Optimal Design of Dome-Shaped Trusses

Chapter

Abstract

Domes are one of the oldest and well-established structural forms and have been used in architecture since the earliest times. These structures are of special interest to engineers as they enclose large spaces with small surfaces and have proven to be very economical in terms of consumption of constructional materials. The main aim of this chapter is frequency constraint optimization of dome truss structures; however, all the domes are also optimized considering strength, stability, and displacement constraints. Structural optimization considering natural frequency constraints is believed to represent nonlinear and non-convex search spaces with several local optima. In this class of problems, large generalized eigenproblems should be solved in order to find the natural frequencies of the structure. The size of the structure affects the dimensions of the matrices involved and thus the required computational time and effort. On the other hand, as the number of optimization variables increases, more and more structural analyses are needed to be performed in order to reach a near-optimal solution.

References

  1. 1.
    Lan TT (2005) Space frame structures. Handbook of structural Engineering. CRC Press, Boca Raton, FL, pp 24–31Google Scholar
  2. 2.
    Bellagamba L, Yang TY (1981) Minimum mass truss structures with constraints on fundamental natural frequency. AIAA J 19:1452–1458CrossRefGoogle Scholar
  3. 3.
    Kaveh A, Zolghadr A (2016) Optimal design and analysis of large-scale domes with frequency constraints. Smart Struct Syst 18(4):733–754CrossRefGoogle Scholar
  4. 4.
    Lin JH, Chen WY, Yu YS (1982) Structural optimization on geometrical configuration and element sizing with static and dynamic constraints. Comput Struct 15:507–515CrossRefGoogle Scholar
  5. 5.
    Konzelman CJ (1986) Dual methods and approximation concepts for structural optimization. M.Sc. Thesis, Department of Mechanical Engineering, University of Toronto, CanadaGoogle Scholar
  6. 6.
    Grandhi RV, Venkayya VB (1988) Structural optimization with frequency constraints. AIAA J 26:858–866CrossRefGoogle Scholar
  7. 7.
    Wang D, Zha W, Jiang J (2004) Truss optimization on shape and sizing with frequency constraints. AIAA J 42:622–630CrossRefGoogle Scholar
  8. 8.
    Sedaghati R (2005) Benchmark case studies in structural design optimization using the force method. Int J Solids Struct 42:5848–5871CrossRefGoogle Scholar
  9. 9.
    Lingyun W, Mei Z, Guangming W, Guang M (2005) Truss optimization on shape and sizing with frequency constraints based on genetic algorithm. Comput Mech 35:361–368CrossRefGoogle Scholar
  10. 10.
    Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968CrossRefGoogle Scholar
  11. 11.
    Kaveh A, Zolghadr A (2012) Truss optimization with natural frequency constraints using a hybridized CSS–BBBC algorithm with trap recognition capability. Comput Struct 102–103:14–27CrossRefGoogle Scholar
  12. 12.
    Miguel LFF, Fadel Miguel LF (2012) Shape and size optimization of truss structures considering dynamic constraints through modern meta-heuristic algorithms. Expert Syst Appl 39:9458–9467CrossRefGoogle Scholar
  13. 13.
    Zuo W, Bai J, Li B (2014) A hybrid OC–GA approach for fast and global truss optimization with frequency constraints. Appl Soft Comput 14:528–535CrossRefGoogle Scholar
  14. 14.
    Kaveh A, Javadi SM (2014) Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm. Acta Mech 225:1595–1605CrossRefGoogle Scholar
  15. 15.
    Kaveh A, Ilchi Ghazaan M (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147CrossRefGoogle Scholar
  16. 16.
    Hosseinzadeh Y, Taghizadieh N, Jalili S (2016) Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints. Neural Comput Appl 27(4):953–971CrossRefGoogle Scholar
  17. 17.
    American Institute of Steel Construction (AISC) (1989) Manual of steel construction: allowable stress design, Chicago, USAGoogle Scholar
  18. 18.
    Kaveh A, Ilchi Ghazaan M (2017) Optimal design of dome truss structures with dynamic frequency constraints. Struct Multidiscip Optim 53(3):605–621MathSciNetCrossRefGoogle Scholar
  19. 19.
    Kaveh A, Ilchi Ghazaan M (2016) Vibrating particles system algorithm for truss optimization with multiple natural frequency constraints. Acta Mech 228(1):307–322. (Published online, 1–16)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Kaveh A, Ilchi Ghazaan M (2018) A new hybrid meta-heuristic algorithm for optimal design of large-scale dome structures. Eng Optimiz 50(2):235–252MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringIran University of Science and TechnologyTehranIran

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