STRUCTURAL DESIGN OF AN UAV FUSELAGE USINGTOPOLOGY OPTIMIZATION METHODS

Daniel de Oliveira Andrade∗ , William Corbelli∗ , Rodrigo de Sá Martins∗ , Ramón RodriguesVieira de Queiroz∗

∗Universidade Federal de Minas Gerais

Keywords: Structural Optimization, Structural Design, Topology Optimization, Discrete Optimization.

Abstract

Aircraft weight reduction is one of the greatestchallenges of the aeronautical sciences, includ-ing the unmanned vehicles. This reduction rep-resents fuel economy and better performance. Inthis paper, in order to design effective structures aoptimization procedure was used. The topologyoptimization was used it characterize and deter-mine the optimum distribution of material intothe domain. After that, a size optimization wasset to finish the structural design. Finally, the re-sults were compared with the same component,that was design without the optimization tools.

1 Introduction

The current paper was motivated by the competi-tion SAE AeroDesign Brazil. Such competitionis a challenge proposed to engineering students,whose main goal is to foster the diffusion andexchange of aeronautical engineering techniquesand knowledge. Thereby, the student can beinvolved in a real case of aeronautical develop-ment project, since its inception, detailed design,building and tests.

The airplane analyzed in this paper is clas-sified in the regular category, which the mainobjective is to design a plane with the highestpayload. The structural efficiency is a veryimportant parameter, since the payload is themaximum take-off weight less the aircraft emptyweight.

The differential adopted by the team wasa modification in the airplane tail, previouslycomposed only by one carbon tube (fig. 1),resulting in a less structural efficient structure toresist torsion and bending.

Fig. 1 UFMG 2015 airplane.

Such configuration was replaced by a trusscone. In this case, a topology optimization canbe very beneficial to the structural design, sincethere are an infinite number of possible architec-tures.

2 Structural Optimization in design

Structural optimization can be generally definedmathematically by the following [1]:

Find x, that minimize f (x), subject tog(x)≤ 0.

Where f (objective function) is a scalar, x(design variable) is a vector of n components and

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DANIEL O. ANDRADE , WILLIAM CORBELLI , RODRIGO S. MARTINS , RAMÓN R. V. DE QUEIROZ

g (constraints) is a vector of m components.

There are several methods for structuraloptimization developed over the years. Severalcommercial software have the algorithms im-plemented and linear programming are usuallyused to find the solution ([2] and [3]). Otherkinds of algorithms, such as genetic (like theone performed by (like the one described by[4] to design Skeleton Structures) or ant colony(developed by [5] can be used to solve theoptimization problem.

The methodology shown in this paper isbased in [6]. [6] divided the optimization in twoparts, the first one is a topology optimization,followed by a discrete size optimization. UsingOptistruct [2], the design could only be per-formed in two steps.

Since the problem was divided in this twoparts, there is no easy way to know that thesolution is global optimum. To perform thewhole design with one optimization analysis,stress constraints should have been taken intoaccount. [7] developed a very robust methodto take into account the final geometry of thecomponent, but his analysis was performed onlyin two dimensions.

2.1 Topology Optimization

In this paper the topology optimization is per-formed by minimize the compliance which isequivalent to maximize the stiffness. Maximiz-ing the stiffness using a constant volume in adesign space, it is possible to find the best loadpath [8].

Selecting the compliance as the objectivefunction and the relative density of each finite el-ement ψ as a design variable, the optimizationproblem can be rewritten as:

Minimize∫

Γ

F izidΓ→∫

Ω

ψ(x)dΩ <V0 (1)

and a side constraint 0≤ ψ(x)≤ 1.

Where F i is the force, zi is the displacement,Γ is the loaded boundary, Ω is the physicaldomain and V0 is the volume fraction.

2.2 Size Optimization

Selecting the final component mass as a objec-tive function and putting Buckling and Stressesas constraints it is possible to size the structurewith the architecture found in the topology opti-mization. Or:

Minimize∫

VρdV →

σ < σuλ≤ FS (2)

Where ρ is the material density, V is the volumeof the component, σ is the maximum stress in theanalysis σu is the strength limit of the material, λ

is the buckling eigenvalue and FS is the bucklingfactor of safety. In this case, the design variablesare the members cross sections, being discretedue to the fact that they are chosen from finiteavailable tubes.

