Skip to main content
SpringerLink
Log in

Topology optimization of trusses by growing ground structure method

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A new method called the growing ground structure method is proposed for truss topology optimization, which effectively expands or reduces the ground structure by iteratively adding or removing bars and nodes. The method uses five growth strategies, which are based on mechanical properties, to determine the bars and nodes to be added or removed. Hence, the method can optimize the initial ground structures such that the modified, or grown, ground structures can generate the optimal solution for the given set of nodes. The structural data of trusses are manipulated using C++ standard template library and the Boost Graph Library, which help alleviate the programming efforts for implementing the method. Three kinds of topology optimization problems are considered. The first problem is a compliance minimization problem with cross-sectional areas as variables. The second problem is a minimum compliance problem with the nodal coordinates also as variables. The third problem is a minimum volume problem with stress constraints under multiple load cases. Six numerical examples corresponding to these three problems are solved to demonstrate the performance of the proposed method.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Achtziger W (2007) On simultaneous optimization of truss geometry and topology. Struct Multidisc Optim 33:285–304

    Article  MathSciNet  Google Scholar 

  • Achtziger W, Bendosoe M, Ben-Tal A, Zowe J (1992) Equivalent displacement based foumulation for maximum strength truss topology design. Impact Comput Sci Eng 4:314–345

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization. Springer, Berlin Heiderberg New York

    Google Scholar 

  • Boost (2007) Boost C++ library http://boost.org/

  • Cheng GD, Guo X (1997) ε-relaxed approach. Struct Multidisc Optim 29:190–197

    Google Scholar 

  • Dorn W, Gomory R, Greenberg H (1964) Automatic design of optimal structures. J Mec 3:25–52

    Google Scholar 

  • Gill PE, Murray W, Saunders M (1997) User’s guide for SNOPT version 7 software for large-scale nonlinear programming. Stanford Business Software, Mountain View

  • Kirsch U (1993) Fundamental properties of optimal topologies. In: Bendsoe MP (ed) Topology optimization of structures. Kluwer, Norwell, pp 3–18

    Google Scholar 

  • Kirsch U (1996) Integration of reduction and expansion processes in layout optimization. Struct Optim 11:13–18

    Article  Google Scholar 

  • Kirsch U (2002) Design-oriented analysis of structures. Kluwer, Norwell

    MATH  Google Scholar 

  • Martinez P, Marti P, Querin OM (2007) Growth method for size, topology, and geometry optimization of truss structures. Struct Multidisc Optim 33:13–26

    Article  Google Scholar 

  • Mckeown JJ (1998) Growing optimal pin-jointed frames. Struct Optim 15:92–100

    Article  Google Scholar 

  • Meyers S (2002) Effective STL. Addison Wesley, Reading

    Google Scholar 

  • Ohsaki M (1998) On simultaneous optimization of topology and geometry of a regular plane truss. Comput Struct 79(6):673–679

    Article  Google Scholar 

  • Ohsaki M (2001) Random search method based on exact reanalysis for topology optimization of trusses with discrete cross-sectional areas. Comput Struct 66(1):69–77

    Article  Google Scholar 

  • Ohsaki M, Katoh N (2005) Topology optimization of trusses with stress and local constraints on nodal stability and member intersection. Struct Multidisc Optim 29:190–197

    Article  MathSciNet  Google Scholar 

  • Pedersen P (1972) On the optimal layout of multi-purpose trusses. Comput Struct 2:695–712

    Article  Google Scholar 

  • Reddy G, Cagan J (1994) An improved shape annealing algorithm for truss topology generation. ASME J Mech Eng 117:315–321

    Article  Google Scholar 

  • Rule WK (1994) Automatic design by optimized growth. ASCE J Struct Eng 120:3063–3070

    Article  Google Scholar 

  • Siek JG, Lee LQ, Lumsdaine A (2002) The boost graph library. C++ in-depth series. Addison Wesley, Reading

    Google Scholar 

  • Stolpe M, Svanberg K (2001) On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization. Struct Multidisc Optim 21:140–151

    Article  Google Scholar 

  • Stolpe M, Svanberg K (2004) A stress-constrained truss-topology and material-selection problem that can be solved by linear programming. Struct Multidisc Optim 27:126–129

    Article  MathSciNet  Google Scholar 

  • West DB (2001) Introduction to graph theory, 2nd edn. Prentice Hall, Englewood Cliffs

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo, Kyoto, Japan

    T. Hagishita & M. Ohsaki

Authors
  1. T. Hagishita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Ohsaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Hagishita.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hagishita, T., Ohsaki, M. Topology optimization of trusses by growing ground structure method. Struct Multidisc Optim 37, 377–393 (2009). https://doi.org/10.1007/s00158-008-0237-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-008-0237-4

Keywords

Search

Navigation