Optimization and Engineering

, Volume 13, Issue 1, pp 79–100 | Cite as

Shape optimal design of materially nonlinear arch dams including dam-water-foundation rock interaction using an improved PSO algorithm

  • Seyed Mohammad Seyedpoor
  • Javad Salajegheh
  • Eysa Salajegheh


An efficient optimization procedure is proposed to find the optimal shape of arch dams including dam-water-foundation rock interaction subject to earthquake. The arch dam is treated as a three-dimensional structure involving the material nonlinearity effects. For this purpose, the nonlinear behavior of the dam concrete is idealized as an elasto-plastic material using the Drucker-Prager model. In order to reduce the computational cost of optimization process, a wavelet back propagation (WBP) neural network is designed to approximate the dam response instead of directly evaluating it by a time-consuming finite element analysis (FEA). An improved particle swarm optimization (IPSO) is also presented. In test example, the computational merits of the proposed methodology for optimizing an existing arch dam are demonstrated.


Concrete arch dam Earthquake loading Nonlinear effects Approximation concept Improved particle swarm optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aftabi Sani A, Lotfi V (2007) Linear dynamic analysis of arch dams utilizing modified efficient fluid hyper-element. Eng Struct 29(10):2654–2661 CrossRefGoogle Scholar
  2. Akkose M, Bayraktar A, Dumanoglu AA (2008a) Reservoir water level effects on nonlinear dynamic response of arch dams. J Fluids Struct 24(3):418–435 CrossRefGoogle Scholar
  3. Akkose M, Adanur S, Bayraktar A, Dumanoglu AA (2008b) Elasto-plastic earthquake response of arch dams including fluid–structure interaction by the Lagrangian approach. Appl Math Model 32(11):2396–2412 CrossRefGoogle Scholar
  4. ANSYS Inc. Theory Reference (2006) Release 10.0 Documentation for ANSYS, ANSYS Inc Google Scholar
  5. Bathe KJ (1996) Finite element procedures. Prentice-Hall, Englewood Cliffs Google Scholar
  6. Chen WF (1982) Plasticity in reinforced concrete. McGraw-Hill, New York Google Scholar
  7. Daubechies I (1992) Ten lectures on wavelets. SIAM, Philadelphia MATHCrossRefGoogle Scholar
  8. Duron ZH, Hall JF (1988) Experimental and finite element studies of the forced vibration response of morrow point dam. Earthquake Eng Struct Dyn 16(7):1021–1039 CrossRefGoogle Scholar
  9. Fok KL, Chopra AK (1985) Earthquake analysis and response of concrete arch dams. Report No. UCB/EERC 85/07, Earthquake Engineering Research Center, University of California, Berkeley Google Scholar
  10. Gholizadeh S, Salajegheh E, Torkzadeh P (2008) Structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network. J Sound Vib 312(1–2):316–331 CrossRefGoogle Scholar
  11. Gholizadeh S, Salajegheh E (2009) Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel. Comput Methods Appl Mech Eng 198(37–40):2936–2949 MATHCrossRefGoogle Scholar
  12. Hall JF, Chopra AK (1983) Dynamic analysis of arch dams including hydrodynamic effects. J Eng Mech 109(1):149–167 CrossRefGoogle Scholar
  13. Hagan MT, Menhaj M (1994) Training feed-forward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5(6):989–993 CrossRefGoogle Scholar
  14. Hamidian D, Seyedpoor SM (2010) Shape optimal design of arch dams using an adaptive neuro-fuzzy inference system and improved particle swarm optimization. Appl Math Model 34(6):1574–1585 MathSciNetMATHCrossRefGoogle Scholar
  15. Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7-8):340–349 CrossRefGoogle Scholar
