Anisogrid Composite Lattice Structures - 2006

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Composite Structures 76 (2006) 182–189

Anisogrid composite lattice structures for spacecraftand aircraft applications

V.V. Vasiliev *, A.F. Razin

Central Research Institute for Special Machinery, Khotkovo, Moscow Region 141371, Russia

Available online 28 July 2006

Abstract

The paper is concerned with Anisogrid (Anisotropic Grid) composite lattice structures whose load-bearing shell is formed by systemsof geodesic unidirectional composite ribs made by automatic wet winding process. Developed about 25 years ago for spacecraft appli-cation, Anisogrid structures are now under serial production in the Russian Central Research Institute for Special Machinery and dem-onstrate high weight and cost efficiency in comparison with rib-stringer stiffened traditional aluminum prototypes and their compositeanalogues. Existing methods of design, analysis and manufacturing of Anisogrid structures are summarized and discussed in applicationto aerospace structures.

Particular emphasis is placed on the correspondence between the Geodesic structural concept developed for wooden and metal air-planes more than 60 years ago and modern Anisogrid composite structures. It is advocated that the combination of the geodesic airframestructures whose load-bearing capacity is provided by the system of properly directed ribs and the Anisogrid technology which allows usto make unidirectional composite ribs with extremely high specific strength and stiffness by continuous winding can result in the struc-tures whose weight and cost efficiency is considerably higher than is demonstrated by traditional stiffened structures (made of metals orcomposites).� 2006 Elsevier Ltd. All rights reserved.

Keywords: Aerospace structures; Commercial airplanes; Lattice structures; Composite materials; Filament winding

1. Introduction

Modern composite materials whose high specificstrength and stiffness are utilized in spacecraft and rocketstructures to a sufficiently high extent are now on theway to be widely used in primary airframe structures ofcommercial airplanes. Existing experience shows that directsubstitution of carbon–epoxy composites for traditionalring-stringer stiffened aluminum airframe structures resultsusually in 10–20% weight reduction accompanied by con-siderable cost increase. Taking into account that modernunidirectional carbon composites, being loaded along thefibers, are characterized with specific strength and stiffnesswhich are at least by the factor of 3 higher than the corre-

0263-8223/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compstruct.2006.06.025

* Corresponding author. Fax: +7 9654 3 18 80.E-mail address: [email protected] (V.V. Vasiliev).

sponding characteristics of aluminum alloys, one can con-clude that the available weight saving is much lower thancan be expected. The reason for this situation is associatedwith specific structural and manufacturing features of tra-ditional airframe rib-stringer stiffened structures which,being made of carbon composites, are sometimes referredto as black aluminum (BA) structures. First, the structureof the skin and the stiffeners of BA structures is not unidi-rectional – the skin and the ribs usually consist of unidirec-tional or sometimes fabric layers with different orientationangles and have efficient mechanical characteristics whichare close to those of aluminum alloys. Second, the weightsaving that can be expected for such structures due to lowerdensity of composite material in comparison with alumi-num is usually not reached because of relatively lowlevel of allowable strain which is reduced in design of com-posite structures because of low deformability of unidirec-tional composites experiencing tension across the fibers [1].

mailto:[email protected]

Fig. 1. Lattice structure.

V.V. Vasiliev, A.F. Razin / Composite Structures 76 (2006) 182–189 183

And third, even though BA structures require usually muchless assembling operations than aluminum prototypes, theycannot be made as completely integral structures, and costsavings gained in assembling do not compensate high costof carbon-epoxy prepregs which are about 25 times moreexpensive than aluminum alloys. Thus, it can be concludedthat BA airframe structures of commercial airplanes pro-vide rather limited possibility for weight saving, whereastheir cost efficiency has yet to be demonstrated. The onlyreal advantage of BA structures is associated with their fea-sibility – they can be designed and built by methods close tothose developed for aluminum airplanes. But it can hardlyjustify low weight savings and high costs. Further reduc-tion of weight accompanied by cost saving can be reachedin composite structures satisfying the following conditions:

• principal load-bearing structural elements shouldhave the unidirectional microstructure of compositematerials,

• fabrication procedure should involve completelyautomated processes and provide completely integralstructures.

