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Optimal analysis and design of large-scale domes with frequency constraints

  • Kaveh, A. (Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology) ;
  • Zolghadr, A. (Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology)
  • Received : 2015.06.10
  • Accepted : 2016.04.26
  • Published : 2016.10.25

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 thanks to their special repetitive patterns. In this paper, 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. Some examples are presented in order to illustrate the efficiency of the presented method.

Keywords

Acknowledgement

Supported by : Iran National Science Foundation

References

  1. Armand, J.L. (1971), "Minimum mass design of a plate like structure for specified fundamental frequency", AIAA J., 9(9), 1739-1745. https://doi.org/10.2514/3.6424
  2. Cardou, A. and Warner, W.H. (1974), "Minimum mass design of sandwich structures with frequency and section constraints", J. Optim. Theory Appl., 14(6), 633-647. https://doi.org/10.1007/BF00932965
  3. Courant, R. (1943), "Variational methods for the solution of problems of equilibrium and vibrations", Bull. Am. Math. Soc., 49, 1-23.
  4. El-Raheb, M. (2011), "Modal properties of a cyclic symmetric hexagon lattice", Comput. Struct., 89, 2249-2260. https://doi.org/10.1016/j.compstruc.2011.08.011
  5. Elwany M.H.S. and Barr A.D.S. (1979), "Minimum weight design of beams in torsional vibration with several frequency constraints", J. Sound Vib., 62(3), 411-425. https://doi.org/10.1016/0022-460X(79)90633-3
  6. Gomes, M.H. (2011), "Truss optimization with dynamic constraints using a particle swarm algorithm", Exp. Syst. Appl., 38(1), 957-968. https://doi.org/10.1016/j.eswa.2010.07.086
  7. Grandhi, R.V. (1993), "Structural optimization with frequency constraints - A review", AIAA J., 31(12), 2296-2303. https://doi.org/10.2514/3.11928
  8. Grandhi, R.V. and Venkayya, V.B. (1988), "Structural optimization with frequency constraints", AIAA J., 26(7), 858-866. https://doi.org/10.2514/3.9979
  9. Hussey, M.J.L. (1967), "General theory of cyclically symmetric frames", J. Struct. Div. - ASCE, 93(3), 167-176.
  10. Karpov, E.G., Stephen, N.G. and Dorofeev, D.L. (2002), "On static analysis of finite repetitive structures by discrete Fourier transform", Int. J. Solids Struct., 39(16), 4291-4310. https://doi.org/10.1016/S0020-7683(02)00259-7
  11. Kaveh, A. (2013), Optimal Structural Analysis Using Symmetry and Regularity, Springer Verlag, Wien.
  12. Kaveh, A. and Koohestani, K. (2009), "Combinatorial optimization of special graphs for nodal ordering and graph partitioning", Acta Mech., 207(1-2), 95-108. https://doi.org/10.1007/s00707-008-0107-6
  13. Kaveh, A. and Rahami, H. (2006), "Block diagonalization of adjacency and Laplacian matrices for graph product; applications in structural mechanics", Int. J. Numer. Meth. Eng., 68(1), 33-63. https://doi.org/10.1002/nme.1696
  14. Kaveh, A. and Rahami, H. (2007), "Compound matrix block diagonalization for efficient solution of eigenproblems in structural mechanics", Acta Mech., 188(3-4), 155-166. https://doi.org/10.1007/s00707-006-0364-1
  15. Kaveh, A. and Zolghadr, A. (2012), "Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability", Comput. Struct., 102-103, 14-27. https://doi.org/10.1016/j.compstruc.2012.03.016
  16. Kaveh, A. and Zolghadr, A. (2014a), "Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints", Adv. Eng. Softw., 76, 9-30. https://doi.org/10.1016/j.advengsoft.2014.05.012
