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Graph and heuristic based topology optimization of crash loaded structures

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For the efficient development of new structural concepts, it is necessary to perform an optimization of the mechanical properties of profile cross-sections taking into account all relevant load cases. Especially for crash load cases, there currently exists no established method for the conceptual design and topology optimization. The main problems are the complicated deformation conditions in the crash, the huge number of design variables, the existence of simulative and physical bifurcation points and the costly determination of sensitivity information. For the application area of developing profile cross-sections, the method presented in this paper attempts to overcome these shortfalls. It has been developed for the combined topology, shape and sizing optimization taking into account all relevant crash load cases. For this a flexible description of the structure’s profile cross-section via mathematical graphs is used. Modifications of the structure’s topology are performed with heuristics (rules), which are based on expert knowledge, whereas the automatically generated shape und sizing parameters of the structure are optimized with mathematic optimization algorithms.

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  • Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224

    Article  Google Scholar 

  • Diestel R (2010) Graph theory. Springer, Heidelberg

    Book  Google Scholar 

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

    Article  Google Scholar 

  • Eschenauer H, Kobelev V, Schumacher A (1994) Bubble method for topology and shape optimization of structures. J Struct Optim 8:42–51

    Article  Google Scholar 

  • Mayer RR, Kikuchi N, Scott RA (1996) Application of topological optimization techniques to structural crashworthiness. Int J Numer Methods Eng 39:1383–1403

    Article  MATH  Google Scholar 

  • Norato JA, Bendsøe MP, Haber RB, Tortorelli DA (2007) A topological derivative method for topology optimization. Struct Multidisc Optim 33:375–386

    Article  MATH  Google Scholar 

  • Olschinka C, Schumacher A (2008) Graph based topology optimization of crashworthiness structures. PAMM Proc Applied Math Mech 8(1):10029–10032

    Article  Google Scholar 

  • Park GJ (2011) Technical overview of the equivalent static loads method for non-linear static response structural optimization. Struct Multidisc Optim 43:319–337

    Article  Google Scholar 

  • Patel NM, Kang BS, Renaud JE, Tovar A (2009) Crashworthiness design using topology optimization. J Mech Des 131:061013.1–061013.12

    Google Scholar 

  • Pedersen CBW (2004) Crashworthiness design of transient frame structures using topology optimization. Comput Methods Appl Mech Eng 193:653–678

    Article  MATH  Google Scholar 

  • Schumacher A (2005a) Optimierung mechanischer Strukturen–Grundlagen und industrielle Anwendungen. Springer, Heidelberg

    Google Scholar 

  • Schumacher A (2005b) Parameter-based topology optimization for crashworthiness structures. In: Proceeding of the 6th WCSMO, Rio de Janeiro, Brazil, 30 May–3 June

  • Soto CA (2004) Structural topology optimization for crashworthiness. Int J Crash 9(3):277–283

    Article  Google Scholar 

  • Yang RJ, Gu L, Soto CA, Li G, Tyan T (2004) Developments and applications of structural optimization and robustness methods in vehicle impacts. In: Proceeding of the ASME 2004 international mechanical engineering congress and exposition, Anaheim, California, USA, November 13–19

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This research was supported by the German Federal Ministry for Education and Research within the scope of the research project “Methodological and technical realization of the topology optimization of crash loaded vehicle structures”. Beside the Hamburg University of Applied Sciences, the Automotive Simulation Center Stuttgart (asc(s), the DYNAmore GmbH and the SFE GmbH are involved in the project. Among others, the associated project partners are: Adam Opel AG, Daimler AG, Dr. Ing. h.c. F. Porsche AG and Volkswagen Osnabrück GmbH.

In the application examples the following commercial software solutions have been used: LS-OPT® as the general purpose optimization software, LS-DYNA® as the finite element solver and Altair HyperMesh® (application examples 1a, 1b and 2b) or SFE CONCEPT® (application example 2a) as the CAE system. The software yWorks yEd Graph Editor® has been used to get a graphical representation of the mathematical graphs.

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Correspondence to Christopher Ortmann.

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

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