Raghav_optimal Design of Aircraft Wing Structures

8/2/2019 Raghav_optimal Design of Aircraft Wing Structures

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OPTIMAL DESIGN OF AIRCRAFT WING STRUCTURES:A COMPUTER AIDED DESIGN METHOD

J os hua A mpofo & Dr. Frederick FergusonCenter for Aerospace Research, Mechanical Engineering DepartmentN or th Caro l ina A&T State Univers i ty, G reensb oro, NC 27411, USA

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ABSTRACTAircraft weight plays a significant role in its design because of its dominating effects on thevehicle overall performance. Statistical results suggested that the amplification impact factor ofany weight-carrying component is about 4.525. That is, a 1. 0 Ih reduction in the structural weigh ttranslates to 4.525 lb reduction in gross aircraft takeoff weight. This paper focuses on thepreliminary design of aircraft with optimized structural weight. The design concept is based onthe optimal arrangement o f the major force-carrying compo nents within the aircraft. Further, it isshown that the optimum locations of the longitudinal wing spars results in, not only, minimumshear flows in s p a r webs and w i n g skins, bu t a l s o , minimum a x i a l stresses in the stringers of thewing spars. The net effect is an aircraft with minimum weight. The weight reduction isdemonstrated by comparing the structural weight corresponding to the optimal arrangement withthat corresponding to a randomly chosen arrangement. The computer aided design programdeveloped in this research effort found the optimal locations of the two wing spars to be at 25%an d 60%of the local chord length, respectively, after 136 iterations. Results indicate a 3.0%structural weight reduction (ie., 13% akeoff) when only two spars are considered.KEYWORDS: Optimization, gross takeoff weight, wing spars, wing ribs

INTRODUCTIONThe National Aeronautics and Space Administration (NASA), in partnership with the Department ofTransportatiodFederal Aviation Administration (FAA), state & local aviation and airport authorities, is currentlyfostering a new program focused on the development of technologies needed for a Small Aircraft TransportationSystem (SATS). The project's initial focus is to prove that four new operating capabilities will enable safe andaffordable access to virtually any runway in the nation in most weather conditions. These new operating capabilitiesrely on on-hoard computing systems, advanced flight controls systems, highway in the sky displays, and automaledair traffic separation and sequenc ing technologies. However, light weight. structurally sound and highlymaneuverable aircraft configurations must be build prior to the design o f these flight controls systems. Theobjective of this research is the optimized design of a small lightweight aircraft, similar to the configurationillustrated in Figure 1.

Fig 1 A SATS Aircraft Candidate, Heaist Cop Fig 2 A New Civil Aviation Industly, ''NASA

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SATS is a multidisciplinary technology development program that consists ofth ree key components, namely,the development o f a new civil aviation and aircraft technology transportation system, refer t o Figure I ,the design of ground facilities (landing and takeoff) and airspace infrastructure to support the new civilaviation system, refer to Figure 2, andthe development of auxiliary facilities and the provision of the required motivation to passengers and userfor their utilization of the new transportation system.The motivation for SATS includ es recognition of increasing transportation de mands (business and pleasure) withtime and speed as valuable c ommodities, the alleviation ofhighw ay gridlock and pending hub-spoke saturation, andthe creation o fjob s and enhanced quality of life.One o f the primary objectives of the SA TS program is to enable portal-to-portal air travel at four times the speedof highways to 25% of the nation's suburban, rural and remote comm unities in IO years. Other SATS goals include:increased mobility, accessibility, sa fety, airspace capacity and efficie ncy, reduce d cost and noise for generalaviation, and provide commercial airline dependability with near all-weather capability at lower passenger costs perseat mile. Research Triangle Institute in Raleigh, North Carolina has been involved since the inception of SATS,providing systems engineering support in areas of program planning, pre-program studies and analysis, systemengineering management plans and market analyses L identi@ corporate, private, and civil users. Planners envisionthat SATS airports would be linked with highways and rail lines, enabling travelers to transfer easily to and fromautomobiles, buses, taxis, trains, and hclicopters.The SATS vision had its origins in 1994 with the Advanced General Aviation Transport Experiment (AGATE)program, a collaborative effort by N ASA , corporations , agencie s, and universities to revitalize the then-depressedgeneral aviation industry. The plan called for the development of simplified, less expensive light airplanes that areeasier to operate and leam to fly. AGATE established the technological basis for this new aircraft concept, aswell asthe framework for developing shorter, less costly pilot training programs. The planes recommended by AGATE areexpected to he comfortable, quiet, and safe, and moreover, they must he equipped with all-glass cockpits featuringgraphical digital displays. The operation of these vehicles must be as intuitive and simple as a Nintendo game, andas responsive as the Global Positioning System is to the Internet. The new aircraft must be equipped withappropriate links and displays that ensure accurate information on location, weather, air traffic and ground servicesare constantly updated.Alrea dy, the Eclipse A viation Corp. announced that in 2003 it expect s to begin delivering a twin-eng ine jetseating six people, including the pilot. The Eclipse 500 will cruise at 42 3 mph at altitudes of up to 41,000 feet andwill fly 2,070 miles on one tank of titel. The company estimates it will cost $775,000 in current dollars, withoperating costs comparable to smaller general aviation aircraft. Science fiction, right? Not according to BruceHolmes, NASA's manager of general aviation. He is the agency's point man in an ambitious plan, worthapproximately $70 million over the next five years. The plan call for the creation of a small aircraft transportationsystem (SATS), modeled on the U S. interstate highway system that would make planes as serious an alternative tocars, as cars became to horse-drawn carriages. He predicts SA TS will make "doorstep-to-destination travel at fourtimes the speed ofhighways" readily available in the nation's suburban and rural communities by 2 0 2 2 .A WlNG BOX CONFIGURAI'ION DESIGN

