American Institute of Aeronautics and Astronautics1

Structural Optimization of the Landing Gear of a Mini-UAV

B. Gürdal Tugay1 and Halit S. Türkmen2

Istanbul Technical University, Faculty of Aeronautics and Astronautics, Maslak, Istanbul, 34469, Turkey

The main purpose of this study is to determine the optimum geometry and material forthe main landing gear of a mini-UAV. The optimization is achieved by using numericalmethods and the results are experimentally validated. Numerical studies are based on thefinite element analysis of the landing gear. Landing gears of UAV’s may be subjected to bothstatic and dynamic loads. Therefore, all load cases should be taken into account during thedesign. However, because the most critical load case is the impact during the landing, theimpact load is also considered in this study. The impact of landing gear on ground duringlanding is modeled using ANSYS finite element software. The landing gear is discretizedusing the layered shell elements. Numerical solutions are obtained for several types oflaminate configurations, materials and geometries. An optimum shape, material andlaminate configuration are determined as a result of the finite element analyses results.Experimental studies followed the numerical studies. A landing gear, which is chosen fromfeasible designs obtained by using the finite element analyses results, is manufactured usingcomposite materials, then, it is tested under a static load. The numerical and experimentalresults are compared and the best design is selected.

NomenclatureE = Young’s modulusG = shear modulusν = Poisson’s ratioσ* = tensile strengthε* = fracture strainσA = stress at region AσB = stress at region BεA = strain at region AεB = strain at region BU = displacementPcr = critical buckling loadF = applied loadµS = microstraint = thickness of the laminate

I. IntroductionHE impact problem during the landing of air vehicles is investigated by several researchers. There are somestudies on the static and dynamic failure analysis of landing gears.1-5 Nguyen et. al. modeled the landing gear of

an UAV using ABAQUS finite element software and they simulated the landing event.6 They compared thenumerical results to the test data. Chan et. al. designed a lightweight landing gear for an UAV.7 They considerd thebuckling failure and analyzed the behavior of the landing gear during landing. The use of composite materials forlanding gears reduced the weight as twenty percent and the additional approximately twenty percent of weightreduction is achieved by using optimization techniques.8 This also reduced the cost. The difficulties of making drop

1 Graduate Student, Aeronautical Engineering, Istanbul Technical University, Faculty of Aeronautics andAstronautics, Maslak, Istanbul, 34469, Turkey and AIAA Student Member.2 Assoc. Prof., Aeronautical Engineering, Istanbul Technical University, Faculty of Aeronautics and Astronautics,Maslak, Istanbul, 34469, Turkey and AIAA Member.

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12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 10 - 12 September 2008, Victoria, British Columbia Canada

AIAA 2008-5878

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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tests during the design phase of landing gears for small utility aircrafts are obvious. Therefore it is important toperform numerical studies to improve the design.

In this study a main landing gear for a mini-UAV is designed and manufactured. The study consists of numericaland experimental sides. In the numerical side of the study, the main landing gear of a mini-UAV is designed and isstructurally optimized. For this purpose, a sample prebuilt main landing gear is modeled using the finite elementmethod. The landing gear is made of carbon epoxy face sheet and foam core. The face sheet and foam core aremodeled using layered shell elements. The material, weight, stresses and deflections are taken into account duringoptimization procedure. The aim is to reduce the stresses and weight with adequate flexibility. The optimizationproblem is constructed by considering a sample prebuilt landing gear as an initial design and by taking the spanlength and weight of it at the beginning. The span length is taken as a geometrical constraint. The weight is chosenas the objective. The goal is twenty percent of weight reduction. The geometrical design parameters are radius ofcurvature, and the laminate parameters which are the stacking sequence, ply orientation angle, and number of plies.

In the experimental side of the study, carbon/epoxy, glass/epoxy, and Kevlar/epoxy type coupon test specimensare manufactured using the wet hand lay-up technique. The coupon tests are performed to determine the materialproperties. In these tests, the composite specimens are tested under static loads. The static tests include the bendingtests. The tests gave the necessary information about the materials.

The material selection is also important for the manufacturing process. This is because the resulting designshould be easily manufacturable. The composite landing gear is manufactured using the wet-layup technique. Thevacuum and heat are applied during the curing process of the composite landing gear on a heated vacuum table.

