Structural Engineering and Mechanics

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Simultaneously evolutionary optimization of several natural frequencies of a two dimensional structure

  • Zhao, Chongbin (CSIRO Division of Exploration and Mining) ;
  • Steven, G.P. (Finite Element Analysis Research Centre, Engineering Faculty University of Sydney) ;
  • Xie, Y.M. (Department of Civil and Building Engineering, Victoria University of Technology)
  • Published : 1999.05.25
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Abstract

This paper presents a solution method, which can be regarded as the further extension of the generalized evolutionary method (Zhao et al. 1998a), for the simultaneous optimization of several different natural frequencies of a structure in general and a two dimensional structure in particular. The main function of the present method is to optimize the topology of a structure so as to simultaneously make several different natural frequencies of interest to be of the corresponding different desired values for the target structure. In order to develop the present method, the new contribution factor of an element is proposed to consider the contribution of an element to the gaps between the currently calculated values for the different natural frequencies of interest and their corresponding desired values in a weighted manner. Using this new contribution factor of an element, the most inefficiently used material can be detected and removed gradually from the design domain of a structure. Through applying the present method to optimize two and three different natural frequencies of a two dimensional structure, it has been demonstrated that it is possible and applicable to use the generalized evolutionary method for tackling the simultaneous optimization of several different natural frequencies of a structure in the structural design.

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References

  1. Bendsoe, M.P. (1989), "Optimal shape design as a material distribution problem", Struct. Optim., 1, 193-202. https://doi.org/10.1007/BF01650949
  2. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Camp. Meth. Appl. Mech. Engng., 71, 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  3. Diaz, A.R. and Kikuchi, N. (1992), "Solutions to shape and topology eigenvalue optimization problems using a homogenization method", Int .J. Num. Meth. Engng., 35, 1487-1502. https://doi.org/10.1002/nme.1620350707
  4. Ma, Z.D., Kikuchi, N., Cheng, H.C. and Hagiwara, I. (1995), "Topological optimization technique for free vibration problems", Journal of Applied Mechanics, ASME, 62, 200-207. https://doi.org/10.1115/1.2895903
  5. Olhoff, N., Bendsoe, M.P. and Rasmussen, J. (1991), "On CAD-integrated structural topology and design optimization", Camp. Meth. Appl. Mech. Engng., 89, 259-279. https://doi.org/10.1016/0045-7825(91)90044-7
  6. Suzuki, K. and Kikuchi, N. (1991), "A homogenization method for shape and topology optimization", Comp. Meth. Appl. Mech. Engng., 93, 291-318. https://doi.org/10.1016/0045-7825(91)90245-2
  7. Tenek, L.H. and Hagiwara, I. (1993), "Optimization of material distribution within isotropic and anisotropic plates using homogenization", Comp. Meth. Appl. Mech. Engng., 109, 155-167. https://doi.org/10.1016/0045-7825(93)90230-U
  8. Xie, Y.M. and Steven, G.P. (1993), "A simple evolutionary procedure for structural optimization", Comput. Struct., 49, 885-896. https://doi.org/10.1016/0045-7949(93)90035-C
  9. Zhao, C., Steven, G.P. and Xie, Y.M. (1996a), "Evolutionary natural frequency optimization of thin plate bending vibration problems", Struct. Optim., 11, 244-251. https://doi.org/10.1007/BF01197040
  10. Zhao,C., Steven, G.P. and Xie, Y.M. (1996b), "General evolutionary path for fundamental natural frequencies of structural vibration problems", Structural Engineering and Mechanics, 4(5), 513-527. https://doi.org/10.12989/sem.1996.4.5.513
  11. Zhao, C., Steven, G.P. and Xie, Y.M. (1997a), "Effect of initial nondesign domain on optimal topologies of structures during natural frequency optimization", Computers and Structures, 62, 119-131. https://doi.org/10.1016/S0045-7949(96)00204-0
  12. Zhao, C., Steven, G.P. and Xie, Y.M. (1997b), "Evolutionary natural frequency optimization of 2D structures with additional nonstructural lumped masses", Engineering Computations, 14, 233-251. https://doi.org/10.1108/02644409710166208
  13. Zhao, C., Steven, G.P. and Xie, Y.M. (1997c), "Evolutionary optimization of maximizing the difference between two natural frequencies of a vibrating structure", Struct. Optim., 13, 148-154. https://doi.org/10.1007/BF01199234
  14. Zhao, C., Steven, G.P. and Xie, Y.M. (1998a), "A generalized evolutionary method for natural frequency optimization of membranes in finite element analysis", Computers and Structures, 66, 353-364. https://doi.org/10.1016/S0045-7949(97)00054-0
  15. Zhao, C., Hornby, P., Steven, G. P. and Xie, Y. M. (1998b), "A generalized evolutionary method for numerical topology optimization of structures under static loading conditions" , Struct. Optim., 15, 251-260. https://doi.org/10.1007/BF01203540
  16. Zhou, M. and Rozvany, G.I.N. (1992), DCOC "An optimality criteria method for large systems, Part I: Theory", Struct. Dptim., 5, 12-25. https://doi.org/10.1007/BF01744690
  17. Zhou, M. and Rozvany, G.I.N. (1993), DCOC "An optimality criteria method for large systems, Part II: Algorithm", Struct. Optim., 6, 250-262. https://doi.org/10.1007/BF01743384

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