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Aeroelastic optimisation of composite wings using the dynamic stiffness method

Published online by Cambridge University Press:  04 July 2016

M. Lillico ,
R. Butler ,
S. Guo  and
J.R. Banerjee
M. Lillico
Affiliation:
School of Mechanical Engineering, University of Bath, UK
R. Butler
Affiliation:
School of Mechanical Engineering, University of Bath, UK
S. Guo
Affiliation:
Department of Mechanical Engineering and Aeronautics, City University, London, UK
J.R. Banerjee
Affiliation:
Department of Mechanical Engineering and Aeronautics, City University, London, UK
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Abstract

A computer program for use in the conceptual stage of aircraft design has been developed. The program obtains minimum mass designs for high aspect ratio, composite wings, subject to constraints on flutter speed, divergence speed and material stress. The wing is modelled as a series of composite beam elements and both flutter speed and divergence speed are calculated using a normal mode approach. Modal analysis is carried out by applying the Wittrick-Williams algorithm to the dynamic stiffness method, whereas unsteady aerodynamic loads are calculated from strip theory, although an option which uses lifting-surface theory is also presented. A previously published example is given to validate the analysis. Single level optimisation is carried out using a sequential quadratic programming strategy combined with the modified methods of feasible directions optimizer, for which flutter sensitivities are obtained by an efficient determinant interpolation technique. Design variables include topological variables such as spar and engine positions as well as layer thicknesses, which are modelled using quadratic functions. The wing of a regional turboprop aircraft is optimized to illustrate the use of the program. The problem was modelled using 10 elements and had 43 design variables, 162 constraints and required just over 20 minutes of CPU time on a workstation. This, coupled with the fact that a full three-dimensional FE model of the same wing would require over 1000 elements, illustrates the suitability of the dynamic stiffness method to the conceptual design stage.

Type
Research Article
Information
The Aeronautical Journal , Volume 101 , Issue 1002 , February 1997 , pp. 77 - 86
Copyright
Copyright © Royal Aeronautical Society 1997 