II. Materials CharacterizationThe mechanical properties of dry fibers and epoxy are taken from the manufacturer. The mechanical properties

of the laminates are calculated by using the mechanical properties of dry fibers and epoxy in Halpin Tsaiformulations. The calculated material properties are shown in columns named as “Original” in Table 1. The bendingtests are performed to validate the calculated material properties. Four sandwich beams are constructed using thefour different fiber types as face sheet material and foam as core material. A single layer is applied to both faces ofthe foam. The dimensions are 240x30xt mm. The thickness is given as “t” because it is different for different facesheet materials. The sandwich beams produced are shown in Figure 1.

In tests, the one end of the sandwich beam is fixed and a static load of 1.4 N is applied to the other free end. Thestrain in the axial direction at a point located at a distance of 80 mm from the fixed end is measured using a straingauge and a static strain meter. The measured strains in the bending tests are shown in Table 2. The sandwich beamis modeled discretizing the domainusing 240 elements (Shell 99) usingAnsys finite element software. Thecalculated strains using the finiteelement method are shown in Table2. There is a big difference betweenthe experimental and analysis results.Therefore, the original materialproperties are modified using theratio between the experimental andanalysis results. The analyses arerepeated using the modified materialproperties and the results are shownin the last column in Table 2. Theresults show the big differencebetween theoretically andexperimentally obtained materialproperties. These modified materialproperties are used in the followinganalyses of the landing gear. Figure 1. Sandwich beams manufactured using foam core and different

face sheet materials (CL 300-12K/Epoxy, CX 490-12K/Epoxy, AX340/Epoxy, LT 600/Epoxy from left to the right).

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III. Selection of an Optimum Landing GearThe landing gear considered in this study is made of a laminated sandwich structure. A suitable landing gear

geometry for the UAV considered is shown in Figure 2. The UAV considered in this study is an approximately 6 kgin weight. The span length, width and thickness of the landing gear stayed constant during the optimization andshown in Figure 2. The design variables are the radius of curvature, the face sheet material type, the number of facesheet layers. The last two variables also effect the laminate thickness. The optimization procedure includes bothstatic and buckling analyses. The state variables are stresses, strains, deflections and the critical buckling load. Theobjective is to minimize the mass of the landing gear while obtaining necessary strength and flexibility.

The landing event is modeled using two different ways. In the first model, named as Case 1, the points attachedto the fuselage are fixed and the landing load is applied to the lines touching the land during the landing (lines C andD). In the second model, the lines touching the land during the landing are simply supported (rotationally freearound the z axis and rotationally fixed around the x and y axes) and the landing load is applied to the points that areattached to the fuselage. The real landing is considered to be between these two conditions. The holes and wheelsare not included in the finite element model. This is because the holes cause the stress concentration and need to bemodeled in detail. This kind of detailed model increases the number of elements. After obtaining an optimumlanding gear configuration the holes should be strengthen so that the material can withstand the stresses concentratedon these portions.

The static and buckling analyses are performed to investigate the deflections, stresses and critical buckling loadunder the weight of UAV. A parametric finite element model of the landing gear is built to be able to repeat theanalysis with different shape and material configurations during optimization process. The span length, height andwidth are considered to be constant to make it consistent with the fuselage of the UAV considered in this study. Theradius of curvature and the laminate configurations are taken as the design variables. The Shell 99 laminated shellelements are used to model the landing gear. The element dimension is chosen as 5 mm and this selection results inthe number of elements between 768 and 648, depending on the radius of curvature.

Table 2. The measured and calculated strains during the bending of the laminated sandwichbeams.

Measured strain (µS) Calculated strain (µS)(Original)

Calculated strain (µS)(Modified)

CL 300-12K/Epoxy 50 13.88 49.98CX 490-12K/Epoxy 283 116.60 282.28AX 340/Epoxy 544 125.85 541.48LT 600/Epoxy 110 47.53 109.93

Table 1. Mechanical properties of the materials used in the production of the landing gear.

Material CL 300-12K/Epoxy CX 490-12K/Epoxy AX 340/Epoxy LT 600/EpoxyOriginal Modified Original Modified Original Modified Original Modified

E1 (GPa) 139.2 38.64 139.2 57.35 64.2 14.83 32.7 14.13E2 (GPa) 7.06 1.96 7.06 2.90 6 1.39 32.7 14.13E3 (GPa) 3 0.83 3 1.24 3 0.69 3 1.29ν12 0.26 0.26 0.26 0.26 0.35 0.35 0.25 0.25ν23 0.25 0.25 0.25 0.25 0.35 0.35 0.25 0.25ν13 0.25 0.25 0.25 0.25 0.35 0.35 0.25 0.25G12 (GPa) 4.08 1.13 4.08 1.68 3.7 0.85 13.08 5.65G23 (GPa) 1 0.28 1 0.41 1 0.23 1 0.43G13 (GPa) 1 0.28 1 0.41 1 0.23 1 0.43σ* (MPa) 2954 820 2954 1217 1845 426 620 267ε* (%) 2.1 2.1 2.7 2.5

In addition to Table 1, mechanical properties of the foam are given as E=28 MPa, G=13 MPa, σ*=0.7 MPa,ε*=8%.

