Acta Mechanica

, Volume 229, Issue 4, pp 1551–1566 | Cite as

Buckling load of laminated composite plates using three variants of the biogeography-based optimization algorithm

  • A. Kaveh
  • A. Dadras
  • N. Geran Malek
Original Paper


This paper presents the application of the biogeography-based optimization (BBO) and some of its variants in the optimization of stacking sequence of laminated composites. Harmony search is also implemented to compare its results with those of the BBO. The optimization objective is to maximize the buckling load of a symmetric and balanced laminated plate. Four laminated composites with different loadings and dimensions are studied, and the statistical comparison of the obtained configurations and buckling load capacities shows the high capability of the BBO with quadratic migration model in terms of robustness and global search.


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  1. 1.
    Ghiasi, H., Pasini, D., Lessard, L.: Optimum stacking sequence design of composite materials. Part I: constant stiffness design. Compos. Struct. 90(1), 1–11 (2009).
  2. 2.
    Setoodeh, S., Abdalla, M.M., Gürdal, Z.: Design of variable-stiffness laminates using lamination parameters. Compos. Part B Eng. 37(4), 301–309 (2006)CrossRefGoogle Scholar
  3. 3.
    Fang, C., Springer, G.S.: Design of composite laminates by a Monte Carlo method. J. Compos. Mater. 27(7), 721–753 (1993)CrossRefGoogle Scholar
  4. 4.
    Kaveh, A.: Applications of Metaheuristic Optimization Algorithms in Civil Engineering. Springer, Basel (2017)CrossRefzbMATHGoogle Scholar
  5. 5.
    Talbi, E.-G.: Metaheuristics: From Design to Implementation, vol. 74. Wiley, Hoboken (2009)CrossRefzbMATHGoogle Scholar
  6. 6.
    Kaveh, A., Dadras, A.: A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv. Eng. Softw. 110(August), 69–84 (2017).
  7. 7.
    Kaveh, A., Dadras, A.: Structural damage identification using an enhanced thermal exchange optimization algorithm. Eng. Optim. (2017).
  8. 8.
    Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12(6), 702–713 (2008)CrossRefGoogle Scholar
  9. 9.
    Soremekun, G., Gürdal, Z., Haftka, R., Watson, L.: Composite laminate design optimization by genetic algorithm with generalized elitist selection. Comput. Struct. 79(2), 131–143 (2001)CrossRefGoogle Scholar
  10. 10.
    Lin, C.-C., Lee, Y.-J.: Stacking sequence optimization of laminated composite structures using genetic algorithm with local improvement. Compos. Struct. 63(3), 339–345 (2004)CrossRefGoogle Scholar
  11. 11.
    Rao, A.R.M., Arvind, N.: A scatter search algorithm for stacking sequence optimisation of laminate composites. Compos. Struct. 70(4), 383–402 (2005)CrossRefGoogle Scholar
  12. 12.
    Erdal, O., Sonmez, F.O.: Optimum design of composite laminates for maximum buckling load capacity using simulated annealing. Compos. Struct. 71(1), 45–52 (2005)CrossRefGoogle Scholar
  13. 13.
    Almeida, F., Awruch, A.: Design optimization of composite laminated structures using genetic algorithms and finite element analysis. Compos. Struct. 88(3), 443–454 (2009)CrossRefGoogle Scholar
  14. 14.
    Karakaya, Ş., Soykasap, Ö.: Buckling optimization of laminated composite plates using genetic algorithm and generalized pattern search algorithm. Struct. Multidiscip. Optim. 39(5), 477–486 (2009)CrossRefGoogle Scholar
  15. 15.
    Sebaey, T., Lopes, C., Blanco, N., Costa, J.: Ant colony optimization for dispersed laminated composite panels under biaxial loading. Compos. Struct. 94(1), 31–36 (2011)CrossRefGoogle Scholar
  16. 16.
    Abachizadeh, M., Tahani, M.: An ant colony optimization approach to multi-objective optimal design of symmetric hybrid laminates for maximum fundamental frequency and minimum cost. Struct. Multidiscip. Optim. 37(4), 367–376 (2009)CrossRefGoogle Scholar
  17. 17.
    Omkar, S., Senthilnath, J., Khandelwal, R., Naik, G.N., Gopalakrishnan, S.: Artificial Bee Colony (ABC) for multi-objective design optimization of composite structures. Appl. Soft Comput. 11(1), 489–499 (2011)CrossRefGoogle Scholar
  18. 18.
    de Almeida, F.S.: Stacking sequence optimization for maximum buckling load of composite plates using harmony search algorithm. Compos. Struct. 143, 287–299 (2016)CrossRefGoogle Scholar
  19. 19.
