Skip to main content

Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata

Abstract

Although topology optimization is well established in most engineering fields, it is still in its infancy concerning highly non-linear structural applications like vehicular crashworthiness. One of the approaches recently proposed and based on Hybrid Cellular Automata is modified here such that it can be applied for the first time to thin-walled structures. Classical methods based on voxel techniques, i.e., on solid three-dimensional volume elements, cannot derive structures made from thin metal sheets where the main energy absorption mode is related to plastic buckling, folding and failure. Because the main components of car structures are made from such thin-walled beams and panels, a special approach using SFE CONCEPT was developed, which is presented in this paper.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

References

  • Abramowicz W (2003) Thin-walled structures as impact energy absorbers. Thin-Walled Struct 41:91–107

    Article  Google Scholar 

  • Alavi Nia A, Parsapour M (2013) An investigation on the energy absorption characteristics of multi-cell square tubes. Thin-Walled Struct 68:26–34

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization - theory, methods, and applications. Springer

  • Bochenek B, Tajs-Zielinska K (2010) Local rules of cellular automata for generating optimal topologies in structural design. In: ECCM 2010, IV Europ. conf. on computational mechanics. Paris

  • Cavazzuti M, Baldini A, Bertocchi E, Costi D, Torricelli E, Moruzzi P (2011) High performance automotive chassis design: a topology optimization based approach. Struct Multidisc Optim 44(1):45–56

    Article  Google Scholar 

  • Christensen J, Bastien C, Blundell MV (2012) Effects of roof crush loading scenario upon body in white using topology optimisation. Int J Crashworthiness 12(1):29–38

    Article  Google Scholar 

  • Chuang CH, Yang RJ (2012) Benchmark of topology optimization methods for crashworthiness design. In: 12th Int LS-DYNA Users Conf. Detroit

  • Duddeck F (2008) Multidisciplinary optimization of car bodies. Struct Multidisc Optim 35(4):375–389

    Article  Google Scholar 

  • Duddeck F, Zimmer H (2013) Modular car body design and optimization by an implicit parameterization technique via SFE CONCEPT. In: FISITA 2012 World autom congr, lecture notes in electr engrg, vol 195. Springer, pp 413–424

  • Erhart A, Schumacher P, Lazarov N, Müllerschön H (2012) Topology optimization with LS-TaSC and Genesis/ESL for crash-loading. In: 11th LS-DYNA German users forum. Ulm

  • Fender J, Duddeck F, Zimmermann M (2014) On the calibration of simplified vehicle crash models. Struct Multidisc Optim 49(3):455–469

    Article  Google Scholar 

  • Forsberg J, Nilsson L (2007) Topology optimization in crashworthiness design. Struct Multidisc Optim 33:1–12

    Article  Google Scholar 

  • Fredricson H (2004) Topology optimization of vehicle body structures. PhD thesis, Linköping Univ, Sweden

  • Vanderplaats Research and Development, Inc. (2012) GENESIS - software for structural analysis and optimization

  • Hunkeler S (2013) Topology optimisation in crashworthiness design via hybrid cellular automata for thin-walled structures. PhD thesis. Queen Mary Univ of London, UK

  • Hunkeler S, Duddeck F, Rayamajhi M (2013) Topology optimisation method for crashworthiness design using hybrid cellular automata and thin-walled ground structures. In: 9th Europ LS-DYNA conf. Manchester

  • Hunkeler S, Duddeck F, Rayamajhi M, Zimmer H (2013) Shape optimisation for crashworthiness followed by a robustness analysis with respect to shape variables. Struct Multidisc Optim 48(2):367–378

    Article  Google Scholar 

  • Kim H (2002) New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency. Thin-Walled Struct 40:311–327

    Article  Google Scholar 

  • Livermore Software Technology Corporation (2006) Livermore, CA USA - LS-DYNA - theory manual

  • Livermore Software Technology Corporation (2012) Livermore, CA, USA. LS-OPT User’s Manual, Version 4.2

  • Livermore Software Technology Corporation (2011)

  • Marsolek JS (2002) Energieabsorptionsverhalten zylinderschalenförmiger Strukturelemente aus Metall und Faserverbundwerkstoff. PhD thesis, RWTH Aachen, Germany

  • Mozumder CK (2010) Topometry optimization of sheet metal structures for crashworthiness design using hybrid cellular automata. PhD thesis, Univ of Notre Dame, USA

  • Ortmann C, Schumacher A (2013) Graph and heuristic based topology optimization of crash loaded structures. Struct Multidisc Optim 47(6):839–854

    Article  MATH  Google Scholar 

  • Park G-J (2011) Technical overview of the equivalent static loads method for nonlinear static response structural optimization. Struct Multidisc Optim 43(3):319–337

    Article  Google Scholar 

  • Patel NM (2007) Crashworthiness design using topology optimization. PhD thesis, Univ of Notre Dame, USA

  • Patel NM, Kang B-S, Renaud JE, Tovar A (2009) Crashworthiness design using topology optimization. ASME - J Mech Design 131(061013):1–12

  • Pedersen CBW (2003) Topology optimization design of crushed 2D-frames for desired energy absorption history. Struct Multidisc Optim 5–6:368–382

    Article  Google Scholar 

  • Penninger CL, Watson LT, Tovar A, Renaud JE (2010) Convergence analysis of hybrid cellular automata for topology optimization. Struct Multidisc Optim 40:271–282

    Article  MathSciNet  MATH  Google Scholar 

  • Rayamajhi M, Hunkeler S, Duddeck F (2014) Geometrical compatibility in structural shape optimisation for crashworthiness. Int J Crashworthiness 19(1):42–56

    Article  Google Scholar 

  • Rayamajhi M (2014) Robust Shape Optimisation for Crashworthiness via Physical Surrogate Models, PhD thesis, Queen Mary University of London, UK

  • Schumacher A (2005) Parameter-based topology optimization for crashworthiness structures. In: 6th World congr struct mutlidisc optim. Rio de Janeiro

  • SFE GmbH (2009) Berlin, Germany. SFE CONCEPT Version 4.2.2.3. Reference Manual

  • Torstenfelt B, Klarbring A (2007) Conceptual optimal design of modular car product families using simultaneous size, shape and topology optimization. Finite Elements Anal. Des 43:1050–1061

    Article  MathSciNet  Google Scholar 

  • Volz K (2011) Physikalisch begründete Ersatzmodelle für die Crashoptimierung von Karosseriestrukturen in frühen Projektphasen, PhD thesis, Technische Universität München. Munich, Germany

  • Volz K, Duddeck F (2012) A new topology optimization approach for crashworthiness of passenger vehicles based on physically defined equivalent static loads. In: ICrash2012, int crashworthiness conf. Milano

  • Walser AF (ed) (2013) Final report of the CrashTopo project. Workshop für nichtlineare Topologieoptimierung crashbeanspruchter Fahrzeugstrukturen, Automotive Simulation Center Stuttgart ASCS. Stuttgart, Germany

  • Zimmermann M, Wölfle F, Zimmer H, Schäfer M, Duddeck F (2012) Subsystem optimization of the vehicle structure for a frontal crash. In: SIMVEC Conf Berechnung, Simulation und Erprobung im Fahrzeugbau, VDI Berichte, vol 2169, pp 225–240

Download references

Acknowledgments

The authors would like to thank SFE GmbH in Berlin and Queen Mary University of London for their financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fabian Duddeck.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duddeck, F., Hunkeler, S., Lozano, P. et al. Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata. Struct Multidisc Optim 54, 415–428 (2016). https://doi.org/10.1007/s00158-016-1445-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-016-1445-y

Keywords