Because the unidirectional composite can work onlyunder uniaxial loading, the corresponding structural ele-ment must be a rib. Aircraft structures whose load-bearingcapacity is controlled mainly by the ribs are known formore than 60 years [2,3] and are referred to as Geodesicstructures. In these structures, bending moments, as wellas torques and transverse forces, are taken by a system ofhelical ribs, whereas the skin transfers the aerodynamicand internal pressure to the ribs and provides the properexternal surface of the structure. In application to compos-ite structures, Geodesic lattice structures (Anisogrid struc-tures) developed about 25 years ago [4] and consisting of asystem of unidirectional carbon-epoxy ribs demonstratehigh weight efficiency and are widely used as spacecraftand rocket structures. In conjunction with continuous fila-ment winding, which is the less expensive of the existingprocesses used to fabricate thin-walled composite struc-tures, Anisogrid lattice structures discussed below satisfyboth foregoing requirements.

2. Design

Cylindrical Anisogrid lattice structures with given diam-eter D and length L are characterized with six design vari-ables, i.e. (Fig. 1)

• the shell thickness (the height of the rib cross-section), h,• the angle of helical ribs with respect to the shell merid-

ian, u,• the widths of the helical and the circumferential (hoop)

ribs cross-sections, dh and dc (for the structure in Fig. 1,dc is the total width of the adjacent hoop ribs),

• the spacings of the helical and the hoop ribs, ah and ac,counted along the normals to the axes.

The ribs are the principal load-bearing elements of thestructure, whereas the skin the necessity of which can becaused by design requirements, is not considered as aload-bearing element in design of lattice structures. More-over, the skin thickness, being treated as a design variable,degenerates in the process of optimization because the skincontribution to the structure mass is higher than that tostrength and stiffness of the structure. Thus, the optimallattice structure has no skin, and if the actual structureneeds a skin, its thickness and structure are preassignedto meet the structural and manufacturing requirements.

Because the most critical type of loading for carbon-epoxy lattice structure is axial compression, the design isperformed for the reduced axial force

P ¼ T þ 4MD

in which T is the acting axial compressive force and M isthe bending moment.

Three basic methods have been developed to designcylindrical lattice structures for axial compression, i.e.,

• geometric programming [5],• minimization of safety factors [6],• numerical optimization [7].

According to the second of these methods, the structureis designed for minimum mass under three constraints pro-viding strength of helical ribs under compression (with thesafety factor ns), global stability of the shell (ng) and localstability of helical ribs (nl). Analytically formulated con-straints allow us to express the design variables in termsof the safety factors, n, and minimize the structure massunder conditions n P 1. Optimal parameters

�h ¼ hD; u; �dh ¼

dh

ah

; �dc ¼dc

ac

are presented in Table 1.Three possible cases exist depending on the normalized

loading parameter

Table 1Optimal structural parameters

Case 1 Case 2 Case 3

p 6 ps ps 6 p 6 po po 6 p

�h ¼ 1

4

48p4k2�q3

EhE3c

p4

!1=10

�h ¼ 1

4

p2k�qEc�r

p2

� �1=4

�h ¼ pp16�r

ffiffiffiffiffiffiffiffiffiffiffiffikEhps

3�rpo

s

tgu ¼ 1

2tg2 u ¼ ps

4ptg2 u ¼ ps

4po

�dh ¼5

4p108p2Ecp2

E3hk4�q

!1=10

�dh ¼2

p sin 2u

ffiffiffiffiffiffiffiffi3�rkEh

s�dh ¼

2

p sin 2u

ffiffiffiffiffiffiffiffi3�rkEh

s

�dc ¼�dh

2�q�dc ¼

ps�dh

2�qp�dc ¼

pspo�dh

�qp2

p2o

p2� 1

2

� �

Fig. 2. Finite-element model of a lattice structure (simulation of globalbuckling).

184 V.V. Vasiliev, A.F. Razin / Composite Structures 76 (2006) 182–189

p ¼ 4P

pD2; ps ¼

48�r2

pEh

ffiffiffiffiffiffiffi�r�qkEc

r;

po ¼ ps

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Eh�q

Ec

þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Eh�q

Ec

� 1

svuut0B@

1CA

vuuuutin which �r is the ultimate stress of helical ribs under com-pression, k is the local buckling coefficient depending onthe boundary conditions at the ends of the helical rib seg-ment lh in Fig. 1 (for a hinged segment, k = 1 and for aclamped segment, k = 4), E is the modulus, q is the density,�q ¼ qc=qh, subscripts h and c correspond to helical and cir-cumferential ribs, respectively. Cases 1 and 2 correspond toaxisymmetric and case 3 – to nonaxisymmetric globalbuckling. In all three cases, ng = nl = 1, i.e., both bucklingconstraints are active. For case 1,

ns ¼ 4�r9�q

4p2p2kE2hEc

!1=5

P 1

i.e., the strength constraint is satisfied with some margin.For cases 2 and 3, ng = nl = ns = 1, i.e., the designed struc-ture is the structure of uniform strength. The structuremass can be found as

