Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 65 (2015) 99 – 106
International Conference on Communication, Management and Information Technology (ICCMIT 2015)
Aircraft composite spoiler fitting design using the variable density model V.A. Komarov*, E.A. Kishov, E.I. Kurkin, R.V. Charkviani Samara State Aerospace University (SSAU), 34, Moskovskoe shosse, Samara, 443086, Russia
Abstract Present paper describes a problem of a fitting unit design for transferring the high concentrated forces to thin-walled layered composite airframe structures. The using of variable density model is offered as new mathematical model for the solution of topology optimization problems. The offered technique is illustrated by the fitting brought to production and carrying out its successful static and resource tests. The resulting optimized aircraft spoiler fitting design has weight twice less than its initial design version obtained without using the variable density model.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Universal Society for Applied Research. Peer-review under responsibility of Universal Society for Applied Research Keywords: load trasferring path; topology optimization; design;spoiler fitting; airframe structures; variable density model.
1. Introduction The using of vacuum infusion or RTM technology is applied for elements of mechanization of aircraft structures1. Thus it is possible to get the finished structure ”in-one-shot”. The experience of the long-range passenger aircraft spoiler design showed that it can be made by the one integral detail using composite materials. One of the main problems is ensuring transferring of the big concentrated forces arising in metal spoiler fitting unit to composite thin-walled part. In this article we investigate a design problem of metal fitting of composite aircraft spoiler, see Fig. 1. The development of the central fitting unit was difficult because
* Corresponding author. Tel.: +7-846-267-4645; fax: +7-846-267-4645. E-mail address:
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1877-0509 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Universal Society for Applied Research doi:10.1016/j.procs.2015.09.085
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V.A. Komarov et al. / Procedia Computer Science 65 (2015) 99 – 106 the big concentrated loads (P1 and P2) acting on it lie in various planes causing the bending moment in the area of considered fitting.
Fig. 1. Loads acting on the spoiler
2. The intuitive design of fitting The initial design of spoiler fitting, see Fig 2a, showed not sufficient strengthwhich were revealed in the series of tests, see Fig 2b. Increasing a thickness of the “weak” walls of the fitting was ineffective and brought only increasing in mass of the part. Therefore the technology of structural topology optimization using model of variable density body was applied to determine an optimal material layout of the fitting.
Fig. 2. (а) intuitive design of the fitting, (b) result of strength tests of the intuitive design
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V.A. Komarov et al. / Procedia Computer Science 65 (2015) 99 – 106 3. Method of determining the optimal material distribution of load-carrying structures The algorithm of using variable density model is offered in2 and in detail described in3. The design domain, in which the fitting should be located, is filled with the continuous elastic medium having a variable stiffness, i.e. Young’s modulus which depends on material density. The similar problem statement can be found in 4. In2 it is offered dE ! 0. In terms of the finite to use a relationship between the elastic modulus press and density E E U such that d Uto stress constraints can be elements method (FEM) the problem of finding the structure with minimum mass subject formulated as follows: (1) m ¦ UeV e o min; V e d >V @e , e 1,..., N where m – mass of structure, Ve - element volume; summation extends over all elements (quantity of N) representing a design domain.
V
V e - equivalent stresses in the element calculated according to the von Mises yield criterion as
ª¬V V V 32 V 1V 2 V 2V 3 V 3V 1 º¼ , ( V 1 , V 2 , V 3 - principal stresses). 2 1
2 2
For calculation and design synthesis on integrity in this article we use the following relationships of elastic modulus and allowable stress with density [5]: (2) E EU ; >V @ >V @U Besides, the nature gives samples of very perfect variable density designs. For example are bones of animals, especially birds. Further for the solution of a task (1) we use model (2) and the following iterative process based on optimally criteria optimization method for updating design variables2 for i 1, N / / loop over iterations
{ for e 1, R / / loop over finite elements
Uie o Uie
V ie
(3)
>V @i
e
if Converged then break / / Algorithm stopping criteria } where the top index means number of an element, inferior – number of iteration, N denotes iterations number, R – elements number used for optimization. max If some cases of loading are investigated, in numerator (3) instead of V i will be V i - the maximum stress in an element from all cases. As a result of the iterative procedure (3) is a design with stress in each point with positive density is equal to the allowed. This structure will have the same strain values in each point6. The analysis of optimization results is made on two pictures: distributions of density giving an idea of clots or discharges of material and on the primary stresses which show the direction of internal efforts. 4. Topology optimization of the spoiler fitting Spoiler is loaded by distributed aerodynamic loadings and concentrated forces in linkage fitting. In a its mounting seat we will establish a continuous body ("continuity model", see Fig. 3) with properties of an aluminum alloy of which it is supposed to make a detail (E=71 GPa, P=0,3, U=2700 кг/м3, [V]=300MPa). Bonded contact is set between the adjoining surfaces of continuity model and a spoiler.