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Consider the typical wing box configuration illustcited in Figure 3. The aircrafl mission requirement is chosen foran appropriate flight Mach number and an appropriate cruising altitude. Using these free stream parameters, thecorresponding air speed, v, and the dynamic pressure, y, are calculated. Also at this stage the geometry of anappropriate airfoil is chosen. The data set required for this analysis is illustrated in Table 1 , [1-3].

I 1 a s ~ 7 ~Fig. 3: Force-Camying Components within the Wing

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T ab le I: Wing Design RequirementsDesign Parameter SymbolTake-off gross weight WOWing area S.Leading-edge sweep angle A LERear-edge sweep angle ARE

Wing loading ( w / s T & e- o l l

Half span h/2Tip-chord length ' CT,pRoot-chord length CRudTape ratio AAspect ratio A

Wing Bo x Force-Carrying ComponentsAs in the case of a ypical F-16 aircraft 161, it is assumed that the force-carrying components of the wing box arecompo sed of two longitudinal wing spars. Further, it is assumed that the spars are running from the wing root to thewing tip, with five ribs in the transversal direction, running from the front edge to the rear edge of the wing box.The wing box is assumed covered, and the thin wing skin covering the wing box provides favorable aerodynamicfeatures, [2-31, sce Figure 3 . In addition, the wing spars are considered to behave as wide-flange beams that aretapered linearly from the wing root to the wing tip. Their locations are described by the parameters, /, and 12,respectively, relative to the front-edge of the wing, [4-51. Also, it is assumed that the width of the liont-sparstringers varies from 8 o 4 ins, from the wing root to wing tip. Where as, he rear-spar stringers varies from 7 to 3ins in the same manner. U sing these assumptions, the equations describing the sha pes of the tiont and rear-sparstringers, in the direction of the x-axis. are as follows:

wh ere WfiO,,,,,, and W,,,,,,,, are the wid th of the front and rear spars. respectively, and the coefficients, A, E. C andDare chosen such that they describe the shape ofthe stringers. In this analysis, A = -0.02156,B =,'?.U,C = -0.02156 and D = 7.0.In order to maintain wing-skin stability, the following constraints were introduced: the m aximum separation a llowedamong ribs, between ribs and wing-root, and between ribs and wing tip is approximately 50 ins. Also, the allowableinterval for span-wise searching for optimal location of each of the four ribs was 5 ins.Wing Box Aerodynamic Local Loads

A detailed integration of the structural and aerodynamic optimization is computationally intensive. due to theneed for repeated calculations of the aerodynamic loads and their derivatives with respects to the flow field variableswithin each iteration ste p during the search process. Since the focus of this paper is on the structural components ofthe wing box, and a preliminary design approximation is used for the evaluation of the pressure distribution, p , onthe wing box, as follows. [6-71:( 3 )

where, vis the free stream velocity, w, nd w, re the wing panel slopes with respects to space and time. q thedynamic pressure, M the Mach number and the symbol, defined as

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p = d h f - l (4 )For the purposes of this paper, only the static loading is considered, thus the air load becomes a function of thewing slope, w,n the forni,

The pressure distrihution,p, describes by the use of equation (5) s illustrated in Figure 4.depicted in Figure 5In addition, the span-wise pressure distributions, [2 , 81, on the wingspan is assumed to be o f the elliptical form

Fig. 4: Wing cross section pressure distribution Fig. 5 : Wing span pressure distributionWing Bo x Concen t ra ted Aerodynamic Loads

The equivalent concentrated load due to the aerodynamic pressure distribution includes the resultant shear force,V, and bending moment, M,.,at the designated cross sections. The wing model illustrated in Figure 6 is used in thisanalysis. Since, in general, the rcsultant shear force Y niust not pass the center of twist of the cross sections, therewill be a torque about the center of twist. Using the illustration of the wing platform, illustrated in Figure 6, theresultant shear force. V, and bending moment, M p, t a designated CI-ossection, x = xt can be obtained through theintegration ofthe pressure distribution, in the forms:

l L ,.

