Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Filtering Technique to Control Member Size in Topology Design Optimization

  • Kim, Tae-Soo (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Kim, Jae-Eun (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Jeong, Je-Hyun (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Kim, Yoon-Young (School of Mechanical and Aerospace Engineering, Seoul National University)
  • Published : 2004.02.01
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Abstract

A simple and effective filtering method to control the member size of an optimized structure is proposed for topology optimization. In the present approach, the original objective sensitivities are replaced with their relative values evaluated within a filtering area. By adjusting the size of the filtering area, the member size of an optimized structure or the level of its topological complexity can be controlled even within a given finite element mesh. In contrast to the checkerboard-free filter, the present filter focuses on high-frequency components of the sensitivities. Since the present filtering method does not add a penalty term to the objective function nor require additional constraints, it is not only efficient but also simple to implement. Mean compliance minimization and eigenfrequency maximization problems are considered to verify the effectiveness of the present approach.

Keywords

References

  1. Beckers, M., 1999, 'Topology Optimization Using a Dual Method with Discrete Variables,' Structrual Optimization, Vol. 17, pp. 12-24 https://doi.org/10.1007/BF01197709
  2. Bendsoe, M. P. and Sigmund, O., 2003, Topology Optimization ; Theory, Methods and Applications, Springer-Verlag Berlin Heidelberg
  3. Bourdin, B., 2001, 'Filters in Topology Optimization,' International Journal for Numerical Methods in Engineering, Vol. 50, pp. 2143-2158 https://doi.org/10.1002/nme.116
  4. Duysinx, P., 1997, 'Layout Optimization : A Mathematical Programming Approach,' DCA-MM Report, No. 540, Technical University of Denmark
  5. Haber, R. B., Jog, C. S. and Bendsoe, M. P., 1996, 'A New Approach to Variable-Topology Shape Desing Using a Constraint on Perimeter,' Structural Optimization, Vol. 11, pp. 1-12 https://doi.org/10.1007/BF01279647
  6. Jeong, J. H., Kim, T. S. and Kim, Y. Y., 2001, 'A New Grain-Sizing Filter in Topology Optimization,' Extended Abstracts of the Fourth World Congress of Structural and Multidisciplinary Optimization, pp. 46-47
  7. Kikuchi, N., Oden, J. T. and Song, Y. J., 1984, 'Convergence of Modified Penalty Methods and Smoothing Schemes of Pressure for Stoke's flow Problems,' Finite elements in Fluids, Vol. 5, pp. 107-126
  8. Kim, T. S. and Kim, Y. Y., 2002, 'Multi-Objective Topology Optimization of a Beam Under Torsion and Distortion,' AIAA Journal, Vol. 40(2), pp. 376-381 https://doi.org/10.2514/2.1656
  9. Kim, Y. Y. and Yoon, G. H., 2000, 'Multi-Resolution Multi-Scale Topology Optimization-A New Paradigm,' International Journal of Solids and Structures, Vol. 37, pp. 5529-5559 https://doi.org/10.1016/S0020-7683(99)00251-6
  10. 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 https://doi.org/10.1007/BF00370133
  11. Ma, Z. D., Kikuchi, N. and Cheng, H. C., 1995, 'Topological Design for Vibrating Structures,' Computer Methods in Applied Mechanics and Engineering, Vol. 121, pp. 259-280 https://doi.org/10.1016/0045-7825(94)00714-X
  12. Park, S. H. and Youn, S. K., 1997, 'A Study on the Topology Optimization of Structures,' KSME Journal, Vol. 21(8), pp. 1241-1249.(In Korean)
  13. Petersson, J. and Sigmund, O., 1998, 'Slope Constrained Topology Optimization,' Intenational Journal for Numerical Methods in Engineering, Vol. 41, pp. 1417-1434 https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8<1417::AID-NME344>3.0.CO;2-N
  14. Sigmund, O., 1994, Design of Material Structures Using Topology Optimization. Ph. D. Thesis, Department of Solid Mechanics, Technical University of Denmark
  15. Youn, S. K. and Park, S. H., 1997, 'A Study on the Shape Extraction in the Structural Topology Optimization Using Homogenized Material,' Computers & Structures, Vol. 62(3), pp. 527-538 https://doi.org/10.1016/S0045-7949(96)00217-9
  16. Zhou, M., Shyy, Y. K. and Thomas, H. L., 2001, 'Checkerboard and Minimum Member Size Control in Topology Optimization,' Structural Optimization, Vol. 21, pp. 152-158 https://doi.org/10.1007/s001580050179