Structural Engineering and Mechanics

  • 제36권1호
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  • Pages.79-94
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  • 2010
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Topological optimized design considering dynamic problem with non-stochastic structural uncertainty

  • Lee, Dong-Kyu (Architecture & Offshore Research Department, Steel Structure Research Division, Research Institute of Industrial Science and Technology (RIST)) ;
  • Starossek, Uwe (Structural Analysis and Steel Structures Institute, Hamburg University of Technology) ;
  • Shin, Soo-Mi (Research Institute of Industrial Technology, Pusan National University)
  • 투고 : 2009.09.03
  • 심사 : 2010.04.30
  • 발행 : 2010.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

This study shows how uncertainties of data like material properties quantitatively have an influence on structural topology optimization results for dynamic problems, here such as both optimal topology and shape. In general, the data uncertainties may result in uncertainties of structural behaviors like deflection or stress in structural analyses. Therefore optimization solutions naturally depend on the uncertainties in structural behaviors, since structural behaviors estimated by the structural analysis method like FEM need to execute optimization procedures. In order to quantitatively estimate the effect of data uncertainties on topology optimization solutions of dynamic problems, a so-called interval analysis is utilized in this study, and it is a well-known non-stochastic approach for uncertainty estimate. Topology optimization is realized by using a typical SIMP method, and for dynamic problems the optimization seeks to maximize the first-order eigenfrequency subject to a given material limit like a volume. Numerical applications topologically optimizing dynamic wall structures with varied supports are studied to verify the non-stochastic interval analysis is also suitable to estimate topology optimization results with dynamic problems.

키워드

참고문헌

  1. Alefeld, G. and Mayer, G. (2000), "Interval analysis: Theory and applications", J. Comput. Appl. Math., 121, 421-464. https://doi.org/10.1016/S0377-0427(00)00342-3
  2. Barbarosie, C. and Toader, A.M. (2009), "Shape and topology optimization for periodic problems", Struct. Multidiscip. O., 40(1-6), 393-408.
  3. Bendsoe, M.P. (1995), Optimization of Structural Topology, Shape and Material, Springer, New York.
  4. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in optimal design using a homogenization method", Comput. Meth. Appl. Mech. Eng., 71(1), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  5. Dwyer, P.S. (1951), Linear Computation, Wiley.
  6. Haug, E.J., Choi, K.K. and Komkov, V. (1986), Design Sensitivity Analysis of Structural Systems, Academic Press Orlando, New York.
  7. Lee, D.K., Shin, S.M. and Park, S.S. (2006a), "Topological optimal design of truss bridge considering structural uncertainties", Proceedings of the 6th International Symposium on Architectural Interchanges in Asia, Daegu, October.
  8. Lee, D.K., Shin, S.M. and Park, S.S. (2006b), "Topological optimal design of beam-to-column connection considering structural uncertainties", Arch. Inst. Korea, 22(9), 27-34.
  9. Lehoucq, R.B., Sorensen, D.C. and Yang, C. (1998), ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM Publications, Philadelphia.
  10. Maglaras, G., Nikolaidids, E., Haftka, R.T. and Cudney, H.H. (1997), "Analytical-experimental comparison of probabilistic methods and fuzzy set based methods for designing under uncertainty", Struct. Multidiscip. O., 13, 69-80. https://doi.org/10.1007/BF01199225
  11. Moore, R.E. (1966), Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ.
  12. Neumaier, A. (2003), "Fuzzy modeling in terms of surprise", Fuzzy Set. Syst., 135, 21-38. https://doi.org/10.1016/S0165-0114(02)00248-8
  13. Neumaier, A. (2004), "Clouds, fuzzy sets and probability intervals", Reliab. Comput., 10, 249-272. https://doi.org/10.1023/B:REOM.0000032114.08705.cd
  14. Pedersen, N.L. (2000), "Maximization of eigenvalues using topology optimization", Struct. Multidiscip. O., 20, 2-11. https://doi.org/10.1007/s001580050130
  15. Rong, J.H., Xie, Y.M., Yang, X.Y. and Liang, Q.Q. (2002), "Topology optimization of structures under dynamic response constraints", J. Sound Vib., 234(6), 177-189.
  16. Sigmund, O. (2001), "A 99 topology optimization code written in Matlab", Struct. Multidiscip. O., 21, 120-127. https://doi.org/10.1007/s001580050176
  17. Sunaga, T. (1958), "Theory of an interval algebra and its application to numerical analysis", RAAG Memoirs, 2, 29-46.
  18. Zhiping, Q. (2003), "Comparison of static response of structures using convex models and interval analysis method", Int. J. Numer. Meth. Eng., 56(12), 1735-1753. https://doi.org/10.1002/nme.636

피인용 문헌

  1. Performance-based topology optimization for wind-excited tall buildings: A framework vol.74, 2014, https://doi.org/10.1016/j.engstruct.2014.05.043
  2. The use of topology optimization in the design of truss and frame bridge girders vol.51, pp.1, 2014, https://doi.org/10.12989/sem.2014.51.1.067
  3. Topology optimization: a review for structural designs under vibration problems vol.53, pp.6, 2016, https://doi.org/10.1007/s00158-015-1370-5
  4. Non-stochastic interval factor method-based FEA for structural stress responses with uncertainty vol.62, pp.6, 2010, https://doi.org/10.12989/sem.2017.62.6.703
  5. Multi-material topology optimization for crack problems based on eXtended isogeometric analysis vol.37, pp.6, 2010, https://doi.org/10.12989/scs.2020.37.6.663