Figure 6: Computation of th e Concentrated Loads Figure 7: Illustration of Concentrated Areas on Flanges

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where p is obtained from the empirical calculations described earlier. Similarly, the chord-wise location, d of theresultant shear force, V, from the front edge, can be found by the moment equilibrium equation, such that,

STRUCTURAL ANALYSISThe mechanical analysis of the wing box structure is based on the theory of thin-walled structures, [4].Since the wing spars consist of thick spar caps separated by a thin shear web, the cross sectional arew ofshear websand wing skin become insignificant compa red to the areas of the spar caps. As such, the caps absorb virtually all o fthe bending moments.The contribution o fthin sheets (webs and wing skin) to bending is assumed to he negligible. Thus, only theareas of the wing-spar string ers are considered in the bending analysis. In addition, an approximate model for awide-flange beam (wing spar) is obtained by lumping the total area of the stringer into a concentrated area, and theweb does not contribute to resisting be nding, a s shown in Figure 7. Since wing spars are tapered from wipg-root towing tip, and the height of the wing spar is also decreased in the same direction, the concentrated areas of thestringers depend on the locations of the ribs. Using equations ( I ) and ( 2 ) , the corresponding width at specifiedlocations can be calculated.Th e axial bending stress, or,or a beam under bi-directional bending due to the M, and &ft bending moments canhe evaluated using the expression, [IO],

where the symbols; lp , : and It,: are the moments of inertia of the specified cross-section. It is of interest to note thatin the case ofM, = 0, the expression for the evaluation of the axial bending stress is simplified as follows

And, in the symmetncal case when M,= 0 and 1,;=0 then a, s evaluated as,M

0. =Yz 1 1)I ,Flexural ShearFlow

Consider the shear flow evaluation illustrated in-Figure S. In general, the flexural shear flow in a thin-walledsingle-cell closed section can be broken in two parts and be calculated as follows:q=q ,+q : (12)

where the quantities. qo and q., are described below.This model allows for the use of a fictitious cut on the wing cross section. Moreover, it allows the openedsection to he treated as having an unknown but existing constant shear flow, 40 . On the other hand, the shear flow,4'. for the open section that is subjected to the applied shear force, V, can be evaluated as follows:

where the symbol, Q, is defined as he first moment of inertia and evaluated by the expression.

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Q = [ l z d A (14)4For the concentrated-area model ofthe wide-tlange beam as shown in Figure 7, the expression, Q = A ,C , , remains thesame for each location. As the result, q'$, s constant along the web. The total shear flow is the superposition of th etwo components, q = qo+ q',, w here the unknown shear flow qa is obtained from the equilibrium equation. Namely,the moment produced by the total shear flow must be equal to the moment produced by the applied shear force V .Even though finding the flexural shear flow in a thin-walled multi-cell closed section is a statically indeterminateproblem. The aforementioned procedure can still be used. However, in this case in addition to the equilibriumequation, i i - I compatibility equations must be used to provide closure, where n represents the number of cells. Inthis analysis the compatibility equations are defined by, 0, = .. = &, for an n-cell section, where 0,is the twistangle of the i'h cell, which can be calculated by the equation,

where A, and t, are the cross-sectional area and wall thickness of the th ell, and the shear modulus, G, isdefined as,

with E an d iU being the Young's modulus and Poisson's ratio, respectively, and the integral with respects to s inequation ( I 5) results in the circumference of the iihell.