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The finite element model of the landing gear is verified against the experimental result. For this purpose thestrain in region A is measured under a load of 6 N applied on the point D in y direction while the landing gear isfixed at midpoint between connection holes. This experiment is also analyzed using the finite element model of thelanding gear to validate the model. The measured strain is 20 µS and the calculated strain is 26 µS . This indicatesthe model can be used for the analyses.

The different landing gear models given in Table 3 are analyzed under a static load corresponding to the weightof the UAV. The maximum displacements in x and y directions, stresses and strains in the longitudinal direction ofthe landing gear at the regions A and B (interior portions) and the buckling load for each configuration are obtained.These results are given in Table 4 and Table 5. In general, Case 1 is found to be more critical compared to Case 2. InTable 4, it is shown that the increase in the radius of curvature increases the factor of safety against buckling alsodecreases the weight of the landing gear (see Table 3). The stresses and strains are found to be lower than the tensilestrength and fracture strain of the face sheet material, respectively. The stresses in foam material are found to muchlower than the stresses in face sheet material as expected. Therefore, they are not given here, but they are lower thanthe tensile strength of the foam material. Only the Case 1 is considered and analyzed for the selection of face sheetmaterial and laminate configuration. In Table 3, it is shown that the LG 4 is the lightest design. In Tables 4 and 5, itis shown that LG 6 is weak against the buckling. LG 7 is more resistant against the buckling. However, it is heaviercompared to LG 5 and 6. LG 6 is also found to be more flexible and this can be too much for the landing gear. LG 8,9 and 10 have two layers on each face. Considering the load during landing will be more than the weight of theUAV, the landing gear is designed using two layers on each face. Between these design, LG 9 is found to be heaviercompared to LG 8 and 10. Finally LG8 is selected as an optimum design.

Figure 2. The geometry of the landing gear (dimensions in milimeters).

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IV. Numerical and Experimental ResultsLG 8 is selected as an optimum design. This landing gear is analyzed during landing. The landing gear is

modeled using the eight nodded layered shell elements. The impact loads during the landing are assumed three timesof the mini-UAV weight.9 The ground reaction forces acting on the landing gear during landing are assumed to be180 N in vertical direction and 60 N in horizontal direction. The vertical force is determined considering theacceleration of the UAV will be 3g in vertical direction during landing and the force in horizontal direction will beobtained taking the 1/3 of the vertical load as a commonly used value for landing. These loads are applied at a timeduration of 0.1 s. and transient analysis is performed to predict the deflections and stresses.

The stresses in the longitudinal direction of the landing gear and total displacements at 0.04 s, when the stressesand displacements reach their maximum value, are shown in Figures 3 and 4, respectively. The stresses are found tobe lower than the tensile strength of the face sheet material (CL 300-12K/Epoxy). The maximum displacement isapproximately 16 mm which gives enough flexibility.

Table 5. The results of materials optimization.

LG Case Uymax (mm) Uxmax (mm) σA (MPa) σB (MPa) εA (µS) εB (µS) Pcrt / F5 1 8.47 11.12 6.99 22.43 1215 1967 6.5146 1 23.57 30.65 8.39 32.07 3075 7822 2.4087 1 5.19 6.58 8.40 34.79 594 2368 11.4838 1 1.10 1.30 4.94 20.76 128 535 11.4159 1 1.21 1.48 5.97 24.99 154 645 23.98010 1 1.48 1.78 7.23 29.67 188 767 17.414

Table 4. The results of the shape optimization.

