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Genetic optimization of vibrating stiffened plates

  • Received : 2004.11.02
  • Accepted : 2006.07.03
  • Published : 2006.11.30

Abstract

This work gives an application of stochastic techniques for the optimization of stiffened plates in vibration. The search strategy consists of substituting, for finite element calculations in the optimization process, an approximate response from a Rayleigh-Ritz method. More precisely, the paper describes the use of a Rayleigh-Ritz method in creating function approximations for use in computationally intensive design optimization based on genetic algorithms. Two applications are presented; their deal with the optimization of stiffeners on plates by varying their positions, in order to maximize some natural frequencies, while having well defined dimensions. In other words, this work gives the fundamental idea of using a Ritz approximation to the response of a plate in vibration instead of finite element analysis.

Keywords

References

  1. Amabili, M. and Garziera, R. (1999), 'A technique for the systematic choice of admissible functions in the Rayleigh-Ritz method', J Sound Vib., 224(3),519-539 https://doi.org/10.1006/jsvi.1999.2198
  2. Belblidia, F., Afonso, S.M.B., Hinton, E. and Antonino, G.C.R. (1999), 'Integrated design optimization of stiffened plate structures', Eng. Computations., 16(8), 934-951 https://doi.org/10.1108/02644409910304185
  3. Brosowski, B. and Ghavami, K. (1997), 'Multi-criteria optimal design of stiffened Plates - II. Mathematical modelling of the optimal design of longitudinally stiffened plates', Thin-Walled Struet., 28(2),179-198 https://doi.org/10.1016/S0263-8231(97)00008-6
  4. Craveur, J.C. (1996), Modelisation des structures, Calcul par eIementsjinis. Masson, Paris
  5. Goldberg, D.E. (1989), Genetic Algorithm in Search, Optimization, and Machine Learning, Addison-Wesley
  6. Inoue, K, Yamanaka, M. and Kihara, M. (2002), 'Optimum stiffener layout for the reduction of vibration and noise of gearbox housing', J Mechanical Design, 124(3), 518-523 https://doi.org/10.1115/1.1480817
  7. Jaunky, N., Knight, N.F. and Ambur, D.R. (1998), 'Optimal design of general stiffened composite circular cylinders for global buckling with strength constraints', Compos. Struct., 41(3-4),243-252 https://doi.org/10.1016/S0263-8223(98)00020-8
  8. Kallassy, A. and Marcelin, J.L. (1997), 'Optimization of stiffened plates by genetic search', Stnlct. Optimiz., 13, 134-141 https://doi.org/10.1007/BF01199232
  9. Liu, Z.S., Hansen, J.S. and Oguamanam, D.C.D. (1998), 'Eigenvalue sensitivity analysis of stiffened plates with respect to the location of stiffeners', Struct. Optimiz., 16(2-3), 155-161 https://doi.org/10.1007/BF01202826
  10. Marcelin, lL. (1999a), 'Evolutionary optimization of mechanical structures', Eng. Optimiz., 31(5), 571-588 https://doi.org/10.1080/03052159908941387
  11. Marcelin, J.L. (1999b), 'Evolutionary optimisation of mechanical structures: Towards an integrated optimization', Eng. Comput., 15, 326-333 https://doi.org/10.1007/s003660050027
  12. Marcelin, J.L. (2001), 'Genetic optimization of stiffened plates and shells', Int. J Numer. Meth. Eng., 51(9), 1079-1088 https://doi.org/10.1002/nme.193
  13. Nallim, L.G, Luccioni, B.M. and Grossi, R.O. (2002), 'A Rayleigh-Ritz approach to transverse vibration of isotropic polygonal plates with variable thickness', Proc. of the Institution of Mechanical Engineers- Part K., 216(3),213-222
  14. Yang, J. and Gupta, A. (2002), 'Ritz vector approach for static and dynamic analysis of plates with edge beams', J Sound Vib., 253(2), 373-388 https://doi.org/10.1006/jsvi.2001.4047
  15. Zienkiewicz, O.C. (1971), The Finite Element Method in Engineering Science, McGraw-Hill, London

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