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Optimal Analysis and Design of Large-Scale Domes with Frequency Constraints

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Applications of Metaheuristic Optimization Algorithms in Civil Engineering

Abstract

Structural optimization involves a large number of structural analyses. When optimizing large structures, these analyses require a considerable amount of computational time and effort. However, there are specific types of structure for which the results of the analysis can be achieved in a much simpler and quicker way due to their special repetitive patterns. In this chapter, frequency constraint optimization of cyclically repeated space trusses is considered. An efficient technique is used to decompose the large initial eigenproblem into several smaller ones and thus to decrease the required computational time significantly (Kaveh and Zolghadr [1]).

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References

  1. Kaveh A, Zolghadr A (2016) Optimal analysis and design of large-scale domes with frequency constraints. Smart Struct Syst 18(5):733–754

    Google Scholar 

  2. Grandhi RV (1993) Structural optimization with frequency constraints—a review. AIAA J 31(12):2296–2303

    Article  MATH  Google Scholar 

  3. Taylor JE (1967) Minimum mass bar for axial vibration at specified natural frequency. AIAA J 5(10):1911–1913

    Article  Google Scholar 

  4. Armand JL (1971) Minimum mass design of a plate like structure for specified fundamental frequency. AIAA J 9(9):1739–1745

    Article  MathSciNet  MATH  Google Scholar 

  5. Cardou A, Warner WH (1974) Minimum mass design of sandwich structures with frequency and section constraints. J Optim Theory Appl 14(6):633–647

    Article  MathSciNet  MATH  Google Scholar 

  6. Elwany MHS, Barr ADS (1979) Minimum weight design of beams in torsional vibration with several frequency constraints. J Sound Vib 62(3):411–425

    Article  MATH  Google Scholar 

  7. Lin JH, Chen WY, Yu YS (1982) Structural optimization on geometrical configuration and element sizing with static and dynamic constraints. Comput Struct 15(5):507–515

    Article  Google Scholar 

  8. Konzelman CJ (1986) Dual methods and approximation concepts for structural optimization. MSc thesis, Department of Mechanical Engineering, University of Toronto, Canada

    Google Scholar 

  9. Grandhi RV, Venkayya VB (1988) Structural optimization with frequency constraints. AIAA J 26(7):858–866

    Article  MathSciNet  MATH  Google Scholar 

  10. Sedaghati R, Suleman A, Tabarrok B (2002) Structural optimization with frequency constraints using finite element force method. AIAA J 40(2):382–388

    Article  Google Scholar 

  11. Lingyun W, Mei Z, Guangming W, Guang M (2005) Truss optimization on shape and sizing with frequency constraints based on genetic algorithm. J Comput Mech 35(5):361–368

    Article  MATH  Google Scholar 

  12. Gomes MH (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38(1):957–968

    Article  Google Scholar 

  13. Kaveh A, Zolghadr A (2014) Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints. Adv Eng Softw 76:9–30

    Article  Google Scholar 

  14. Kaveh A, Zolghadr A (2014) Democratic PSO for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21

    Article  Google Scholar 

  15. Kaveh A, Rahami H (2006) Block diagonalization of adjacency and Laplacian matrices for graph product; applications in structural mechanics. Int J Numer Methods Eng 68(1):33–63

    Article  MathSciNet  MATH  Google Scholar 

  16. Kaveh A, Rahami H (2007) Compound matrix block diagonalization for efficient solution of eigenproblems in structural mechanics. Acta Mech 188(3–4):155–166

    Article  MATH  Google Scholar 

  17. Kaveh A (2013) Optimal analysis of structures by concepts of symmetry and regularity. Springer, Wien, New York, NY

    Book  MATH  Google Scholar 

  18. Koohestani K, Kaveh A (2010) Efficient buckling and free vibration analysis of cyclically repeated space truss structures. Finite Elem Anal Des 46(10):943–948

    Article  Google Scholar 

  19. Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc 49:1–23

    Article  MathSciNet  MATH  Google Scholar 

  20. Leung AYT (1980) Dynamic analysis of periodic structures. J Sound Vib 72(4):451–467

    Article  MATH  Google Scholar 

  21. Williams FW (1986) An algorithm for exact eigenvalue calculations for rotationally periodic structures. Int J Numer Methods Eng 23(4):609–622

    Article  MathSciNet  MATH  Google Scholar 

  22. Vakakis AF (1992) Dynamics of a nonlinear periodic structure with cyclic symmetry. Acta Mech 95(1–4):197–226

    Article  MathSciNet  MATH  Google Scholar 

  23. Karpov EG, Stephen NG, Dorofeev DL (2002) On static analysis of finite repetitive structures by discrete Fourier transform. Int J Solids Struct 39(16):4291–4310

    Article  MATH  Google Scholar 

  24. Liu L, Yang H (2007) A paralleled element-free Galerkin analysis for structures with cyclic symmetry. Eng Comput 23(2):137–144

    Article  Google Scholar 

  25. El-Raheb M (2011) Modal properties of a cyclic symmetric hexagon lattice. Comput Struct 89:2249–2260

    Article  Google Scholar 

  26. Zingoni A (2014) Group-theoretic insights on the vibration of symmetric structures in engineering. Philos Trans R Soc A 372:20120037

    Article  MathSciNet  Google Scholar 

  27. Tran D-M (2014) Reduced models of multi-stage cyclic structures using cyclic symmetry reduction and component mode synthesis. J Sound Vib 333:5443–5463

    Article  Google Scholar 

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Authors and Affiliations

  1. Iran University of Science and Technology, Centre of Excellence for Fundamental Studies in Structural Engineering, Tehran, Iran

    A. Kaveh

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  1. A. Kaveh
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Kaveh, A. (2017). Optimal Analysis and Design of Large-Scale Domes with Frequency Constraints. In: Applications of Metaheuristic Optimization Algorithms in Civil Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-48012-1_14

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  • DOI: https://doi.org/10.1007/978-3-319-48012-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48011-4

  • Online ISBN: 978-3-319-48012-1

  • eBook Packages: EngineeringEngineering (R0)

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