Three-dimensional Topology Optimization using the CATO Algorithm

  • LEE, Sang Jin (Engineering Research Institute, Gyeongsang National University) ;
  • BAE, Jung Eun (SJ.MIRAE & ADOPT Research Group, Department of Architectural Engineering, Gyeongsang National University)
  • Received : 2009.01.04
  • Published : 2009.06.30

Abstract

An application of the constrained adaptive topology optimization (CATO) algorithm is described for three-dimensional topology optimization of engineering structures. The enhanced assumed strain lower order solid finite element (FE) is used to evaluate the values of objective and constraint functions required in optimization process. The strain energy (SE) terms such as elastic and modal SEs are employed as the objective function to be minimized and the initial volume of structures is introduced as the constraint function. The SIMP model is adopted to facilitate the material redistribution and also to produce clearer and more distinct structural topologies. The linearly weighted objective function is introduced to consider both static and dynamic characteristics of structures. Several numerical tests are tackled and it is used to investigate the performance of the proposed three-dimensional topology optimization process. From numerical results, it is found to be that the CATO algorithm is easy to implement and extremely applicable to produce the reasonable optimum topologies for three dimensional optimization problems.

References

  1. Hassani, B. & Hinton, E. (1998) Homogenization and Structural topology optimization, Springer-Verlag
  2. Hsu, M. & Hsu, Y. (2005) "Interpreting three-dimensional structural topology optimization results." Computers and Structures, 83: 327-337 https://doi.org/10.1016/j.compstruc.2004.09.005
  3. Lee, S.J. & Bae, J.E. (2006) "The strain energy based topology optimization technique maximizing the fundamental frequency of the structures." In Proceedings of the 10th East Asia-Pacific Conference on Structural Engineering & Construction (EASEC-10): Analytical and Computational Methods, Bangkok, 229-234
  4. Tenek, L.H. & Hagiwara, I. (1993) "Static and vibrational shape and topology optimization using homogenization and mathematical programming." Computer Methods in Applied Mechanics and Engineering, 109: 143-154 https://doi.org/10.1016/0045-7825(93)90229-Q
  5. Bendsoe, M.P. & Kikuchi, N. (1988) "Generating optimal topologies in structural design using homogenization method." Computer Methods in Applied Mechanics and Engineering, 71: 197-224 https://doi.org/10.1016/0045-7825(88)90086-2
  6. Young, V., Querin, Q.M., Steven, G.P. & Xie, Y.M. (1999) "3D and multiple load case bi-directional evolutionary structural optimization (BESO)." Structural Optimization, 18: 183-192 https://doi.org/10.1007/BF01195993
  7. Bulman, S.D. & Hinton, E. (1999) "Constrained adaptive topology optimization of engineering structures." Design Optimization, 1: 419-439
  8. Walther, F. & Mattheck, C. (1993) "Local stiffening and sustaining of shell structures by SKO and CAO." In Proceeding of International Conference on structural optimization, Edited by C.A. Brebbia and S. Hernandez, 181-188, Computational Mechanics, Southampton, UK
  9. Campelo, F., Watanabe, K. & Igarashi, H. (2007) "3D topology optimization using immune algorithm." International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 26(3): 677-688 https://doi.org/10.1108/0332164071075114510.1108/0332164071075114510.1108/0332164071075114510.1108/0332164071075114510.1108/0332164071075114510.1108/0332164071075114510.1108/03321640710751145
  10. Cheng, G. & Olhoff, N. (1981) "An investigation concernng optimal design of solid elastic plates." International Journal of Solids and Structures, 17: 305-323 https://doi.org/10.1016/0020-7683(81)90065-2
  11. Xie, Y.M. & Steven, G.P. (1997) Evolutionary structural optimization, Springer-Verlag
  12. Bendsoe, M.P. & Sigmund, O. (2004) Topology optimization, Springer-Verlag
  13. Beckers, M. (1999) "Topology optimization using a dual method with discrete variables." Structural Optimization, 17: 14-24 https://doi.org/10.1007/BF01197709
  14. Diaz, A. & Lipton, R. (1997) "Optimal material layout for 3D elastic structures." Structural Optimization, 13: 60-64 https://doi.org/10.1007/BF01198376
  15. Fernandes, P. R., Guedes, J.M. & Rodrigues, H. (1999) "Topology optimization of 3D linear elastic structures." Computers & Structures, 73: 583-594 https://doi.org/10.1016/S0045-7949(98)00312-5
  16. Hinton, E. & Sienz, J. (1995) "Fully stressed topological design of structures using an evolutionary approach." Engineering Computations, 12: 229-244 https://doi.org/10.1108/02644409510799578
  17. Lee, S.J. & Lee, Y.J. (2005) "A comparative study on the free vibration analysis of shell structures with lower order solid finite elements." Journal of the Architectural Institute of Korea, 21(4): 39-46
  18. Rozvany, G. I. N. (2001) "Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics." Structural and Multidisciplinary Optimization, 21(2): 90-108 https://doi.org/10.1007/s001580050174
  19. Bendsoe, M.P. (1995) Optimization of structural topology shape; and material. Springer-Verlag
  20. James, K.A., Martins, J.R.R.A. & Hansen, J.S. (2008) "Three-dimensional structural topology optimization of an aircraft wing using level set methods." In Proceedings of the 12th AIAA/ISSMO Multidisciplinary and Optimization Conference, Victoria, British Columbia, Canada, 1-12
  21. Lee, S.J., Bae, J.E. Hinton, E. (2000) "Shell topology optimization using layered artificial material model." International Journal for Numerical Methods in Engineering, 47: 843-867 https://doi.org/10.1002/(SICI)1097-0207(20000210)47:4<843::AID-NME801>3.0.CO;2-5
  22. Olhoff, N., Ronholt, E. & Scheel, J. (1998) "Topology optimization of three-dimensional structures using optimum microstructures." Structural Optimization, 16:1-18 https://doi.org/10.1007/BF01213995
  23. Coelho, P.G., Fernandes, J.B., Cardoso, J.B., Guedes, J.M. & Rodrigues, H.C. (2006) "A three-dimensional hierarchical model for topology optimization of structures." In Proceedings of the 3rd European Conference on Computational Mechanics Solid, Structures and Coupled Problems in Engineering, Lisbon, Portugal, 5-8 https://doi.org/10.1007/1-4020-5370-3
  24. Youn, S.K. & Park, S.H. (1997) "A study on the shape extraction process in the structural topology optimization using homogenization material." Computers & Structures, 62: 527-538 https://doi.org/10.1016/S0045-7949(96)00217-9