3 Structural Design

The first step in the structural design is thedetermination of loads. In this case, the loads aremainly aerodynamic coming from the horizontaland vertical stabilizers.

The fuselage was divided in two parts (fig. 2).The truss distributions are calculated analyticallyin the part 1, since the loads are mainly from thewing, landing gear and cargo compartment (fig.3). The part 2 will be design space in the topol-ogy optimization developed in this paper.

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STRUCTURAL DESIGN OF AN UAV FUSELAGE USING TOPOLOGY OPTIMIZATION METHODS

Fig. 2 Design space.

Fig. 3 Cargo bay detail.

The truss cone was idealized as a triangulargeometry. This configuration does not need diag-onal web members, therefore, is more structuralefficient than a rectangular shape (fig. 4). Besidesthat, the truss cone is manufactured by three sep-arated planes (fig. 5). Thus, it is preferable toidealize the design space as plane elements.

Fig. 4 Tail geometry.

Fig. 5 Truss manufacturing.

The regular class aircraft’s from 2017 SAEBrazil AeroDesign Competition had to fit into

a cone with 2900 mm of diameter and 750 mmof height. Therefore, the vertical stabilizer wasthereabout placed in the middle of the truss cone(fig. 6)

Fig. 6 Cone restriction.

Two different types of attachments were pro-posed for the vertical stabilizer, shown in fig. 7and fig. 8.

Fig. 7 Vertical tail attachment type 1.

Fig. 8 Vertical tail attachment type 2.

The SIMP method (Optistruct topologysolver) is only available for isotropic materials[2]. Therefore, the carbon fiber was assumedisotropic. This is a valid approximation, since thetrusses are designed to mainly resist axial loadsand the carbon fiber tubes are unidirectional andpultruded.

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DANIEL O. ANDRADE , WILLIAM CORBELLI , RODRIGO S. MARTINS , RAMÓN R. V. DE QUEIROZ

3.1 Truss Topology

The optimization objective is minimize thecompliance of the structure. Thus, only themembers who most contribute to the stiffnessof the structure will be kept. The optimizationconstraint is the volume fraction. Higher valuesof volume fraction tend to concentrate mass,creating large members. Lower values canoverlook some members, making the structureincomplete.

The criteria to choose the best volumefraction was the uniformity and size of themembers. A manual bisection method was usedin an interval from 0.3 to 0.1 to converge thevolume fraction value. In the both cases (fig. 9and fig. 10), the chosen value was 0.12, whichwas closest to a truss like structure.

The chosen results are exported to the CADthough the OSSmoth with a threshold value (min-imum density of element) of 0.15. The trusses aresketched, exported to a STEP file and importedback to the Hypermesh.

Fig. 9 Topology optimization (First type of at-tachment).

Fig. 10 Topology optimization (Second type ofattachment).

3.2 Final Layout

After the structural architecture was obtained forthe two kinds of vertical stabilizer attachments,the final layouts were obtained using a discretesize optimization. Tab. 1 shows the availabletubes for the tail truss.

Table 1 Available Carbon Tubes

TubeOtter

Diameter(mm)Inner

Diameter (mm)1 5 32 4 33 4 24 3 25 2 1

The finite element model was built using theresults from the topology optimization. Fig. 11shows the finite element model, highlighting thethe constraints and loads.

Fig. 11 Analysis setup

To apply the size discrete algorithm, there isan extra difficulty: the discrete design variablesare entangled, that is, the inner and outer diame-ter for each tube are related. To simplify the op-timization, an analysis was performed using onlythe smallest tubes. The stress analysis is shownin fig. 12.

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STRUCTURAL DESIGN OF AN UAV FUSELAGE USING TOPOLOGY OPTIMIZATION METHODS

Fig. 12 Stress analysis of tail truss using thesmallest tubes (Stresses in MPa).

According to fig. 12 and the allowable ten-sile/compressive stress of tab. 2, the safety factorcan be calculated:

Table 2 Material Properties [9].

FS =σ

σu<

157010919

= 0.14 (3)

The buckling analysis was performed and theresults are shown in fig. 13.

Fig. 13 Buckling analysis of tail truss using thesmallest tubes.

