Skip to main content
Log in

An investigation of structural optimization in crashworthiness design using a stochastic approach

A comparison of stochastic optimization and the response surface methodology

  • Industrial applications
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In this paper the response surface methodology (RSM) and stochastic optimization (SO) are compared with regard to their efficiency and applicability in crashworthiness design. Optimization of simple analytic expressions and optimization of a front rail structure are the applications used to assess the respective qualities of both methods. A low detail vehicle structure is optimized to demonstrate the applicability of the methods in engineering practice. The investigations reveal that RSM is better compared to SO for fewer than 10–15 design variables. The convergence behaviour of SO improves compared to RSM when the number of design variables is increased. A novel zooming method is proposed which improves the convergence behaviour. A combination of both the RSM and the SO is efficient, stochastic optimization could be used in order to determine appropriate starting points for an RSM optimization, which continues the optimization. Two examples are investigated using this combined method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Craig, K.J.; Stander, N.; Dooge, D.A.; Varadappa, S. 2002: Multidiciplinary design optimization of automotive crashwothiness and NVH using response surface methods. AIAA-paper 2002-5507, Mistree, F. (ed.) 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia

  2. Duddeck, F.; Heiserer, D.; Lescheticky, J. 2003: Stocastic methods for optimization of crash and NVH problems. Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, Cambridge

  3. Etman, L.F.P.; Adriaens J.M.T.A.; van Slagmaat, M.T.P.; Schoofs, A.J.G. 1996: Crashworthiness design using multipoint sequential linerar programming. Struct Optim12, 222–8

    Google Scholar 

  4. Etman, L.F.P. 1997: Optimization of multibody system using approximation concepts. Ph.D. thesis, Technical University Eindhoven, The Netherlands

  5. Forsberg, J. 2002: Simulation Based Crashwothiness Design – Accuracy aspects of structural optimization using response surfaces. LIU-TEK-LIC-2002:27, Linköping university, Linköping

  6. Marczyk, J. 1999: Principles of Simulation-Based Computer-Aided Engineering. Barcelona: FIM Publication

  7. Marklund, P-O.; Nilsson, L. 2001: Optimization of a car body component subjected to impact. Struct Multidisc Optim21, 383–392

    Google Scholar 

  8. Myers, R.H.; Montgomery, D.C. 1995: Response Surface Methodology. New York: Wiley

  9. Nelder, J.A.; Mead, R. 1965: A simplex method for function minimization. Comput J7, 308–313

    Google Scholar 

  10. Redhe, M. 2001: Simulation Based Design – Structural optimization at early design stages. LIU-TEK-LIC-2001:51, Linköping university, Linköping

  11. Redhe, M.; Nilsson, L. 2002a: A method to determine structural sensitivities in vehicle crashworthiness design. Int J Crashworthiness7(2), 179–190

  12. Redhe, M.; Forsberg, J.; Jansson, T.; Marklund, P-O.; Nilsson, L. 2002b: Using the response surface methodology and the d-Optimality criterion in crashworthiness related problems – an analysis of the surface approximation error versus the number of function evaluations. Struct Multidisc Optim24(3), 185–194

  13. Redhe, M.; Nilsson, L. 2002c: Using space mapping and surrogate models to optimize vehicle crashworthiness design. AIAA-Paper 2002-5536, Mistree, F. (ed.) 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia

  14. Roux W.; Stander, N.; Haftka, R. 1998: Response surface approximations for structural optimization. Int J Numer Methods Eng42, 517–534

    Google Scholar 

  15. Schramm, U.; Thomas, H. 1998: Structural optimization in occupant safety and crash analysis. Des Optim1(4), 374–387

    Google Scholar 

  16. Schramm, U.; Thomas, H. 1999: Crashworthiness design using structural optimization. AIAA Pap, 98-4729

  17. Schramm, U. 2001, Multi-disciplinary optimization for NVH and crashworthiness. The First MIT Conference on Computational Fluid and Solid Mechanics (Boston, June 12–15), Bathe, K.J. (ed.) Oxford, Elsevier Science

  18. Schramm, U. 2002: Designing with structural optimization – A practical point of view. AIAA Paper 2002-5191, Mistree, F. (ed.) 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia

  19. Sobieszczanski-Sobieski, J.; Kodiyalam, S.; Yang, R-J. 2000: Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. AIAA Pap 2000-1521

  20. Stander, N.; Burger, M.; Balasubramanyam, S.; Varadappa, S. 2001a: Shape optimization for head and knee impact featuring. Third LS-DYNA Conference, Paris

  21. Stander, N.; Craig, K.; Roux, W. 2002a: LS-OPT User’s Manual v. 2. Livermore: Livermore Software Technology Corporation

  22. Stander, N.; Craig, K. 2002b: On the robustness of a simple domain reduction scheme for simulation-based optimization. Eng Comput16(4), 431–450

  23. ST-ORM 2.0 User’s Manual, EASi Engineering, November 2000

  24. Torczon, V. 1997: On the convergence of pattern search methods. SIAM J Optim7, 1–26

    Google Scholar 

  25. Yamazaki, K.; Han, J. 1998: Maximization of the crushing energy absorption of tubes. Struct Optim16, 37–46

    Google Scholar 

  26. Yang, R-J.; Gu, L.; Tho, C.; Sobieszczanski-Sobieski, J. 2001: Multidisciplinary design optimization of a full vehicle with high performance computing. AIAA Pap, 2001-1273

  27. Yang, R-J.; Tho, C.H.; Gu, L. 2002: Recent development in Multidisciplinary design optimization of vehicle structures. AIAA-paper 2002-5606, Mistree, F. (ed.) 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia

  28. Yang, R-J.; Gu, L.; Fu, Y.; Tho, C-H. 2003: Experience With Sequential Stochastic Design Improvement Methods. Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, Cambridge

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Redhe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Redhe, M., Giger, M. & Nilsson, L. An investigation of structural optimization in crashworthiness design using a stochastic approach. Struct Multidisc Optim 27, 446–459 (2004). https://doi.org/10.1007/s00158-004-0400-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0400-5

Keywords

Navigation