    Geem, Z.W., Kim, J.H., Loganathan, G.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)CrossRefGoogle Scholar
  20. 20.
    Vosoughi, A., Darabi, A., Forkhorji, H.D.: Optimum stacking sequences of thick laminated composite plates for maximizing buckling load using FE-GAs-PSO. Compos. Struct. 159, 361–367 (2017)CrossRefGoogle Scholar
  21. 21.
    Setoodeh, A., Shojaee, M.: Critical buckling load optimization of functionally graded carbon nanotube-reinforced laminated composite quadrilateral plates. Polym. Compos. (2017).
  22. 22.
    Guo, W., Wang, L., Wu, Q.: Numerical comparisons of migration models for multi-objective biogeography-based optimization. Inf. Sci. 328, 302–320 (2016)CrossRefGoogle Scholar
  23. 23.
    Simon, D., Ergezer, M., Du, D., Rarick, R.: Markov models for biogeography-based optimization. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 41(1), 299–306 (2011)Google Scholar
  24. 24.
    Bhattacharya, A., Chattopadhyay, P.K.: Biogeography-based optimization for different economic load dispatch problems. IEEE Trans. Power Syst. 25(2), 1064–1077 (2010)CrossRefGoogle Scholar
  25. 25.
    Wang, L., Xu, Y.: An effective hybrid biogeography-based optimization algorithm for parameter estimation of chaotic systems. Expert Syst. Appl. 38(12), 15103–15109 (2011)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Roy, P., Ghoshal, S., Thakur, S.: Optimal var control for improvements in voltage profiles and for real power loss minimization using biogeography based optimization. Int. J. Electr. Power Energy Syst. 43(1), 830–838 (2012)CrossRefGoogle Scholar
  27. 27.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H.: An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl. Math. Model. 38(9), 2454–2462 (2014)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Aydogdu, I.: Cost optimization of reinforced concrete cantilever retaining walls under seismic loading using a biogeography-based optimization algorithm with Levy flights. Eng. Optim. 49(3), 381–400 (2017)CrossRefGoogle Scholar
  29. 29.
    Aydogdu, I., Akin, A.: Biogeography based Co\(_{2}\) and cost optimization of RC cantilever retaining walls. In: 17th International Conference on Structural Engineering, pp. 1480–1485 (2015)Google Scholar
  30. 30.
    Saka, M., Carbas, S., Aydogdu, I., Akin, A., Geem, Z.: Comparative study on recent metaheuristic algorithms in design optimization of cold-formed steel structures. In: Engineering and Applied Sciences Optimization, pp. 145–173. Springer, Berlin (2015)Google Scholar
  31. 31.
    Jalili, S., Hosseinzadeh, Y., Taghizadieh, N.: A biogeography-based optimization for optimum discrete design of skeletal structures. Eng. Optim. 48(9), 1491–1514 (2016)CrossRefGoogle Scholar
  32. 32.
    Çarbaş, S.: Optimum structural design of spatial steel frames via biogeography-based optimization. Neural Comput. Appl. 28(6), 1525–1539 (2017)CrossRefGoogle Scholar
  33. 33.
    Yang, G., Liu, Y.: Optimizing an equilibrium supply chain network design problem by an improved hybrid biogeography based optimization algorithm. Appl. Soft Comput. 58, 657–668 (2017)Google Scholar
  34. 34.
    Kaveh, A., Dadras, A.: Optimal decomposition of finite element meshes via k-median methodology and different metaheuristics. Int. J. Optim. Civil Eng. 8(2), 227–246 (2018)Google Scholar
  35. 35.
    Ma, H., Simon, D.: Evolutionary Computation with Biogeography-Based Optimization. Wiley, Hoboken (2017)CrossRefGoogle Scholar
  36. 36.
    Wu, J., Vankat, J.L.: Island biogeography: theory and applications. Encycl. Environ. Biol. 2, 371–379 (1995)Google Scholar
  37. 37.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning, vol. 2. Addison-Wesley, Reading (1989)Google Scholar
  38. 38.
    Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)zbMATHGoogle Scholar
  39. 39.
    Haftka, R.T., Gürdal, Z.: Elements of Structural Optimization, vol. 11. Springer Science & Business Media, Berlin (2012)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Centre of Excellence for Fundamental Studies in Structural EngineeringIran University of Science and TechnologyTehranIran
  2. 2.School of Automotive EngineeringIran University of Science and TechnologyNarmak, TehranIran

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