Structural Engineering and Mechanics

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Theoretical and experimental study of robustness based design of single-layer grid structures

  • Wu, Hui (School of Business Administration, Zhejiang University of Finance & Economics) ;
  • Zhang, Cheng (Civil Department, East China Electric Power Design Institute) ;
  • Gao, Bo-Qing (College of Civil Engineering and Architecture, Zhejiang University) ;
  • Ye, Jun (College of Civil Engineering and Architecture, Zhejiang University)
  • Received : 2012.11.13
  • Accepted : 2014.05.09
  • Published : 2014.10.10
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Abstract

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions on methods of robustness based structural design are rare. Firstly, taking basis in robust $H_{\infty}$ control theory, structural robustness is assessed by $H_{\infty}$ norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the $H_{\infty}$ structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, Science Foundation of Zhejiang Province

References

  1. Au, F., Cheng, Y.S., Tham, L.G. and Zeng, G.W. (2003), "Robust design of structures using convex models", Comput. Struct., 81(28-29), 2611-2619. https://doi.org/10.1016/S0045-7949(03)00322-5
  2. Baker, J.W., Schubert, M. and Faber, M.H. (2008), "On the assessment of robustness", Struct. Saf., 30(3), 253-267. https://doi.org/10.1016/j.strusafe.2006.11.004
  3. Beer, M. and Liebscher, M. (2008), "Designing robust structures - a nonlinear simulation based approach", Comput. Struct., 86(10), 1102-1122. https://doi.org/10.1016/j.compstruc.2007.05.037
  4. Bendsøe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Method. Appl. Mech. Eng., 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  5. Branco, J.M. and Neves, L. (2011), "Robustness of timber structures in seismic areas", Eng. Struct., 33(11SI), 3099-3105. https://doi.org/10.1016/j.engstruct.2011.02.026
  6. Cizmar, D., Kirkegaard, P.H., Sorensen, J.D. and Rajcic, V. (2011), "Reliability-based robustness analysis for a Croatian sports hall", Eng. Struct., 33(11SI), 3118-3124. https://doi.org/10.1016/j.engstruct.2011.05.006
  7. de Kruijf, N., Zhou, S.W., Li, Q. and Mai, Y.W. (2007), "Topological design of structures and composite materials with multiobjectives", Int. J. Solid. Struct., 44(22-23), 7092-7109. https://doi.org/10.1016/j.ijsolstr.2007.03.028
  8. Doyle, J.C., Glover, K., Khargonekar, P.P. and Francis, B.A. (1989), "State-space solutions to standard H2 and $H_{\infty}$ control problems", IEEE Tran. Auto. Control, 34(8), 831-847. https://doi.org/10.1109/9.29425
  9. EN 1991-1-7 (2006), Eurocode 1-actions on structures, Part 1-7: general actions-accidental actions, Brussels.
  10. Jakiela, M.J., Chapman, C., Duda, J., Adewuya, A. and Saitou, K. (2000), "Continuum structural topology design with genetic algorithms", Comput. Method. Appl. Mech. Eng., 186(2-4), 339-356. https://doi.org/10.1016/S0045-7825(99)00390-4
  11. Kanno, Y. and Ben-Haim, Y. (2011), "Redundancy and robustness, or when is redundancy redundant?", J. Struct. Eng., ASCE, 137(9SI), 935-945. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000416
  12. Khandelwal, K. and El-Tawil, S., (2011), "Pushdown resistance as a measure of robustness in progressive collapse analysis", Eng. Struct., 33(9), 2653-2661. https://doi.org/10.1016/j.engstruct.2011.05.013
  13. Lee, M., Kelly, D.W., Degenhardt, R. and Thomson, R.S. (2010), "A study on the robustness of two stiffened composite fuselage panels", Compos. Struct., 92(2), 223-232. https://doi.org/10.1016/j.compstruct.2009.07.009
  14. Luo, Z., Tong, L.Y. and Kang, Z. (2009), "A level set method for structural shape and topology optimization using radial basis functions", Comput. Struct., 87(7-8), 425-434. https://doi.org/10.1016/j.compstruc.2009.01.008
  15. Mei, S.W., Shen, T.L. and Liu, K.Z. (2008), Modern Robust Control Theory and Application, Tsinghua University Press, Beijing, China.
  16. Rozvany, G., Zhou, M. and Birker, T. (1992), "Generalized shape optimization without homogenization", Struct. Optim., 4(3-4): 250-252. https://doi.org/10.1007/BF01742754
  17. Rozvany, G.. (2009), "A critical review of established methods of structural topology optimization", Struct. Multidisc. Optim., 37(3), 217-237. https://doi.org/10.1007/s00158-007-0217-0
  18. Smith, J.W. (2003), "Energy approach to assessing corrosion damaged structures", Proceedings of the Institution of Civil Engineers-Structures and Buildings, 156(2), 121-130. https://doi.org/10.1680/stbu.2003.156.2.121
  19. Soremekun, G., Gurdal, Z., Haftka, R.T. and Watson, L.T. (2001), "Composite laminate design optimization by genetic algorithm with generalized elitist selection", Comput. Struct., 79(2), 131-143. https://doi.org/10.1016/S0045-7949(00)00125-5
  20. Sorensen, J.D. (2011), "Framework for robustness assessment of timber structures", Eng. Struct., 33(11SI), 3087-3092. https://doi.org/10.1016/j.engstruct.2011.02.025
  21. Takezawa, A., Nii, S., Kitamura, M. and Kogiso, N. (2011), "Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system", Comput. Method. Appl. Mech. Eng., 200(25-28), 2268-2281. https://doi.org/10.1016/j.cma.2011.03.008
  22. Wang, S.Y., Tai, K. and Wang, M.Y. (2006), "An enhanced genetic algorithm for structural topology optimization", Int. J. Numer. Method. Eng., 65(1), 18-44. https://doi.org/10.1002/nme.1435
  23. Xia, Q., Shi, T.L., Liu, S.Y. and Wang, M.Y. (2012), "A level set solution to the stress-based structural shape and topology optimization", Comput. Struct., 90-91, 55-64. https://doi.org/10.1016/j.compstruc.2011.10.009
  24. Yan, D. and Chang, C.C. (2010), "Vulnerability assessment of single-pylon cable-stayed bridges using plastic limit analysis", Eng. Struct., 32(8), 2049-2056. https://doi.org/10.1016/j.engstruct.2010.03.005
  25. Yang, X.Y., Xie, Y.M. and Steven, G.P. (2005), "Evolutionary methods for topology optimisation of continuous structures with design dependent loads", Comput. Struct., 83(12-13), 956-963. https://doi.org/10.1016/j.compstruc.2004.10.011
  26. Zheng, J., Long, S.Y. and Li, G.Y. (2012), "Topology optimization of free vibrating continuum structures based on the element free Galerkin method", Struct. Multidisc. Optim., 45(1), 119-127. https://doi.org/10.1007/s00158-011-0667-2
  27. Zuo, Z.H., Xie, Y.M. and Huang, X.D. (2012), "Evolutionary topology optimization of structures with multiple displacement and frequency constraints", Adv. Struct. Eng., 15(2), 359-372. https://doi.org/10.1260/1369-4332.15.2.359

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