M ¼ pDLhqhð2�dh þ �q�dcÞ

Fig. 3. Winding of the ribs into the grooves in the elast

3. Analysis

Designed lattice structures are analyzed with allowancefor the skin, doors, joints etc. by finite-element methodbased on discrete or continuum models of the structure[4]. Discrete model of a lattice interstage composed ofbeam-type elements is shown in Fig. 2 (the upper part isa simulator of the adjacent metal section of Proton-Mlaunch vehicle).

4. Manufacturing

The typical manufacturing process involves the follow-ing operations [4]

• forming of the silicon rubber elastic coating which hasgrooves for helical and hoop ribs and is fixed on the sur-face of the mandrel as in Fig. 3(a),

ic coating (a) and removal of the elastic coating (b).


• wet winding of the ribs and the skin and dry winding ofthe sacrificed layer providing the pressure compactingthe material,

• curing,• machining of the end rings,• removal of the mandrel by pulling it out of the structure,• removal of the elastic coating by pulling it inside the

structure as in Fig. 3(b).

5. Application

5.1. Spacecraft structures

Anisogrid composite lattice structures are successfullyused in rocket technology and, being in operation for morethan 10 years, demonstrate high performance and weightefficiency. The most highly loaded and large-scale latticestructures are manufactured now for Proton-M Russiancommercial spacecraft launcher [8] whose diameter exceeds4 m.

One of the primary structures of a commercial launchvehicle is the payload attach fitting (adapter) which pro-vides the interface between a rocket and a spacecraft.Weight efficiency of the adapter is extremely importantbecause it separates from the satellite in the orbit. Pro-ton-M carbon-epoxy lattice adapter shown in Fig. 4 hasthe following characteristics:

Fig. 4. Lattice composite adapter: (a) winding (b), testing (c) and finite-

• larger and smaller diameters 2500 mm and 1300 mm,• height 900 mm,• total mass 50 kg in which the mass of the lattice struc-

ture is 28 kg,• design axial compressive force 2 MN,• axial stiffness 440 kN/mm.

Designed by analytical [9] or numerical [10] methods,lattice composite adapters demonstrate more than 40%weight saving with respect to aluminum prototypes. Bynow, eight successful launches of Proton-M have beenundertaken with lattice adapters. One of them, the 303thlaunch of June 17, 2004, has resulted in a record for Protonmass of the geosynchronized satellite – 5575 kg [8]. Upperand lower interstages for the second stage of Proton-M arepresented in Figs. 5 and 6. Application of lattice interstageshas resulted in 30% weight reduction in comparison withrib-stringer stiffened aluminum prototypes.

5.2. Aircraft structures

High specific strength and stiffness of modern compositematerials, particularly of carbon-epoxy composites, havecaused considerable progress in application of compositesto commercial airplane airframe structures. Today, com-posites are on the way to be used not only for secondarystructures like control-surfaces, fairings, landing geardoors, etc. or for structures like radomes, horizontal and

element simulation of buckling under compression and bending (d).

Fig. 5. External (a) and internal (b) views of the upper interstage (winding is shown in Fig. 3(a)).

Fig. 6. Winding (a) and the inner view (b) of the lower interstage.


vertical stabilizes whose loading level is relatively low, butalso for heavily loaded primary structures like wing andfuselage structures [11,12]. However, traditional10–20% weight savings associated with substitution of car-bon-epoxy composites for aluminum structures are consid-erably lower than could be expected referring to highmechanical characteristics and low density of moderncomposites.

To be specific, consider a typical carbon-epoxy unidirec-tional composite having the following elastic properties:E1 = 140 GPa, E2 = 11 GPa, G12 = 5.5 GPa, m12 = 0.024,m21 = 0.3; strength under tension, compression and shear:�rþ1 ¼ 2100 MPa, �r�1 ¼ 1200 MPa, �rþ2 ¼ 45 MPa, �s12 ¼70 MPa, density qc = 1550 kg/m3 (subscript 1 denotes thefiber direction and subscript 2 – the orthogonal direction).Typical properties of the aluminum alloy used for airframestructures are as follows: elastic modulus Ea = 71.5 GPa,Poisson’s ratio ma = 0.3, yield stress under tension or com-pression �ra ¼ 300 MPa, density qa = 2700 kg/m3.

