Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Design of space thrusters: a topology optimization problem solved via a Branch and Bound method

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this paper, an exact Branch and Bound Algorithm has been developed to solve a difficult global optimization problem concerning the design of space thrusters. This optimization problem is hard to solve mainly because the objective function to be minimized is implicit and must be computed by using a Finite Element method code. In a previous paper, we implement a method based on local search algorithms and we then proved that this problem is non convex yielding a strong dependency between the obtained local solution and the starting points. In this paper, by taking into account a monotonicity hypothesis that we validated numerically, we provide properties making it possible the computation of bounds. This yields the development of a topology optimization Branch and Bound code. Some numerical examples show the efficiency of this new approach.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Allaire, G.: Conception optimale de structures. Springer, Berlin-Heildelberg (2007)

    Google Scholar 

  2. Allaire, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 363–393 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bäck, T.: Evolutionary Algorithms in Theory and Practice. Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Dortmund, Germany (1995)

    MATH  Google Scholar 

  4. Barba, P.D.: Multiobjective Shape Design in Electricity and Magnetism, Lecture Notes in Electrical Engineering vol. 47, Springer (2010)

  5. Bendsøe, M.P., Kikuchi, N.: Generating optimal toplogies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988)

    Article  MATH  Google Scholar 

  6. Bendsøe, M.P., Sigmund, O.: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69, 635–654 (1999)

    Article  MATH  Google Scholar 

  7. Bendsøe, M.P., Sigmund, O.: Topology Optimization Theory, Methods and Applications. Springer, Berlin (2003)

    MATH  Google Scholar 

  8. Céa, J., Garreau, S., Guillaume, P., Masmoudi, M.: The shape and topological optimizations connection. Comput. Methods Appl. Mech. Eng. 188(4), 713–726 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Goebel, D.M., Katz, I.: Fundamentals of Electric Propulsion. Wiley, Hoboken (2008)

    Book  Google Scholar 

  10. Jia, H., Beom, H.G., Wang, Y., Lin, S., Liu, B.: Evolutionary level set method for structural topology optimization. Comput. Struct. 89, 445–454 (2011)

    Article  Google Scholar 

  11. Korovkin, N.V., Chechurin, V.L., Hayakawa, M.: Inverse Problem in Electric Circuits and Electromagnetics. Springer, Berlin (2007)

    MATH  Google Scholar 

  12. Meeker, D.: Finite Element Method Magnetics Version 4.2 User’s Manual, October 16, (2010). www.femm.info/wiki/HomePage

  13. Moore, R.E.: Methods and Applications of Interval Analysis, Studies in Applied Mathematics. SIAM, Philadelphia (1979)

    Book  Google Scholar 

  14. Messine, F.: A deterministic global optimization algorithm for design problems. In: Audet, C., Hansen, P., Savard, G. (eds.) Essays and Surveys in Global Optimization, pp. 267–294. Springer, New York (2005)

    Chapter  Google Scholar 

  15. Novotny, A.A., Feijóo, R.A., Taroco, E., Padra, C.: Topological sensitivity analysis. Comput. Methods Appl. Mech. Eng. 192, 803–829 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ratschek, H., Rokne, J.: New Computer Methods for Global Optimization. Ellis Horwood Ltd, Chichester (1988)

    MATH  Google Scholar 

  17. Rozvany, G.I.N.: Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct. Multidisc. Optim. 21, 90–108 (2001)

    Article  Google Scholar 

  18. Jahn, R.G.: Physics of Electrical Propulsion. McGraw-Hill, New York (1968)

    Google Scholar 

  19. Sanogo, S., Messine, F., Henaux, C., Vilamot, R.: Topology optimization for magnetic circuits dedicated to electric propulsion. IEEE Trans. Magn. 50(12), 1–13 (2014)

    Article  Google Scholar 

  20. Sokołowski, J., Żochowski, A.: On topological derivative in shape optimization, Rapport de recherches, no. 3170, 31 pages, INRIA Lorraine, Mai (1997)

  21. Sokołowski, J., Żochowski, A.: Topological derivatives of shape functionals for elasticity systems. Mech. Struct. Mach. 29(3), 331–349 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  22. Vilamot, R.: Optimisation de la configuration magnétique d’un propulseur à effet Hall par résolution du problème inverse., PhD, thesis, Department of Electrical Engineering, INP-ENSEEIHT Université de Toulouse, (2012)

  23. Wang, M.Y., Wang, X., Guo, D.: A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yamasaki, S., Nishiwaki, S., Yamada, T., Izui, K., Yoshimura, M.: A structural optimization method based on the level set method using a new geometry-based re-initialization scheme. Int. J. Numer. Methods Eng. 83(12), 1580–1624 (2010)

  25. Yulin, M., Wang, X.: A level set method for structural topology optimization and its applications. Adv. Eng. Softw. 35, 415–441 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Toulouse, Laplace (CNRS UMR5213, Toulouse INP), 31071, Toulouse, France

    Satafa Sanogo & Frédéric Messine

Authors
  1. Satafa Sanogo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frédéric Messine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frédéric Messine.

Additional information

The work of Frédéric Messine has been funded by the Junta de Andaluca (P11-TIC7176), by the Spanish Ministry (TIN2012-37483) and by the grant ANR 12-JS02-009-01ATOMIC.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sanogo, S., Messine, F. Design of space thrusters: a topology optimization problem solved via a Branch and Bound method. J Glob Optim 64, 273–288 (2016). https://doi.org/10.1007/s10898-015-0334-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-015-0334-z

Keywords

Search

Navigation