master creep curve for 0/90 orientation specimen (Tref = 30°C).

3-19 Creep compliance curves at different isothermals for ±45 specimen.

3-20 Master creep curve for ±45 orientation specimen (Tref = 30°C).

3-21 Comparison of normalized master creep curves for ±45 and 0/90 specimen (Tref = 30°C). Curves are normalized using their respective initial creep compliance values and show % change in the creep compliance values.

4-1 Wing root airfoil control variables.

4-2 Wing planform shape control variables.

4-3 Example of equally spaced panel distribution (left), same number of panels with chord-wise cosine and span-wise half sine spacing (right).

4-4 Change in aerodynamic coefficient predictions for straight camber wing with the inverse of the number of panels.

–  –  –

4-6 Comparison of results from aerodynamic model and wind tunnel testing of straight camber wing at Re = 7x104. (Model uses 14x24 cosine/half sine panel distribution)...... 79 4-7 Completely buckled shape of the baseline wing (left), buckling analysis possible wing structural behavior plots (right).

4-8 Singly curved specimens: 45 deg and 60 deg (left) [94] and the three point bend test schematic (right).

4-9 Comparison of experimental and model predictions for 60 deg singly curved specimen.

4-10 60 deg singly curved specimen: tradeoff between prediction error and element size (left), tradeoff between prediction error and normalized computational cost (right)........ 86 4-11 Comparison of experimental and model predictions for 40, 45 and 60 deg singly curved specimen three point bend test.

4-12 Comparison of experimental observations and model predictions (20x36 mesh) for straight and swept camber wing three point bend tests detailed in Chapter 3.................. 87 4-13 Straight camber wing: tradeoff between prediction error and element size (left), tradeoff between prediction error and normalized computational cost (right)................. 88 4-14 Comparison of wind tunnel test data and the results from analysis model

4-15 Rectangular strain rosettes G1, G2 and G3 are mounted on the underside of the swept camber wing

4-16 Predicted and measured chord-wise strains for different folding diameters (left), similar measurements for span-wise strains (right).

4-17 Model percent prediction error in chord-wise strains for different folding diameters (left), similar measurements for span-wise strains (right).

4-18 Bending force required for flat plate wing laminate layups (left) and diameter to which wings can be folded without bending stress induced failure (right).

4-19 Pareto optimal front: tradeoff between Limit flight velocity and L/D ratio................... 101 4-20 Root airfoil shapes (top), curvatures along root airfoils (left) and planforms of semiwings for designs A, B, C, D, E and baseline wing.

4-21 Wing flight load analysis for the baseline design and Pareto front designs A, B, C, D and E.

–  –  –

4-23 Root airfoil shapes (left) and planforms of semi-wings for designs 1, 1’, 2, 3 and baseline wing noted in Figure 4-22.

4-24 Pareto optimal fronts: effect of Cm constraint.

4-25 Root airfoil shapes (left) and planforms of semi-wings for designs 4, 5, 6, 7 and baseline wing noted in Figure 4-24.

5-1 Selected Pareto optimal design points’ a1, a2 and a3 for uncertainty propagation and probability of failure study.

5-2 Pareto optimal fronts: Deterministic designs compared with RBDO designs of different levels of reliability index constraint.

5-3 Root airfoil shapes (left) and planforms of semi-wings for designs R1, R2, R3 and baseline wing noted in Figure 5-2.

5-4 Pareto optimal fronts: Deterministic designs compared with RBDO designs of different levels of reliability index constraint.

5-5 Root airfoil shapes (left) and planforms of semi-wings for designs R4, R5, R6, R7 and baseline wing noted in Figure 5-4.

–  –  –

EXPERIMENTAL CHARACTERIZATION AND MULTIDISCIPLINARY CONCEPTUAL

DESIGN OPTIMIZATION OF A BENDABLE LOAD STIFFENED UNMANNED AIR

VEHICLE WING

–  –  –

Chair: Peter G. Ifju Cochair: Bhavani V. Sankar Major: Mechanical Engineering Demand for deployable MAVs and UAVs with wings designed to reduce aircraft storage volume led to the development of a bendable wing concept at the University of Florida (UF).



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