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References

1. Neill, D.J., Johnson, E.H. and Canfield, R. Astros — a multidisciplinary automated structural design tool. J Aircr, 1990, 27, (12), pp 1021–1027.Google Scholar
2. Wilkinson, K., Markowitz, J., Lerner, E., George, D. and Batill, S.M. Fastop: a flutter and strength optimization program for lifting-surface structures, J Airer. 1977, 14, (6), pp 581–587.Google Scholar
3. Dodd, A.J., Kadrinka, K.E., Loikkanen, M.J., Rommel, B.A., Sikes, G.D., Strong, R.C. and Tzong, T.J. Aeroelastic design optimization program, J Aircr, 1990, 27, (12), pp 1028–1036.Google Scholar
4. Bartholomew, P. and Wellen, H.K. Computer aided optimization of aircraft structures, J Aircr, 1990, 27, (12), pp 1079–1086.Google Scholar
5. Cornuault, C., Petiau, C., Coiffier, B. and Paret, A. Structural optimization of aircraft practice and trends, 72nd Meeting of the Agard Structures and Materials Panel, Bath, 1991, Agard Report 784, pp 14.1-14.11.Google Scholar
6. Brama, T. The structural optimization system Optsys — current status and applications, 72nd Meeting of the Agard Structures and Materials Panel, Bath, 1991, Agard Report 784, pp 6.1-6.9.Google Scholar
7. McCullers, L.A. and Lynch, R.W. Dynamic characteristics of advanced filamentary composite structures, Volume II Aeroelastic synthesis procedure development, and Volume III Demonstration Component Program, AFDL-TR-111, Sept 1974.Google Scholar
8. Wakayama, S. and Kroo, I. Subsonic wing design using multidisciplinary optimization, 5th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City, Florida, USA, 1994, AIAA Paper No. 94-4409-CP, pp 1358-1368.Google Scholar
9. Austin, F., Hadcock, R., Hutchings, D., Sharp, D., Tang, S. and Waters, S. Aeroelastic tailoring of advanced composite lifting surfaces in preliminary design, 17th AIAA/ASME/SAE Structures, Structural Dynamics and Materials Conference, 1976, pp 69-79.Google Scholar
10. Lillico, M., Butler, R., Banerjee, J.R. and Guo, S. Aeroelastic optimization of high aspect wings using an exact dynamic matrix method, 5th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City, Florida, 1994, AIAA Paper 94-4401 -CP, pp 1301 -1309.Google Scholar
11. Butler, R., Lillico, M., Banerjee, J.R., and Guo, S. Optimum design of high aspect ratio wings subject to aeroelastic constraints, 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, New Orleans, Louisiana, 1995, AIAA-95-1223-CP, pp 558-566.Google Scholar
12. Banerjee, J.R. Use and capability of Calfun — A program for calculation of flutter speed using normal modes, Proceedings of the International AMSE Conference on Modelling and Simulation, Athens, Greece, June 1984, pp 121-131.Google Scholar
13. Berdichevsky, V., Armanios, E.A. and Badir, A. Theory of anisotropic thin-walled closed-section beams, Comp Eng, 1992, 2, (5-7), pp 411–432.Google Scholar
14. Armanios, E.A. and Badir, A.M. Free vibration analysis of anisotropic thin-walled closed-section beams, 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Hilton Head, South Carolina, 1994, AIAA Paper 94-1327-CP, pp 164-171.Google Scholar
15. Banerjee, J.R. Coupled bending-torsional dynamic stiffness matrix for beam elements, Int J Numer Meth Eng, 1989, 28, pp 1283–1298.Google Scholar
16. Banerjee, J.R. and Williams, F.W. Coupled bending-torsional dynamic stiffness matrix for Timoshenko beam elements, Comput Struct, 1992, 42, (3), pp 301–310.Google Scholar
17. Banerjee, J.R. and Williams, F.W. Free vibration of composite beams — an exact method using symbolic computation, J Aircr, 1995, 32, (3), pp 636–642.Google Scholar
18. Wittrick, W. H. and Williams, F.W. A general algorithm for computing natural frequencies of elastic structures, Q J Mech Appl Math, 1971, 24. pp 263–284.Google Scholar
19. Theodorsen, T. General Theory of Instability and Mechanisms of Flutter, Naca Tech Report 496, 1934.Google Scholar
20. Bisplinghoff, B.L., Ashley, H. and Halfman, R.L. Aeroelasilicity, Addison-Wesley, 1955.Google Scholar
21. Davies, D.E. Theoretical Determination of Subsonic Oscillatory Air-force Coefficients, Aeronautical Research Council, R & M 3804, 1976.Google Scholar
22. Dowell, E.H., Curtiss, H.C., Scanlan, R.H. and Sisto, F. A Modern Course in Aeroelasticity, Sijthoff and Noordhoff, 1980.Google Scholar
23. Vanderplaats Research & Development, Dot User manual Version 4.20, 1995.Google Scholar
24. Berkes, U.L. Efficient optimization of aircraft structures with a large number of design variables, J Aircr, 1990, 7, (12), pp 1073–1078.Google Scholar
25. Butler, R. and Williams, F.W. Optimum design using Viconopt, a buckling and strength constraint program for prismatic assemblies of anisotropic plates, Comput Struct, 1992, 43, (4), pp 699–708.Google Scholar
26. Rudisill, C.S. and Bhatia, K.G. Second derivatives of die flutter velocity and die optimization of aircraft structures, AIAA J, 1972, 10, (2), pp 1569–1572.Google Scholar
27. Striz, A.G. and Venkayya, V.B. Multidisciplinary optimization studies using Astros, 72nd Meeting of die Agard Structures and Materials Panel, Baui, 1991, Agard Report 784, pp 8.1- 8.29.Google Scholar
28. Balis-Crema, L. Mastroddi, F. and Coppotelli, G. Structural modelling effects on aeroelastic analysis. International Forum on Aeroelasticity and Structural Dynamics, Manchester, 1995, pp 40.1- 40.11.Google Scholar
29. Shirk, M.H., Hertz, T.J. and Weisshaar, T.A. Aeroelastic tailoring — theory, practice and promise, J Aircr, 1986, 23, (1), pp 6–18.Google Scholar
30. Haftka, R.T. and Gurdal, Z. Elements of Structural Optimization, 3rd Edition, Kluwer, The Netherlands, 1992, pp 256–263.Google Scholar