, Volume 47, Issue 3, pp 719–730 | Cite as

Stacking sequence optimization of composite plates for maximum fundamental frequency using particle swarm optimization algorithm

  • H. Ghashochi Bargh
  • M. H. Sadr


The paper illustrates the application of the particle swarm optimization (PSO) algorithm to the lay-up design of symmetrically laminated composite plates for maximization of fundamental frequency. The design variables are the fiber orientation angles, edge conditions and plate length/width ratios. The formulation is based on the classical laminated plate theory (CLPT), and the method of analysis is the semi-analytical finite strip approach which has been developed on the basis of full energy methods. The performance of the PSO is also compared with the simple genetic algorithm and shows the good efficiency of the PSO algorithm. To check the validity, the obtained results are compared with those available in the literature and some other stacking sequences, wherever possible.


Composite plates PSO algorithm Finite strip Optimization 


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  1. 1.
    Bert CW (1977) Optimal design of a composite material plate to maximise its fundamental frequency. J Sound Vib 50:229–237 CrossRefADSGoogle Scholar
  2. 2.
    Bert CW (1978) Design of clamped composite plates to maximise fundamental frequency. J Mech Des 100:274–278 CrossRefGoogle Scholar
  3. 3.
    Grenested JL (1989) Lay-up optimization and sensitivity analysis of fundamental eigenfrequency of composite plates. Compos Struct 12(3):193–209 CrossRefGoogle Scholar
  4. 4.
    Chow ST, Liew KM, Lam KY (1992) Transverse vibration of symmetrically laminated rectangular composite plates. Compos Struct 20:213–226 CrossRefGoogle Scholar
  5. 5.
    Fan SC, Cheung YK (1984) Flexural free vibrations of rectangular plates with complex support conditions. J Sound Vib 93:81–94 CrossRefADSGoogle Scholar
  6. 6.
    Leissa AW, Martin AF (1990) Vibration buckling of rectangular composite plates with variable fibre spacing. Compos Struct 14:339–357 CrossRefGoogle Scholar
  7. 7.
    Qatu MS (1991) Free vibration of laminated composite rectangular plates. Int J Solids Struct 28(8):941–954 CrossRefGoogle Scholar
  8. 8.
    Rao MK, Desai YM (2003) Analytical solutions for vibrations of laminated and sandwich plates using mixed theory. Compos Struct 63:361–373 CrossRefGoogle Scholar
  9. 9.
    TY Kam, Chang RR (1993) Design of laminated composite plate for maximum buckling load and vibration frequency. Comput Methods Appl Mech Eng 106:65–81 CrossRefGoogle Scholar
  10. 10.
    Chen J, Dawe DJ (1996) Linear transient analysis of rectangular laminated plates by a finite strip-mode superposition method. Compos Struct 35:213–228 CrossRefGoogle Scholar
  11. 11.
    Chai GB (1994) Free vibration of generally laminated composite plates with various edge support conditions. Compos Struct 29:249–258 CrossRefGoogle Scholar
  12. 12.
    Narita Y (2003) Layerwise optimization for the maximum fundamental frequency of laminated composite plates. J Sound Vib 263:1005–1016 CrossRefADSGoogle Scholar
  13. 13.
    Apalak MK, Yildirim M, Ekici R (2008) Layer optimisation for maximum fundamental frequency of laminated composite plates for different edge conditions. Compos Sci Technol 68:537–550 CrossRefGoogle Scholar
  14. 14.
    Khalil MR, Olson MD, Anderson DL (1988) Non-linear dynamic analysis of stiffened plates. Comput Struct 29:929–941 CrossRefMATHGoogle Scholar
  15. 15.
    Houlston R (1989) Finite strip analysis of plates and stiffened panels subjected to air blast loads. Comput Struct 32:647–659 CrossRefMATHGoogle Scholar
  16. 16.
    Loughlan J (2001) The shear buckling behaviour of thin composite plates with particular reference to the effects of bend-twist coupling. Int J Mech Sci 43:771–792 CrossRefMATHGoogle Scholar
  17. 17.
    Ovesy HR, Ghannadpour SAM, Morada G (2005) Geometric non-linear analysis of composite laminated plates with initial imperfection under end shortening, using two versions of finite strip method. Compos Struct 71:307–314 CrossRefGoogle Scholar
  18. 18.
    Assaee H, Ovesy HR (2007) A multi-term semi-energy finite strip method for post-buckling analysis of composite plates. Int J Numer Methods Eng 70:1303–1323 CrossRefMATHGoogle Scholar
  19. 19.
    Assaee H (2008) Post-local buckling analysis of composite thin-walled sections using semi-finite strip method. PhD Thesis, Amirkabir University of Technology, Iran Google Scholar
  20. 20.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proc. IEEE int’l conf on neural networks, vol IV. IEEE Service Center, Piscataway, pp 1942–1948 CrossRefGoogle Scholar
  21. 21.
    Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, Nagoya, Japan. IEEE Service Center, Piscataway, pp 39–43 CrossRefGoogle Scholar
  22. 22.
    Kathiravan R, Ganguli R (2007) Strength design of composite beam using gradient and particle swarm optimization. Compos Struct 81:471–479 CrossRefGoogle Scholar
  23. 23.
    Nadjah N (2006) Swarm intelligent systems. Springer, Berlin CrossRefGoogle Scholar
  24. 24.
    Perera R, Fang SE, Ruiz A (2010) Application of particle swarm optimization and genetic algorithms to multiobjective damage identification inverse problems with modeling errors. Meccanica 45:723–734 CrossRefMATHGoogle Scholar
  25. 25.
    Vinson JR, Sierakowski RL (1986) The behavior of structures composed of composite materials. Martinus Nijhoff, Dordrecht MATHGoogle Scholar
  26. 26.
    Ganguli R, Chopra I (1995) Aeroelastic optimization of a helicopter rotor with composite coupling. J Aircr 32:1326–1334 CrossRefGoogle Scholar
  27. 27.
    Ganguli R, Chopra I (1996) Aeroelastic optimization of a helicopter rotor with two-cell composite blades. AIAA J 34:835–841 CrossRefADSGoogle Scholar
  28. 28.
    Murugan MS, Ganguli R (2005) Aeroelastic stability enhancement and vibration suppression in a composite helicopter rotor. J Aircr 42:1013–1024 CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Aerospace Engineering Department, Center of Excellence in Computational Aerospace EngineeringAmirkabir University of TechnologyTehranIran

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