Direct comparison of the foregoing data for compositeand aluminum is not consistent, because airframe compos-

ite elements have laminated structures consisting of unidi-rectional plies with different orientation angles. Stringersare usually formed by 80% of unidirectional plies and20% of ±45� plies. Calculation in accordance with the lam-ination theory [1] yields for the efficient modulus of thestringer Est = 115 GPa. For the skin, the quasi-isotropic(0�, 90�, +45�, �45�) structure is traditionally used provid-ing the efficient skin modulus Esk = 55 GPa and Poisson’sratio msk = 0.3.

Introduce the following structural efficiency coefficientsspecifying the mass ratio of the composite stringer withrespect to the corresponding aluminum having he sameshape and designed for the same load [13]

gstcn ¼

qcEa

qaEc

; gsttn ¼

qc�ra

qa�rc

ð1Þ

The first of these coefficients corresponds to compressionand the second to tension. Subscripts c and a denote com-posite and aluminum. Similar expressions for the quasi-iso-tropic skin panel are


gskcn ¼

qc

qa

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1� m2

cÞEa

ð1� m2aÞEc

3

s; gsk

tn ¼qc�ra

qa�rc

ð2Þ

Consider the case of compression. Substituting Ec = Est

and Ec = Esk in Eqs. (1) and (2), we get gstcn ¼ 0:36 for the

stringer and gcn = 0.63 for the skin. These results mean thatthe mass of a composite stringer makes 36% of the mass ofthe analogous aluminum stringer, whereas for a skin panel,the corresponding value is 63%. As can be seen, a compos-ite skin is much less weight efficient than a compositestringer.

For the case of tension, we should first preassign theallowable stress, �rc. Calculation of the ultimate strainsfor the unidirectional carbon–epoxy composite with prop-erties listed above yields �e1 ¼ 1:5% and �e2 ¼ 0:4%. The firstof these values corresponds to the fiber failure, and the sec-ond specifies the deformation at which the cracks in thematrix appear in the material [1]. Usually, these cracksdo not affect the material strength and are allowed inspacecraft structures in which composite materials providerather high weight savings. However, this is not the case forthe primary composite structures of commercial airplanesin which the operational strain must not exceed �ec ¼ 0:4%(for the material under consideration). Actually, the situa-tion is even worse – at an altitude of 10–11 km typical forcommercial airplanes, the temperature is about �60 �C,and �ec can be lower by about 20–30%. Taking �ec ¼ 0:4%;we get the allowable stress for the stringer �rst ¼ 460 MPaand for the skin �rsk ¼ 220 MPa. Then, the correspondingEq. (1) gives gst

tn ¼ 0:37 for the stringer and gsktn ¼ 0:78 for

the skin. Thus, we can expect the weight saving about60% for the stringers, about 20% for the skin under ten-sion, and about 35% for skin under compression. Becausethe skin is much heavier than the stringers, the averagemass reduction is about 30%. This value is further reducedby ribs and rings which are fastened mechanically to string-ers or skin panels and by allowance for environmentaleffects reducing mechanical characteristics of polymericcomposite materials.

Fig. 7. Carbon–epoxy lattice fuselage se

As follows from the foregoing discussion, relatively lowweight efficiency of traditional stringer stiffened structuresmade of composite materials is associated with the load-bearing skin which must have a multidirectionally rein-forced structure to resist compression or tension in combi-nation with shear. However, before the metal skin has beendeveloped, the airplanes were actually composite and uti-lized load-bearing wooden frames and doped fabric skinswhich were not load-bearing elements. The same designconcept was used in metal and composite Geodesic air-frame structures [2,3,14]. So, it looks natural to combinethe Geodesic design concept with the Anisogrid compositetechnology discussed above. In thus developed airframestructure, the operation loads are taken by unidirectionalcarbon–epoxy ribs for which the g-coefficient specified byEq. (1) is about 0.35. The skin which provides the structuresealing and increases the safety factor is made of carbon–epoxy or glass–epoxy fabric composites. The fabric skinallows us to increase the allowable deformation in tension�ec up to 0.6% (no cracks appear in the matrix of the fabriccomposite under this strain), and the g-coefficient for theskin which does not buckle under compression is about0.5. Note that the skin stability is provided by the materialtype and structure. For example, ±45� angel-ply fabric skinhas relatively low membrane stiffness which results in rela-tively low load taken by the skin and relatively high criticalstress under compression. In cylindrical lattice structureslike shown in Figs. 5 and 6, the weight of even relativelythick skin does not exceed one third of the structure mass.So, the g-coefficient for a lattice fuselage section is about0.4 which means that the structure is 60% lighter thanthe aluminum prototype. For actual lattice structures withend rings, doors, joints, etc., the weight saving can be about40%. Lattice composite fuselage structures are shown inFig. 7.

