369
Views
36
CrossRef citations to date
0
Altmetric
Articles

Identification of optimal topologies for crashworthiness with the evolutionary level set method

ORCID Icon, , ORCID Icon & ORCID Icon
Pages 395-416 | Received 16 Feb 2017, Accepted 14 May 2017, Published online: 02 Jun 2017

References

  • G. Allaire, E. Bonnetier, G. Francfort, and F. Jouve, Shape optimization by the homogenization method, Numer. Math. 76 (1997), pp. 27–68.
  • G. Allaire, F. Jouve, and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method, J. Comput. Phys. 194 (2004), pp. 363–393.
  • G. Allaire, F. De Gournay, F. Jouve, and A. Toader, Structural optimization using topological and shape sensitivity via a level set method, Control Cybernet. 34 (2005), pp. 59–80.
  • N. Aulig, S. Menzel, E. Nutwell, and D. Detwiler, Towards multi-objective topology optimization of structures subject to crash and static load cases, 4th International Conference on Engineering Optimization, Lisbon, Portugal, 2014.
  • N. Aulig, S. Menzel, E. Nutwell, and D. Detwiler, Preference-based topology optimization of body-in-white structures for crash and static loads, 14th LS-DYNA International Conference, Dearborn, MI, 2016.
  • N. Aulig and M. Olhofer, State-based representation for structural topology optimization and application to crashworthiness, IEEE Congress on Evolutionary Computation, Vancouver, 2016.
  • M.P. Bendsøe, Optimal shape design as a material distribution problem, Struct. Optim. 1 (1989), pp. 193–202.
  • M.P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng. 71 (1988), pp. 197–224.
  • M.P. Bendsøe and O. Sigmund, Topology Optimization, Springer, Berlin Heidelberg, 2004.
  • T. Buhl, C.B.W. Pedersen, and O. Sigmund, Stiffness design of geometrically nonlinear structures using topology optimization, Struct. Multidisc. Optim. 19 (2000), pp. 93–104.
  • M. Bujny, Development of a hybrid evolutionary approach for level set topology optimization, M.Sc. thesis, Technical University of Munich, 2015.
  • M. Bujny, N. Aulig, M. Olhofer, and F. Duddeck, Evolutionary crashworthiness topology optimization of thin-walled structures, 11th ASMO UK/ISSMO/NOED2016: International Conference on Numerical Optimisation Methods for Engineering Design, Munich, 2016.
  • M. Bujny, N. Aulig, M. Olhofer, and F. Duddeck, Evolutionary level set method for crashworthiness topology optimization, ECCOMAS Congress 2016, Crete Island, 2016.
  • M. Bujny, N. Aulig, M. Olhofer, and F. Duddeck, Hybrid evolutionary approach for level set topology optimization, IEEE Congress on Evolutionary Computation, Vancouver, 2016.
  • M. Cavazzuti, A. Baldini, E. Bertocchi, D. Costi, E. Torricelli, and P. Moruzzi, High performance automotive chassis design: A topology optimization based approach, Struct. Multidisc. Optim. 44 (2010), pp. 45–56.
  • J. Christensen, C. Bastien, and M.V. Blundell, Effects of roof crush loading scenario upon body in white using topology optimisation, Int. J. Crashworthiness 17 (2012), pp. 29–38.
  • C.A. Coello Coello, Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art, Comput. Methods Appl. Mech. Engrg. 191 (2002), pp. 1245–1287.
  • N.P.v. Dijk, K. Maute, M. Langelaar, and F.v. Keulen, Level-set methods for structural topology optimization: A review, Struct. Multidisc. Optim. 48 (2013), pp. 437–472.
  • F. Duddeck, S. Hunkeler, P. Lozano, E. Wehrle, and D. Zeng, Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata, Struct. Multidisc. Optim. 54 (2016), pp. 415–428.
  • F. Duddeck and K. Volz, A new topology optimization approach for crashworthiness of passenger vehicles based on physically defined equivalent static loads, ICRASH Conference, Milano, 2012.
  • H. Fredricson, T. Johansen, A. Klarbring, and J. Petersson, Topology optimization of frame structures with flexible joints, Struct. Multidisc. Optim. 25 (2003), pp. 199–214.
  • X. Guo, W. Zhang, and W. Zhong, Doing topology optimization explicitly and geometrically – a new moving morphable components based framework, J. Appl. Mech. 81 (2014), pp. 31–32.
