Abstract
This paper aims to obtain the optimal composite box-beam design for a helicopter rotor blade. The cross-sectional dimensions and the ply angles of the box beam are considered as design variables. The objective is to optimize the box beam to attain a target vector of stiffness values and maximum elastic coupling. The target vector is the optimal stiffness values of helicopter rotor blade obtained from a previous aeroelastic optimization study. The elastic couplings introduced by the box beam have beneficial effects on the aeroelastic stability of helicopter. The optimization problem is addressed by decomposing the optimization into two levels, a global level and a local level. The box-beam cross-sectional dimensions are optimized at the global level. The local-level optimization is a subproblem which finds optimal ply angles for each cross-sectional dimension considered in the global level. Real-coded genetic algorithm (RCGA) is used as the optimization tool in both the levels of optimization. Hybrid operators are developed for the RCGA, thereby enhancing the efficiency of the algorithm. Min–max method is used to scalarize the multiobjective functions used in this study. Optimal geometry and ply angles are obtained for composite box-beam designs with ply angle discretization of \(10\), \(15\), and \(45^o\).
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References
Adali S, Walker M, Verjinko VE (1996) Multi-objective optimization of laminated plates for maximum prebuckling, buckling and postbuckling strength using continuous and discrete ply angles. Compos Struct 35:117
Antonio C (1995) Optimization of laminated composite structures using a bi-level strategy. Compos Struct 33:193–200
Antonio C (2001) A multilevel genetic algorithm for optimization of geometrically nonlinear stiffened composite structures. Struct Multidisc Optim 24:372–386
Akira T, Ishikawa T (2004) Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation. Compos Struct 64:349–357
Chattopadhyay A, Walsh, Joanne L, Michael RF (1991) Integrated aerodynamic load/dynamic optimization of helicopter rotor blades. J Aircr 28:58–65
Chattopadhyay A, McCarthy TR, Narayanan P (1995) Multilevel decomposition procedure for efficient design optimization of helicopter rotor blades. AIAA J 33:223–230
David L (1991) Handbook of genetic algorithms. Van Nostrand Reingold, New York
Deb K (2002) Multi-objective optimization using evolutionary algorithms. Wiley, Singapore
Ganguli R (2002) Optimum design of helicopter rotor for low vibration using aeroelastic analysis and response surface methods. J Sound Vib 258:327–344
Ganguli R, Chopra I (1995) Aeroelastic optimization of a helicopter rotor with composite coupling. J Aircr 32:1326–1334
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, New York
Gurdal Z, Haftka RT, Nagendra S (1994) Genetic algorithms for the design of laminated composite panels. SAMPE Journal 30(3):29–35
Hajela P (2002) Soft computing in multidisciplinary aerospace design new directions for research. Prog Aerosp Sci 38:1–21
Herrera F, Lozano M, Sanchez AM (2002) Hybrid crossover operators for real coded genetic algorithms: an experimental study. Soft computing—a fusion of foundations, methodologies and applications. Springer, Berlin Heidelberg New York
Herrera F, Lozano M, Snchez AM (2003) A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study. Int J Intell Syst 18:309–338
Holland HJ (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI
Horn J, Nafpliotis N, Goldberg DE (1994) A niched pareto genetic algorithm for multi-objective optimization. IEEE Proc Evol Comput 1:82–87
Houck CR, Joines JA, Kay MG (1996) Genetic algorithm for function optimization: a Matlab implementation. ACM Trans Math Softw 22:1–14
Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto Archived Evolution Strategy. Evol Comput 8(2):149–172
Kogiso N, Watson LT, Gurdal Z, Haftka RT (1994) Genetic algorithms with local improvement for composite laminate design. Struct Optim 7(4):207–218
Kumar N, Tauchert TR (1992) Multi-objective design of symmetrically laminated plates. Trans ASME 114:620–625
Lee J, Hajela P (1997) GA’s in decomposition based design subsystem interactions through immune network simulation. Struct Multidisc Optim 14:248–255
Le Riche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J 31(5):951–956
Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidisc Optim 26:369–395
Mesquita L, Kamat MP (1987) Optimization of stiffened laminated composite panels with frequency constraints. Eng Optim 11:77–86
Michalewicz Z (1994) Genetic algorithms + data structures = evolution programs. Springer, Berlin Heidelberg New York
Mitchell M (1996) An introduction to genetic algorithms. MIT Press, Cambridge, MA
Murugan S, Ganguli R (2005) Aeroelastic stability enhancement and vibration suppression in a composite helicopter rotor. J Aircr 42:1013–1024
Nam C, Chattopadhyay A, Kim Y (2000) Optimal wing planform design for aeroelastic control. AIAA J 38:1465–1470
Nagendra S, Jestin D, Gurdal Z, Haftka RT, Watson LT (1996) Improved genetic algorithms for the design of stiffened composite panels. Comput Struct 58(3):543–555
Oyama A, Obayashi S, Nakamura T (2001) Real-coded adaptive range genetic algorithm applied to transonic wing optimization. Appl Soft Comput 1:179–187
Paik J, Volovoi V, Hodges D (2002) Cross-sectional sizing and optimization of composite blades. AIAA-2002-1322, 43rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Denver, CO, 22–25 April 2002
Park JH, Hwang JH, Lee CS, Hwang W (2001) Stacking sequence design of composite laminates for maximum strength using genetic algorithms. Compos Struct 52:217–231
Periaux J, Sefioui M, Stoufflet B, Mantel B, Laporte E (1995) Robust genetic algorithms for optimization problems in aerodynamic design. Genetic algorithms in engineering and computer science. Wiley, New York, pp 370–396
Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. Proceedings of the 1st International Conference on Genetic Algorithm, vol 1, pp 93–100
Schmidt LA, Farshi B (1973) Optimum laminate design for strength and stiffness. Int J Numer Methods Eng 7:519–536
Smith EC, Chopra I (1991) Formulation and evaluation of an analytical model for composite box-beams. J Am Helicopter Soc 36:23–35
Sobieszczanski-Sobieski J (1993) Two alternative ways for solving the coordination problem in multilevel optimization. Struct Multidisc Optim 6:205–215
Song SR, Hwang W, Park HC, Han KS (1995) Optimum stacking sequence design of composite laminates for maximum strength. Mech Compos Mater 31:77–86
Soremekun G, Gurdal Z, Haftka RT, Watson LT (2001) Composite laminate design optimization by genetic algorithm with generalized elitist selection. Comput Struct 79(2):131–143
Soykasap O, Hodges DH (2000) Performance enhancement of a composite tilt rotor using aeroelastic tailoring. J Aircr 37:850–858
Tauchert TR, Adibhatla S (1984) Design of laminated plate for maximum stiffness. J Compos Mater 18:58–69
Wolpert WG, Macready (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 11:67–82
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Murugan, M.S., Suresh, S., Ganguli, R. et al. Target vector optimization of composite box beam using real-coded genetic algorithm: a decomposition approach. Struct Multidisc Optim 33, 131–146 (2007). https://doi.org/10.1007/s00158-006-0030-1
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DOI: https://doi.org/10.1007/s00158-006-0030-1