  16. Li S, Ding L, Zhao L, Zhou W (2009) Optimization design of arch dam shape with modified complex method. Adv Eng Softw 40:804–808 MATHCrossRefGoogle Scholar
  17. Perez RE, Behdinan K (2007) Particle swarm approach for structural design optimization. Comput Struct 85(19–20):1579–1588 CrossRefGoogle Scholar
  18. PEER: Pacific Earthquake Engineering Research Center (2009) Available from:
  19. Salajegheh E, Heidari A (2005) Optimum design of structures against earthquake by wavelet neural network and filter banks. Earthquake Eng Struct Dyn 34(1):67–82 CrossRefGoogle Scholar
  20. Salajegheh E, Gholizadeh S, Khatibinia M (2008a) Optimal design of structures for earthquake loads by a hybrid RBF-BPSO method. Earthq Eng Eng Vib 7(1):14–24 CrossRefGoogle Scholar
  21. Salajegheh J, Salajegheh E, Seyedpoor SM (2008b) Optimum design of socket joint systems for space structures using second order approximation. Int J Space Struct 23(1):35–43 CrossRefGoogle Scholar
  22. Salajegheh E, Salajegheh J, Seyedpoor SM, Khatibinia M (2009) Optimal design of geometrically nonlinear space trusses using adaptive neuro-fuzzy inference system. Sci Iran 16(5):403–414 Google Scholar
  23. Seyedpoor SM, Salajegheh J, Salajegheh E, Golizadeh S (2009) Optimum shape design of arch dams for earthquake loading using a fuzzy inference system and wavelet neural networks. Eng Optim 41(5):473–493 MathSciNetCrossRefGoogle Scholar
  24. Seyedpoor SM, Salajegheh J, Salajegheh E, Gholizadeh S (2011) Optimal design of arch dams subjected to earthquake loading by a combination of simultaneous perturbation stochastic approximation and particle swarm algorithms. Appl Soft Comput 11(1):39–48 CrossRefGoogle Scholar
  25. Schroeder EA, Marcus MS (1975) Finite element solution of fluid-structure interaction problems. Presented at 46th shock and vibration symposium, San Diego, CA Google Scholar
  26. Sun L, Zhang W, Xie N (2007) Multi-objective optimization for shape design of arch dams. In: Computational methods in engineering and science, part 9: Structural optimization. Springer Berlin. Available from: Google Scholar
  27. Tan H, Chopra AK (1996) Dam-foundation rock interaction effects in earthquake response of arch dams. J Struct Eng 122(5):528–538 CrossRefGoogle Scholar
  28. USBR United State Department of Interior Bureau of Reclamation (1977) Design criteria for concrete arch and gravity dams. US Government Printing Office, Washington Google Scholar
  29. Varshney RS (1982) Concrete dams. Oxford IBH, New Delhi Google Scholar
  30. Wasserman K (1983) Three dimensional shape optimization of arch dams with prescribed shape function. J Struct Mech 11(4):465–489 CrossRefGoogle Scholar
  31. William KJ, Warnke ED (1975) Constitutive model for the triaxial behavior of concrete. In: Proceedings of international association for bridge and structural engineering, vol 19, ISMES, Bergamo, p 174 Google Scholar
  32. Yao TM, Choi KK (1989) Shape optimal design of an arch dam. J Struct Eng 115(9):2401–2405 CrossRefGoogle Scholar
  33. Zhang XF, Li SY, Chen YL (2009) Optimization of geometric shape of Xiamen arch dam. Adv Eng Softw 40:105–109 MATHCrossRefGoogle Scholar
  34. Zhu B, Rao B, Jia J, Li Y (1992) Shape optimization of arch dam for static and dynamic loads. J Struct Eng 118(11):2996–3015 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Seyed Mohammad Seyedpoor
    • 1
  • Javad Salajegheh
    • 2
  • Eysa Salajegheh
    • 2
  1. 1.Department of Civil EngineeringShomal UniversityAmolIran
  2. 2.Department of Civil EngineeringUniversity of KermanKermanIran

Personalised recommendations