  17. Kaveh, A. and Zolghadr, A. (2014b), "Democratic PSO for truss layout and size optimization with frequency constraints", Comput. Struct., 130, 10-21. https://doi.org/10.1016/j.compstruc.2013.09.002
  18. Konzelman, C.J. (1986), Dual methods and approximation concepts for structural optimization, M.Sc. thesis, Department of Mechanical Engineering, Univ. of Toronto.
  19. Koohestani, K. and Kaveh, A. (2010), "Efficient buckling and free vibration analysis of cyclically repeated space truss structures", Finite Elem. Anal. Des., 46(10), 943-948. https://doi.org/10.1016/j.finel.2010.06.009
  20. Leung, A.Y.T. (1980), "Dynamic analysis of periodic structures", J. Sound Vib., 72(4), 451-467. https://doi.org/10.1016/0022-460X(80)90357-0
  21. Lin, J.H., Chen, W.Y. and Yu, Y.S. (1982), "Structural optimization on geometrical configuration and element sizing with static and dynamic constraints", Comput. Struct., 15(5), 507-515. https://doi.org/10.1016/0045-7949(82)90002-5
  22. Lingyun, W., Mei, Z., Guangming, W. and Guang, M. (2005), "Truss optimization on shape and sizing with frequency constraints based on genetic algorithm", J. Comput. Mech., 35(5), 361-368. https://doi.org/10.1007/s00466-004-0623-8
  23. Liu, L. and Yang, H. (2007), "A paralleled element-free Galerkin analysis for structures with cyclic symmetry", Eng. Comput., 23(2), 137-144. https://doi.org/10.1007/s00366-006-0050-x
  24. Rahami, H., Kaveh, A. and Shojaei, I. (2015), "Swift analysis for size and geometry optimization of structures", Adv. Struct. Eng., 18(3), 365-380. https://doi.org/10.1260/1369-4332.18.3.365
  25. Sedaghati, R., Suleman, A. and Tabarrok, B. (2002), "Structural optimization with frequency constraints using finite element force method", AIAA J., 40(2), 382-388. https://doi.org/10.2514/2.1657
  26. Shi, C., Parker, R.G. and Shaw, S.W. (2013), "Tuning of centrifugal pendulum vibration absorbers for translational and rotational vibration reduction", Mech. Mach. Theory. 66, 56-65. https://doi.org/10.1016/j.mechmachtheory.2013.03.004
  27. Shojaei, I., Kaveh, A., Rahami, H. and Bazrgari, B. (2015), "Efficient non-linear analysis and optimal design of mechanical and biomechanical systems", Adv. Biomech. Applic., Techno, 2(1), 11-27.
  28. Taylor, J.E. (1967), "Minimum mass bar for axial vibration at specified natural frequency", AIAA J., 5(10), 1911-1913 https://doi.org/10.2514/3.4336
  29. 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. https://doi.org/10.1016/j.jsv.2014.06.004
  30. Vakakis, A.F. (1992), "Dynamics of a nonlinear periodic structure with cyclic symmetry", Acta Mech., 95(1-4), 197-226. https://doi.org/10.1007/BF01170813
  31. Williams, F.W. (1986), "An algorithm for exact eigenvalue calculations for rotationally periodic structures", Int. J. Numer. Meth. Eng., 23(4), 609-622. https://doi.org/10.1002/nme.1620230407
  32. Zingoni, A. (2005), "A group-theoretic formulation for symmetric finite elements", Finite Elem Anal. Des., 41 (6), 615-635. https://doi.org/10.1016/j.finel.2004.10.004
  33. Zingoni, A. (2012), "Symmetry recognition in group-theoretic computational schemes for complex structural systems", Comput. Struct., 94-95, 34-44. https://doi.org/10.1016/j.compstruc.2011.12.004
  34. Zingoni, A. (2014), "Group-theoretic insights on the vibration of symmetric structures in engineering", Philos. T. R. Soc. A., 372, 20120037.

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