Bio-inspired Optimization Algorithms for Limit Analysis of Frame Structures

  • Annalisa GrecoEmail author
  • Alessandro Pluchino
  • Francesco Cannizzaro
  • Ilaria Fiore
Conference paper


The present study applies the method of combination of elementary mechanisms to the evaluation of collapse conditions of planar frames. The collapse load is evaluated seeking the absolute lowest value among all the mechanisms that can be obtained combining the elementary ones. The optimization procedure is developed through three different bio-inspired optimization algorithms. In particular, genetic, immune and ant colony algorithms are considered. Original codes developed in the agent-based programming language NetLogo allow building into a virtual metrical space and visualizing in the user interface every single mechanism and the correspondent collapse load. The elementary mechanisms are then combined and the minimum collapse load, together with the corresponding collapse mechanism, is obtained. Several applications have been performed with reference to frames of different size subjected to a seismic load scenario consisting of horizontal forces with increasing magnitude acting on each floor, and permanent vertical loads applied to the beams. The collapse loads and related mechanisms, obtained by means of the proposed optimization procedures, have been compared to the correspondent ones provided by nonlinear push over analysis, showing a very good correspondence.


Limit analysis Seismic behaviour Elementary mechanisms method Ant colony system optimization Genetic algorithms Immune algorithms 


  1. 1.
    Neal, B.G., Symonds, P.S.: The calculations of collapse loads for framed structures. J. Inst. Civ. Eng. 35, 21–40 (1951)CrossRefGoogle Scholar
  2. 2.
    Rajeev, S., Krishnamoorthy, C.S.: Discrete optimization of structures using genetic algorithms. J. Struct. Eng. 118(5), 1233–1250 (1992)CrossRefGoogle Scholar
  3. 3.
    Chou, J.-H., Ghaboussi, J.: Genetic algorithm in structural damage detection. Comput. Struct. 79(14), 1335–1353 (2001)CrossRefGoogle Scholar
  4. 4.
    Kaveh, A., Jahanshahi, M.: Plastic analysis of planar frames using kinematic method and genetic algorithm. Asian J. Civ. Eng. (Build. Hous.) 5(3), 145–160 (2004)Google Scholar
  5. 5.
    Greco, A., Cannizzaro, F., Pluchino, A.: Seismic collapse prediction of frame structures by means of genetic algorithms. Eng. Struct. 143, 152–168 (2017)CrossRefGoogle Scholar
  6. 6.
    Greco, A., D’Urso, D., Cannizzaro, F., Pluchino, A.: Damage identification on spatial Timoshenko arches by means of genetic algorithms. Mech. Syst. Signal Process. 105, 51–67 (2018)CrossRefGoogle Scholar
  7. 7.
    Greco, A., Pluchino, A., Cannizzaro, F., Caddemi, S., Caliò, I.: Closed-form solution based genetic algorithm software: application to multiple cracks detection on beam structures by static tests. Appl. Soft Comput. J. 64, 35–48 (2018)CrossRefGoogle Scholar
  8. 8.
    Greco, A., Cannizzaro, F., Pluchino, A.: Automatic evaluation of plastic collapse conditions for planar frames with vertical irregularities. Eng. Comput. (2018).
  9. 9.
    De Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Berlin (2002)zbMATHGoogle Scholar
  10. 10.
    Dorigo, M., Di Caro, G.: The Ant Colony Optimization Meta-Heuristic. McGraw-Hill Ltd., New York (1999)CrossRefGoogle Scholar
  11. 11.
    Kaveh, A., Jahanshahi, M.: Plastic limit analysis of frames using ant colony systems. Comput. Struct. 86, 1152–1163 (2008)CrossRefGoogle Scholar
  12. 12.
    Mazzolani, F., Piluso, V.: Plastic design of seismic resistant steel frames. Earthq. Eng. Struct. Dynm. 26, 167–191 (1997)CrossRefGoogle Scholar
  13. 13.
    Greco, A., Cannizzaro, F., Pluchino, A.: An improved ant colony optimization algorithm for limit analysis of frame structures. Eng. Optim. Under reviewGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Annalisa Greco
    • 1
    Email author
  • Alessandro Pluchino
    • 2
  • Francesco Cannizzaro
    • 1
  • Ilaria Fiore
    • 1
  1. 1.Department of Civil Engineering and ArchitectureUniversity of CataniaCataniaItaly
  2. 2.Department of Physics and AstronomyUniversity of CataniaCataniaItaly

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