Geometrically Nonlinear Analysis of Trusses Using Particle Swarm Optimization

  • Rasim Temür
  • Yusuf Sait Türkan
  • Yusuf Cengiz TokluEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 585)


Particle swarm optimization (PSO) algorithm is a heuristic optimization technique based on colony intelligence, developed through inspiration from social behaviors of bird flocks and fish schools. It is widely used in problems in which the optimal value of an objective function is searched. Geometrically nonlinear analysis of trusses is a problem of this kind. The deflected shape of the truss where potential energy value is minimal is known to correspond to the stable equilibrium position of the system analyzed. The objective of this study is to explore the success of PSO using this minimum total potential energy principle, in finding good solutions to geometrically nonlinear truss problems. For this purpose analyses are conducted on three structures, two plane trusses and a space truss. The results obtained show that in case of using 20 or more particles, PSO produces very good and robust solutions.


Particle swarm optimization Structural analysis Truss systems Nonlinear analysis Potential energy TPO/MA 


  1. 1.
    Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan (1995). doi: 10.1109/MHS.1995.494215
  2. 2.
    Oden, J.T.: Mechanics of Elastic Structures. McGraw-Hill, New York (1967)Google Scholar
  3. 3.
    Toklu, Y.C.: Nonlinear analysis of trusses through energy minimization. Comput. Struct. 82(20–21), 1581–1589 (2004). doi: 10.1016/j.compstruc.2004.05.008 CrossRefGoogle Scholar
  4. 4.
    Merkle, D., Middendorf, M.: Swarm Intelligence. In: Burke, E.K., Kendall, H. (eds.) Search Methodologies Introductory Tutorials in Optimization and Decision Support Techniques, p. 417. Springer, New York (2005)Google Scholar
  5. 5.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings IEEE International Conference on Neural Networks, November–December 1995, vol. 4, p. 1942. Perth, Australia (1995). doi: 10.1109/ICNN.1995.488968
  6. 6.
    Ortakcı, Y., Göloğlu, C.: Determination of cluster numbers via particle swarm optimization. In: Proceedings of 14th Conference on Academic Information 1–3 February 2012, Usak University, Usak, Turkey, pp. 335–341 (2012)Google Scholar
  7. 7.
    Shi, Y.H., Eberhart, R.C.: (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 69–73. doi: 10.1109/ICEC.1998.699146
  8. 8.
    Mises, R.V.: Über die stabilitätsprobleme der elastizitätstheorie. ZAMM-J Appl. Math. Mech./Z. für Angew Math. und Mechanik 3(6), 406–422 (1923). doi: 10.1002/zamm.19230030602 CrossRefzbMATHGoogle Scholar
  9. 9.
    Mises, R.V., Ratzersdorfer, J.: Die knicksicherheit von fachwerken. ZAMM-J. Appl. Math. Mech./Z. für Angew. Math. und Mechanik 5(3), 218–235 (1925). doi: 10.1002/zamm.19250050305 CrossRefzbMATHGoogle Scholar
  10. 10.
    Kondoh, K., Atluri, S.N.: Influence of local buckling on global instability: Simplified, large deformation, post-buckling analyses of plane trusses. Comput. Struct. 21(4), 613–627 (1985). doi: 10.1016/0045-7949(85)90140-3 CrossRefzbMATHGoogle Scholar
  11. 11.
    Kaveh, A., Rahami, H.: Nonlinear analysis and optimal design of structures via force method and genetic algorithm. Comput. Struct. 84(12), 770–778 (2006). doi: 10.1016/j.compstruc.2006.02.004 CrossRefGoogle Scholar
  12. 12.
    Kaveh, A., Hassani, M.: Ant colony algorithms for nonlinear analysis and optimal design of structures. Int. J. Optim. Civil Eng. 1(4), 571–595 (2011)Google Scholar
  13. 13.
    Toklu, Y.C., Bekdaş, G., Temur, R.: Analysis of trusses by total potential optimization method coupled with harmony search. Struct. Eng. Mech. 45(2), 183–199 (2013). doi: 10.12989/sem.2013.45.2.183 CrossRefGoogle Scholar
  14. 14.
    Venkayya, V.B.: Design of optimum structures. Comput. Struct. 1(1–2), 265–309 (1971). doi: 10.1016/0045-7949(71)90013-7 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Rasim Temür
    • 1
  • Yusuf Sait Türkan
    • 2
  • Yusuf Cengiz Toklu
    • 3
    Email author
  1. 1.Department of Civil Engineering, Faculty of EngineeringIstanbul UniversityIstanbulTurkey
  2. 2.Open and Distance Education FacultyIstanbul UniversityIstanbulTurkey
  3. 3.Department of Civil Engineering, Faculty of EngineeringBilecik Seyh Edebali UniversityBilecikTurkey

Personalised recommendations