  • N. Hansen and A. Ostermeier, Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation, Proceedings of IEEE International Conference on Evolutionary Computation, pp. 312–317, 1996.
  • K. Hamza, M. Aly, and H. Hegazi, A Kriging-interpolated level-set approach for structural topology optimization, J. Mech. Design 136 (2014), pp. 011008–011008-12.
  • N. Hansen and A. Ostermeier, Completely derandomized self-adaptation in evolution strategies, Evol. Comput. 9 (2001), pp. 159–195.
  • N. Hansen, J.A. Lozano, P. Larrañaga, I. Inza, and E. Bengoetxea, The CMA Evolution Strategy: A Comparing Review, in Studies in Fuzziness and Soft Computing 192, eds., Springer, Berlin Heidelberg, 2006, pp. 75–102.
  • N. Hansen and S. Kern, X. Yao, E.K. Burke, J.A. Lozano, J. Smith, J.J. Merelo-Guervós, J.A. Bullinaria, J.E. Rowe, P. Tiňo, A. Kabán, and H.-P. Schwefel, Evaluating the CMA evolution strategy on multimodal test functions, in Lecture Notes in Computer Science 3242, eds., Springer, Berlin Heidelberg, 2004, pp. 282–291.
  • N. Hansen, S. Müller, and P. Koumoutsakos, Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES), Evol. Comput. 11 (2003), pp. 1–18.
  • B. Hassani and E. Hinton, A review of homogenization and topology optimization homogenization theory for media with periodic structure, Comput. Struct. 69 (1998), pp. 707–717.
  • S. Hunkeler, Topology optimisation in crashworthiness design via hybrid cellular automata for thin-walled structures, Ph.D. diss., Queen Mary University of London, 2013.
  • C.K. Mozumder, Topometry optimization of sheet metal structures for crashworthiness design using hybrid cellular automata, Ph.D. diss., University of Notre Dame, 2010.
  • S.D. Müller, N. Hansen, and P. Koumoutsakos, J.J.M. Guervós, P. Adamidis, H.-G. Beyer, H.-P. Schwefel, and J.-L. Fernández-Villacañas, Increasing the serial and the parallel performance of the CMA-evolution strategy with large populations, in Lecture Notes in Computer Science 2439, eds., Springer, Berlin Heidelberg, 2002, pp. 422.
  • C. Ortmann and A. Schumacher, Graph and heuristic based topology optimization of crash loaded structures, Struct. Multidisc. Optim. 47 (2013), pp. 839–854.
  • S. Osher and R.P. Fedkiw, Level set methods: An overview and some recent results, J. Comput. Phys. 169 (2001), pp. 463–502.
  • G.-J. Park, Technical overview of the equivalent static loads method for non-linear static response structural optimization, Struct. Multidisc. Optim. 43 (2010), pp. 319–337.
  • N.M. Patel, Crashworthiness design using topology optimization, Ph.D. diss., University of Notre Dame, 2007.
  • C.B.W. Pedersen, Topology optimization design of crushed 2d-frames for desired energy absorption history, Struct. Multidisc. Optim. 25 (2003), pp. 368–382.
  • S.S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, USA, Hoboken, 2009.
  • G.I.N. Rozvany, M. Zhou, and T. Birker, Generalized shape optimization without homogenization, Struct. Optim. 4 (1992), pp. 250–252.
  • J.A. Sethian, Evolution, implementation, and application of level set and fast marching methods for advancing fronts, J. Comput. Phys. 169 (2001), pp. 503–555.
  • O. Sigmund, A 99 line topology optimization code written in Matlab, Struct. Multidisc. Optim. 21 (2014), pp. 120–127.
  • K. Suzuki and N. Kikuchi, A homogenization method for shape and topology optimization, Comput. Methods Appl. Mech. Engrg. 93 (1991), pp. 291–318.
  • M.Y. Wang, X. Wang, and D. Guo, A level set method for structural topology optimization, Comput. Methods Appl. Mech. Engrg. 192 (2003), pp. 227–246.
  • M. Yulin and W. Xiaoming, A level set method for structural topology optimization and its applications, Adv. Engrg. Softw. 35 (2004), pp. 415–441.
  • D. Zeng and F. Duddeck, Improved hybrid cellular automata for crashworthiness optimization of thin-walled structures, Struct. Multidisc. Optim. (2017). doi:10.1007/s00158-017-1650-3

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.