LG Case Uymax (mm) Uxmax (mm) σA (MPa) σB (MPa) εA (µS) εB (µS) Pcrt / F1 2.68 3.16 0.59 43.10 15 1113 1.82912 2.66 0.21 22.13 18.23 572 472 21.8521 2.65 3.23 4.63 43.09 119 1112 2.37

22 2.11 0.28 17.32 15.42 447 400 25.5341 2.68 3.30 9.74 43.41 252 1121 3.894

32 1.28 0.29 12.52 10.78 324 280 30.4981 2.72 3.29 10.37 43.64 268 1127 5.113

42 0.98 0.27 10.91 8.80 282 228 32.132

Table 3. The landing gear configurations.

LG R (mm) Layer Configuration Face sheet material Length (mm) Weight (gm)1 10 CE/F/CE CL 300-12K/Epoxy 613.42 26.922 50 CE/F/CE CL 300-12K/Epoxy 579.08 25.413 100 CE/F/CE CL 300-12K/Epoxy 536.20 23.534 115 CE/F/CE CL 300-12K/Epoxy 520.80 22.855 115 CE/F/CE CX 490-12K/Epoxy 520.80 25.936 115 AE/F/AE AX 340/Epoxy 520.80 25.917 115 GE/F/GE LT 600/Epoxy 520.80 35.698 115 CE/CE/F/CE/CE CL 300-12K/Epoxy 520.80 44.379 115 CE/GE/F/GE/CE CL 300-12K/Epoxy

LT 600/Epoxy520.80 56.41

10 115 CE/AE/F/AE/CE CL 300-12K/EpoxyAX 340/Epoxy

520.80 46.63

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The landing gear is manufactured using the wet hand layup technique. A wooden mold is designed andmanufactured. This mold is used for the manufacturing of the landing gear. A vacuum and a moderate heat (50 °C)are applied for 24 hours during the manufacturing process. The landing gear is shown in Figure 5. The landing gearis tested under a static load which is equivalent of the weight of the UAV.

Figure 4. The total displacements on the landing gear during landing.

Figure 3. The stresses on the landing gear during landing.

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V. ConclusionThe experimentally obtained modulus of elasticity and shear modulus of the test specimens are lower than their

theoretical values obtained using the data given by manufacturer. The difference between experimental andtheoretical values differs depending on the laminate material type. Therefore, it is found to be important to validatethe material properties against test before performing an optimization. The buckling of the landing gear is found tobe an important problem and it should be considered in design optimization. The increase of the radius of curvatureprovides smoother stress distribution. So, the different portions of the material will be subjected to the stress close tothe each other. This is one of the key results particularly for the optimization of the structures made of the laminatedcomposites.

AcknowledgmentsSupport for this work has been provided by the Scientific and Technological Research Council of Turkey under

Project Number 106M194 and Istanbul Technical University research fund.

References1Ossa, E.A., “Failure Analysis of a Civil Aircraft Landing Gear,” Engineering Failure Analysis, Vol. 13, No. 7,

2006, pp. 1177-1183.2 Lee, Hong-Chul, Hwang, Young-Ha and Kim, Tae-Gu., “Failure Analysis of Nose Landing Gear Assembly,”

Engineering Failure Analysis, Vol. 10, No. 1,2003, pp. 77-84.3 de Farias Azevedo, C. R. and Hippert Jr., E., “Fracture of an Aircraft's Landing Gear,” Engineering Failure

Analysis, Vol. 9, No. 3,2002, pp. 265-275.4 Azevedo, C. R. F., et al., “Aircraft Landing Gear Failure: Fracture of the Outer Cylinder Lug,” Engineering

Failure Analysis, Vol. 9, No. 1,2002, pp. 1-15.

Figure 5. The manufactured landing gear.

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5 Franco, L.A.L., et al., “Fatigue Fracture of a Nose Landing Gear in a Military Transport Aircraft,” EngineeringFailure Analysis, Vol. 13, No. 3,2006, pp. 474-479.

6Nguyen, Phu, Mak, Stanley and Panza, Jose., “Simulation of Landing Events for an Unconventional UAV,”AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 1762,AIAA, Newport,Rhode Island, 2006.

7Chan, Brendan J., et al., “Modeling and Simulation of a VTOL UAV for Landing Gear PerformanceEvaluation,” SPIE Modeling and Simulation for Military Operations II Conference, Vol. 6564, Proceedings of SPIEVA, United States, 2007, pp. 65640T.

8Reinforced Plastics, “Composite Landing Gear for F-16,” Reinforced Plastics, Vol. 47, No. 4, 2003, p. 4.9Currey, Norman S., Aircraft Landing Gear Design: Principles and Practice, American Institute of Aeronautics

and Astronautics, Washington,D.C., 1988, pp. 34-35.