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Fig. 3. Variable density model using for spoiler fitting optimization
The strength analysis is carried out in ANSYS. The algorithm of topology optimization (3) is realized in APDL language (Ansys Parametric Design Language). The following results, see Fig. 4 are received after 10 iterations of density redistribution.
Fig. 4. Density distribution with a cut-off low values (a) isometric view, (b) side view
After topology optimization result analysis, it is possible to draw a conclusion that directly between lug pairs it is necessary to put a wall which will balance the shear stress, generated by the reactions of attachment points. This wall, together with the top and lower berth, and also with a front wing spar, will form the closed contour which is effectively working under torsion.The parametrical CAD-model of a part is developed using ANSYS DesignModeler system (Fig. 5) on the basis of distribution of density, see Fig. 4. Technological features of detail production by the mechanical operation (milling) taken into account in this model. The unique feature of model2 and the used algorithm is opportunity to come to a thin-walled spatial design.
V.A. Komarov et al. / Procedia Computer Science 65 (2015) 99 – 106
Fig. 5. Parametrical CAD-model of linkage unit
Deformation behaviors shows that design needs taking into account deformation of counterpart (spoiler composite part), see Fig. 6a. The general level of stresses in a wall is close to a limit of material strength, and in places of concentration exceeds it, see Fig. 6b. It should be noted that a simplified bolt modeling approach is used. Concentration of stresses arises in a central area between two pairs of lug. Out of the central zone the level of stresses is rather low that speaks about possibility of reducing the weight of the structure.
Fig. 6. (a) fragment of the deformed finite element model (10x deformation), (b) equivalent stress in fitting unit after topology optimization
5. Parametrical optimization of the fitting The parametrical model allows making changes to a design easily. Fig. 7 shows the taken measures for decrease in mass of a detail and decrease in concentration of stresses in area of lugs attachment to a wall. Options 2 and 3 have cuts and a lightening hole, places for them got out proceeding from a picture of distribution of equivalent stresses. The increase in rounding radius (option 4) didn't lead to essential decrease in concentration. Addition of smoothed connection between lugs and wall (option 5) appeared the effective decision. The technical solutions presented on Fig. 6 and received with using of variable density model, allowed to reduce significantly weight in comparison with intuitively offered option, see Fig. 2.
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Fig. 7. Parametrical optimization of linkage unit
The final version of a design is presented on Fig. 8.
Fig. 8 (a) the final version of design (b) equivalent stress distribution on it, (Vmax = 422 MPa)
V.A. Komarov et al. / Procedia Computer Science 65 (2015) 99 – 106 6. Static tests of the manufactured spoiler fitting A tests under design load were carried out for design technique correctness check and mathematical modelling adequacy. Spoiler deformations can have essential impact on stress conditions of the fitting. Therefore tests of the fitting are carried out assembled with a spoiler, see Fig. 9a, in special tool for bracing on a wing imitation and air loading application, see Fig. 9b. By the results of tests, see Fig. 10 it is possible to draw a conclusion that the fitting successfully withstands the design load.
Fig 9. (a) fitting assembled with a spoiler, (b) the tool for bracing on a wing imitation and air loading application
25 Papplied
Load, kN
20 15 10 5 0
0
5
10
15
20
25
30
Displasement, mm Fig. 10 ”Load-displacement” curve of the whole assembly
7. Conclusion The optimized aircraft spoiler fitting design, see Fig. 8, has weight twice less at the comparable integrity in comparison with intuitively offered option, see Fig. 2. Thus the method of using variable density model can be recommended for determining an optimal structure layout of high-loaded spatial parts at the early design stages. Topology optimization is the powerful design tool which able to get a non-trivial solutions in area where traditional heuristic engineering approaches doesn’t work at sufficient level. Future investigations are directed to improving a clarity of optimization results in order to incorporate a modern manufacturing technologies e.g. additive manufacturing into a product development cycle. Also, it should be noted that there is a great opportunity for application of methodology described in the article to designing a complex integral composite structures.
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V.A. Komarov et al. / Procedia Computer Science 65 (2015) 99 – 106 Acknowledgements Authors wish to thanks to Kuznetsov Anton Sergeyevich for discussions about this article. References 1. Nelyub VA, Grashchenkov DV, Kogan DI, Sokolov IA. The application of direct methods of molding in the production of large parts of fiberglass. Chemical technology 2012; 13(12): 735 - 739. 2. Komarov VA. Designing power circuits aircraft structures. Mechanical engineering 1984: 114-129. 3. Komarov VA, Boldyrev AV, Kuznetsov AS, Lapteva MYu. Aircraft design using a variable density model. Aicraft Engineering and Aerospace Techology: An Int Journal 2012; 84(3): 162-171. 4. Bendsoe MP. Sigmund O. Topology Optimization: Theory, Methods and Applications. Springer 2003. 5. Komarov VA. Rational design of aircraft structures. Dr. tehn. sci. thesis. Moscow aviation. Inst 1976. 6. Boldyrev AV. Development of methods for the design of power aircraft structures based on models of deformable body with variable density. Dr. tehn. sci. thesis. SSAU 2012.