+Figure 8: Superposition of Shear Flows

OPTIMAL ARRANGEMENT FORCE-CARRYING COMPONENTSThe objective of the optimization problem is. the optimal arrangement of the transversal force-carryingcomponcnts within wing-box under specified aircraft flight conditions. The optimization problem described herein isthe definition of the 'he.~t'span -wise ocations of four transversal wing ribs. In this paper, the teim 'best'mea ns thatthe shear flows in spar webs and wing skins, and the axial stresses in the stringers of the wing spars will be thesmallest under the prescribed tlight conditions.In general, the mathematical statement for an optimization problem is defined asMinimize: F(x) (1 7)Subject to : C,(x)=O, i = 1, 2 ..., m'

C,(x)rO, i = m'+ l , ..., mwhere, J is the design parameter vector, F is the cost function, and C,s are the constraint functions. Theoptimization problem of interest to this study is an unconstrained optimization problem, with a number ofcomplexities.First, the problem discussed in this paper is actually a multi-objective optimization problem, since the costknct ion , F, is not a single objective function, but instead, a vector of objective functions, such that, F(x)={F,(x),F2(x), . ., F,,(x) /.The components o f the vector include the maximum shear flow in spar webs of the two wing spars,the maximum she ar flow in wing skins, and the maximum axial stress in the stnng ers of the two wing spars. In this

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analysis, the design criterion is set to consider the maximum stress component in the overall wing structure. And assuch, the objective hnction is chosen as the maximum stress among all o f the stress components resulting in anoptimization problem with a single-valued cost hnction.Second, there are four independent variables that define the computational search space, each of which representsthe span-wise location of the four ribs. In an effort to reduce the computational domain, the searching process isconducted in two stages. The optimizer begins the search for an optimal location of one rib by fixing the other threeribs in all possible locations; then, choosing the best from he optimunis corresponding to each individual riblocation. As a result. the objective function, F(x), becomes a uni-variable function with respects to an independentvariable, x, that represents the distance between ribs, rihs and the wing root, and ribs and the wing tip. Further, toreduce the computational cost, the objective function, F(x), is discretized such that the interval for span-wisesearch ing for optimal location of ach of the four ribs is 5.0 111s.n addition, the maximum separations among ribs,between rib and wing-root, and between rib and wing tip mnst be less than 50.0 ns , to keep wing-skin stability.Third, the cost function described herein cannot be represented by an explicit mathematical function with well-understood properties. Rather, the cost function is implicitly the result of a complex sequence of calculations formthe aero-structural analysis. As a result, computation of the gradient vector of ost function becomes a challenge.Thus, the algorithm used to find the minimum is the cost function is based on the Comparison Method, [I ]. heComparison Method does not depend on the derivatives of the cost function, but systematically shrinks an interval inwhich the minimum is known to lie. However, this simplicity requires that the objective function, F(x). satisfy theunimodality condition. In other words, it is assumed that there exists a unique minimum point x* , such that,X E [a,b] or the objective function F(x). so that, given any x, , x2 E [a,h] or which xI x * then F(xl)


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Weight ReductionThe weight reduction is demonstrated by comparing the structural weight corresponding to the optimalarrangcment with that of a corresponding arrangement chosen at random. For comparative purposes, two identicalwings are compared, with the only difference being the location of the front and rear spars. In the optimal design,the locations of the front and rear spars were computed and found to lie at 25 % and 60% of the local chord. In therandom case, the two spars are placed at the 30% an d 50% locations of the local chord.Adding the weights of its three components, namely, the weight of the skin, the weight of the two spars and theweight of the five ribs results in the total wing weight. The weight of each component is calculated by firstevaluating its volume, and later multiplying it to the density of the material. In this case, the assumed material is7075-aluminum, and its density is given in Table 2.The computer aided design analysis allows for the evaluation of the maximum normal stresses in the front andrear spars, and the maximum shear flows in the aircraft skin and webs. In the procedure outlined in sections 1-4, thisinformation is used to evaluate the wing w eight. Both arrange ments must satisfy the failure criterion, IS < oaallowable,.However, the strength margins and therefore the potential for sustainin g heavier external loads are differe nt. Sincethe non-optimal configuration has a smaller safety margin, it value can be used for the critical case. In order to keepthe safety margins for both design the same, the structural dimensions in the optimal design can be further reduced,resulting in greater weight r eduction . The results for the two cases outlined in this study are illustrated in Table 6.

