Topology Design of a Structure with a Specified Eigenfrequency

주어진 고유주파수를 갖는 구조물의 위상최적설계

  • 이종환 (현대중공업 선박해양연구소 구조연구실) ;
  • 민승재 (한양대학교 기계공학부)
  • Published : 2003.07.01


Topology optimization is applied to determine the layout of a structural component with a specified frequency by minimizing the difference between the specified structural frequency and a given frequency. The homogenization design method is employed and the topology design problem is solved by the optimality criteria method. The value of a weighting factor in the optimality criteria plays an important role in this topology design problem. The modified optimality criteria method approximated by using the binomial expansion is suggested to determine the suitable value of the weighting factor, which makes convergence stable. If a given frequency is set as an excited frequency, it is possible to avoid resonance by moving away the specified structural frequency from the given frequency. The results of several test problems are compared with previous works and show the validity of the proposed algorithm.


Topology Optimization;Eigenfrequency;Homogenization Design Method;Optimality Criteria Method


  1. Kim, T. S. and Kim, Y. Y., 1999. 'MAC-Based Mode Tracking in Structural Topology Optimization,' Computers & Structures, Vol. 74, No. 3, pp. 375-383
  2. Lim, O. K. and Lee, J. S., 2000, 'Structural Topology Optimization for the Natural Frequency of a Designated Mode,' KSME International Journal, Vol. 14, No. 3, pp. 306-313
  3. Song, Y. J., Min, S. and Kikuchi, N., 1999, Finite Element Method and Structural Optimization CAE, Sungandang, pp.323-358
  4. Haftka, R. T. and Gurdal, Z., 1992, Elements of structural optimization (3nd Ed.), Kluwer, Dordrecht
  5. Ma, Z. -D., Hagiwara, I., 1991, 'Sensitivity Aalysis Methods for Coupled Acoustic Structural Systems, Part I: Modal Sensitivities,' AIAA Journal, Vol. 29, No. 11, pp. 1787-1795
  6. Park, S. H. and Yoon, S. K., 1997, 'A Study on the Topology Optimization of Structures,' Transactions of the KSME, A, Vol. 21, No. 8, pp. 1241-1249
  7. Kim. B. S. and Suh, M. W., 1999, 'Topology Optimization using an Optimality Criteria Method,' Transactions of the KSAE, Vol. 7, No. 8, pp. 224-232
  8. Ma, Z. -D., Kikuchi, N., and Hagiwara, I., 1993, 'Structural Topology and Shape Optimization for a Frequency Response Problem,' Computational Mechanics, Vol. 13, pp. 157-174
  9. Ma, Z. -D., Kikuchi, N., Cheng, H. -C., and Hagiwara, I., 1995, 'Topology Optimization Technique for Free Vibration Problems,' J. of Applied Mechanics, Vol. 62, pp. 200-207
  10. Ma, Z. -D., Kikuchi, N., Cheng, H. -C., and Hagiwara, I., 1995, 'Topological Design for Vibrating Structures,' Computer Methods in Applied Mechanics and Engineering, Vol. 121, pp. 259-280
  11. Xie, Y. M. and Steven, G. P., 1966. 'Evolutionary Structural Optimization for Dynamic Problem,' Computers & Structures, Vol. 53, No. 6, pp. 1067-1073
  12. Prager, W. and Taylor, J.E., 1968, 'Problems of Optimal Structural Design,' J. of Applied Mechanics, Vol. 35, No. 1, pp. 102-106
  13. Bendsoe, M. P., and Kikuchi, N., 1988, 'Generating Optimal Topologies for Structural Design Using a Homogenization Method,' Computer Methods in Applied Mechanics and Engineering, Vol. 71, pp. 197-224
  14. Koh, B. -C., 1995, 'Topology Optimization in the Process of Conceptual Design,' Journal of the KSME, Vol. 35, No. 8, pp. 716-724