Since the buckling eigenvalue is lower thanthe strength factor of safety, it was consideredthat the structure is dimensioned by buckling.Thus, it is assumed that the important design vari-able is the the inertia and not the cross-section ar-

eas. The tubes were changed by equivalent barswith the same inertia (fig. 14).

Fig. 14 Section transformation

I =π(D4

out−D4inn)

64= Ieq =

πR4eq

4(4)

Req =4

√(D4

out−D4inn)

16(5)

The equivalent radius for each tube are shownin tab. 3.

Table 3 Equivalent radius for optimization

TUBEINERTIA

(mm4)EQUIVALENTRADIUS (mm)

1 26.70354 2.4152 8.890292 1.8163 11.78097 1.9684 3.19068 1.4205 0.736311 0.984

Using the equivalent radius as a design vari-able, it is possible to set the optimization withdiscrete and independent design variables. Forthe first geometry, the results are shown in fig.15.

Fig. 15 Optimization results for the first struc-tural architecture.

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DANIEL O. ANDRADE , WILLIAM CORBELLI , RODRIGO S. MARTINS , RAMÓN R. V. DE QUEIROZ

For the second geometry, the results areshown in fig. 16.

Fig. 16 Optimization results for the second struc-tural architecture.

4 Discussion

The mass value of both structures found in thisstudy were similar. The first model weight 54 gand the second one weight 51 g. Since the analy-sis performed in the optimization was an approxi-mation (it used the concept of equivalent radius),it is necessary to check the strength of the finaldesign (model 2). Fig. 17 shows the final analy-sis results.

Fig. 17 Stress and buckling analysis of the finalconfiguration.

The design of the same structure performed

without optimization ended up with a 100 g tailtruss. That means that the optimization processrepresented a 49% weight reduction.

5 Conclusions

In the present paper the following conclusioncould be made:

• The optimization analysis was proven to bevery effective when comparing the designof the tail truss with and without optimiza-tion analysis.

• The equivalent radius approach was veryimportant to simplify the problem.

• A concise optimization process was essen-tial to obtain the good results shown here.

• For further work, the authors recommendto redo the optimization with only oneanalysis (using an hybrid topology/size al-gorithm).

References

[1] William R. Spillers Keith M. MacBain. Struc-tural optimization. 2009.

[2] Altair Engineering. Optistruct User Manual.2017.

[3] R. J. Yang. Optimal topology design using linearprograming. Computers & Structures, 52:265–275, 1993.

[4] Kevin Gillman Richard J. Balling,Ryan R. Briggs. Multiple optimumsize/shape/topology designs for skeletal struc-tures using a genetic algorithm. Journal ofStructural Engineering, 132:1158–1165, 2006.

[5] Barron J. Bichon Charles V. Camp. Designof space trusses using ant colony optimization.Journal of Structural Engineering, 132:1158–1165, 2004.

[6] Dianzi Liu Osvaldo M. Querin, VassiliV. Toropov. Parametric optimization of alattice aircraft fuselage barrel using metamod-els built with genetic programming. In TheFourteenth International Conference on Civil,Structural and Environmental Engineering.

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STRUCTURAL DESIGN OF AN UAV FUSELAGE USING TOPOLOGY OPTIMIZATION METHODS

[7] C. Brampton J. Norato H.A. Kim R. Picellia,S. Townsend. Stress-based shape and topologyoptimization with the level set method. Computermethods in applied mechanics and engineering,329:1–23, 2018.

[8] Martin P. Bendsœ. Topology Design of Struc-tures. 1993.

[9] Torayca. Technical data sheet no. cfa-001. Tech-nical report.

6 Contact Author Email Address

For contacting the authors, please refer to:danielandrade.aero@gmail.comcorbelli.william@gmail.comrodrigomartins@demec.ufmg.brramonrvq@gmail.com

Copyright Statement

The authors confirm that they, and/or their companyor organization, hold copyright on all of the origi-nal material included in this paper. The authors alsoconfirm that they have obtained permission, from thecopyright holder of any third party material includedin this paper, to publish it as part of their paper. Theauthors confirm that they give permission, or have ob-tained permission from the copyright holder of thispaper, for the publication and distribution of this pa-per as part of the ICAS proceedings or as individualoff-prints from the proceedings.

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