Table 3: Wing-Box Configuration Design Requirements, [5]Design Param eter Inputs SymbolTake-off gross weight I6480 wu

'bfWing loading 56 (w/s)T&e.Wing areaLeading-edge sweep angleRear-edge sweep angleHalfspanTip-chord lengthRoot-chord lengthTape ratioAspect ratio

294f?40'15"I86 in44 in176 in0.253.5

Material propertiesDensity (7075-Alum inum) . 0 101 P

Table 4: Optimum Weight-bearing Component LocationsSpars Front Spar 987.79 in 941.96 in

Rear Spar 942.71 in 792.09 inRibs Rib 1 134.82 inRi b 2 117.21 inRi b 3 99.68 inRi b 4 82.15 inRib 5 64 61 in

Baseline Optimum

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Table 6: Calculated Shear Forces and Bending MomentsRibs Resultant Shear Force Torque About Bending MomentI 9721.21 53.09 5 16069.7 686559.22 6009.98 46. I5 277378.5 328584.53 3167.19 39.23 12430.5.9 126521 I4 1274 56 32.34 41220.4 33255.55 278. 71 25.43 7087.6 3558.1

# Magnitude (IbA Distance to LE (in) LE ( lhf-in) ( lbf-in)

__I_able 7: Structural Weight of Wing, Optimum vs. BaselineComponents Baselin e Configuration Optimal ConfigurationSkin 381.73 359.62Front Spar Stringer 25.19 29.33

We b 21 . 31 34 . 98Rear Spar Stringer 20.99 21.533 We b 17.92 lR.89Ribs # I IO 80 10.14

#2 8.16 7 . 66#3 5.83 5.47#4 4 . 01 3 . 76#5 2 48 2 33

Total 498 . 42 483 . 71% Reduction 3.0%

CONCLUSIONAircraft weight plays a significant role in its design because o fit s dominating effects on the vehicle overallperformance. In general, more weight leads to more drag, which requires larger engines, which in tum leads to evenmore weight. Statistical results suggested that the amplification impact factor of any weight-carrying component isabout 4 5 2 5 . That is, a 1. 0 Ih reduction in the structural weight translates to 4.525 Ih reduction in gross aircrafttakeoff weight. As such, preliminary design concepts leading towards the development of aircraft with optimizedgross takeoff weight hold significant promise.This paper focuses on the preliminary design of aircraft with optimized structural weight. The designconcept is based on the optimal arrangement of the major force-carrying components within an aircraft wing. In thispaper, the optimum locations of the longitudinal wing spars and ribs under specified air-loading conditions becomethe design parameter that leads to weight reduction. Further, it is shown that the optimum locations of thelongitudinal wing spars results in, not only, minimum shear flows in spar webs and wing skins, but also, minimumaxial stresses in the stringers of the wing spars. The net effect is an aircraft wing structure with minimum weight.The weight reduction is demonstrated by comparing the structural weight corresponding to the optimal arrangementwith that corresponding to a randomly chosen arrangement. The computer aided design program developed in thisresearch effort found the optimal locations of the two wing spars to be at 25 % and 60% of the local chord length,respectively, after 136 iterations. Results indicate a 3.0% weight reduction when only two spars are considered. Thismethod is very promising since the inclusion of all force-carrying components can potentially lead to greaterefficiency.

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REFERENCESI . Reitinger, R. and Kainm, E. , "Maximizing Structural Efficiency Including Baciding and Imperfection

Sensitivity", MAA-94-4390, 1994.2. Sean Wakayama and llan Kroo, "Subsonic Wing Design Using Multi-Disciplinary Optimization", MAA-94-4409, July 1994.3. Grossman, B., Hafika, R., et al., "Integrated Aerodynainic-Struclural Design of a Transport Wing", Journal ofAircraH, Vo1.27,No.12, lYYO,P.1050-lO56.4. Sohieszczanski-Sohieski,. and Haftka, R.T., "Multidisciplinary Aero space Design 0ptimiz ation:Su rvey ofRecent Developments", A lAA 96-071 1, Sept.1998.5. O.R. Kimura, T.Z., Guo, and Iwamiya, T., "Coupled Aero-Structural Model: Approach and Application to HighAspect-Ratio Wing-Box Structures", MAA 98-4837, Sept. 1998.6 . Raymer, D P., "Aircraft Design: A Conceptual Approach", MAA Education Series, 1992.7. Xue, D.Y., et al. "Finite Element Nonlinear Flutter and Fatigue Life of Two-Dimensional Panels withTemperature Effects", Proceedings of the 3'd AIAAIASMEIASCEIASC Structures, Structural Dynamics, andMaterials C onference, Baltimore, MD., April 1991, pp.1981-1991.8. Mei, C., "A Finite Element Approach tor Nonlinear Panel Flutter", AlA A Journal, Vo1.15, 1977, pp.1107-1 I IO .9. Anderson, J.D., "Introduction to Flight", McGraw-H ill, 1989, pp.2 19.IO . Sun, C.T., "Mechanics of Aircraft Structures", JohnWiley & Sons, 1998.I I . Gill. Philip E., Murray. W., and Wright, M.H., "Practical Optimization", Academic Press, 1981.

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Raghav_optimal Design of Aircraft Wing Structures