Flat lattice structures shown in Fig. 8 can be used asload-bearing fuselage rings, wing and stabilizer ribs andspars [15], cabin floor beams, etc. Lattice shear webs forwings and stabilizers (Fig. 8(b)) demonstrate extremely

ction (a) and the window frame (b).

Fig. 8. Composite lattice ring (a) and lattice shear web under testing (b).


high weight efficiency – they can be several times lighterthan aluminum prototypes. A typical stabilizer structurecan consist of a system of spars and ribs with unidirectionalflanges and lattice shear webs and of ±45� fabric skin stiff-ened with unidirectional stringers placed into the groovesformed in the skin. Flat lattice structures combine low den-sity with high thickness providing high specific bendingstiffness which is necessary for the airplane floor panels.

6. Cost

For commercial aircraft structures, in contrast to space-craft structures, cost is more important than weight [16].Moreover, possible weight saving is usually associated withthe reduction of the operating cost. Existing methods [17]allow us to calculate that the increase of the payload inaccordance with the airframe weight reduction results fora middle-range 300-seat plane in $950 per 1 kg for year.

The main contribution to the cost of a composite struc-ture belongs to carbon fibers. The average cost of the typ-ical carbon-epoxy composite with the properties listedabove is about 60$/kg, whereas the cost of aircraft alumi-num alloy is about 5$/kg. Thus, the unit of mass for thecomposite is 12 time higher than for aluminum. Note thatthis is true only for the so-called wet manufacturing pro-cesses which include the fiber impregnation. The so-calleddry processes utilize prepregs whose cost is about 120$/kgand which are about 24 times more expensive than alumi-num. However, the direct comparison of material cost forunit mass is not consistent, because composites and metalshave different densities and different mechanical properties.Introduce the material cost efficiency coefficient as [13]

k ¼ gcc

ca

ð3Þ

in which g is specified by Eqs. (1) and (2) and c is the mate-rial cost per unit mass. Because traditional stringer stiff-ened airframe structures are made by prepreg lay-up, wetake cc = 120$/kg and ca = 5$/kg. Then, Eqs. (1)–(3) yield

kstcn ¼ 8:6; kst

tn ¼ 15:1

kskcn ¼ 8:9; ksk

tn ¼ 18:7

As can be seen, the k-coefficient is much lower than the ratioof material costs, and the quasi-isotropic skin material ismore expensive than the stringer material by the factor of1.24. For a stringer stiffened structure, k is about 15 whichmeans that the material consumed by the composite struc-ture is, on average, 15 times more expensive than aluminum.For the ribs of the lattice structures made by wet winding,we take cc = 60$/kg and arrive at the coefficient about 4.For the skin made of carbon fabric prepreg (cc = 160$/kg)we get k about 16. Thus, for the lattice composite fuselagesection, k = 7.6 which is about 2 times less than for tradi-tional composite stiffened structure. Because the skin isnot a primary load-carrying element in Geodesic structures(it take only the internal pressure which is relatively low) thecost can be further reduced if the skin is made of glass fabric(cg = 20$/kg). For such a structure, k is about 3 which 5times less than for carbon–epoxy stringer structure.

In composite technology, the higher by an order of mag-nitude material cost is expected to be compensated by theintegral nature of composite structures requiring less jointsand assembling operations than metal parts. If this expec-tation becomes true, the advantages of Geodesic Anisogridfuselage composite structures are further enhanced,because the ribs and the skin of the lattice structure forma completely integral part made by continuous windingwhich is the most highly productive process [18].

7. Conclusion

Geodesic Anisogrid composite lattice structures madeby wet filament winding promise considerable weight andcost savings with respect to traditional stiffened compositeparts of airplane fuselage, wing and empennage structures.

References

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Anisogrid Composite Lattice Structures - 2006