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The stiffness spreading method for layout optimization of truss structures

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Abstract

A novel optimization method, stiffness spreading method (SSM), is proposed for layout optimization of truss structures. In this method, stiffness matrices of the bar elements in a truss structure are represented by a set of equivalent stiffness matrices which are embedded in a weak background mesh. When the proposed method is used, it is unnecessary for the bar elements in a truss structure to be connected to each other during the optimization process, and each of the bar elements can move independently in the design domain to form an optimized design. Another feature of the method is that the sensitivity analysis can be done analytically, making gradient based optimization algorithms applicable in the solution. This method realizes the size, shape and topology design optimization of truss structures simultaneously and allows for more flexibility in topology change. Numerical examples illustrate the feasibility and effectiveness of the proposed method.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  • Amir O, Sigmund O (2013) Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization. Struct Multidiscip Optim 47:157–174

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Buhmann MD (2004) Radial basis functions: theory and Implementations. Cambridge University Press, New York

    Google Scholar 

  • Cao M, Ma H, Wei P (2012) Modified stiffness spreading method for layout optimization of truss structures. The 7th China-Japan-Korea joint symposium on optimization of structural and mechanical systems, Huangshan

  • Cox HL (1958) The theory of design. Report of Aeronautical Research Council, No 2037

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

    Google Scholar 

  • Gaynor AT, Guest JK, Moen CD (2013) Reinforced concrete force visualization and design using bilinear truss-continuum topology optimization. J Struct Eng 139(4):607–618

    Article  Google Scholar 

  • Hemp WS (1997) Optimum structures. Clarendon, Oxford

    Google Scholar 

  • Kirsch U (1990) On the relationship between optimum structural topologies and geometries. Struct Optim 2:39–45

    Article  Google Scholar 

  • Luo Z, Wang MY, Wang SY, Wei P (2008) A level setbased parametrization method for structural shape and topology optimization. Int J Numer Methods Eng 76(1):1–26

    Article  MATH  MathSciNet  Google Scholar 

  • Michell AGM (1904) The limits of economy of material in frame-structures. Phil Mag 8(6):589–597

    Article  MATH  Google Scholar 

  • Prager W, Rozvany GIN (1977) Optimal layout of grillages. J Struct Mech 5(1):1–18

    Article  Google Scholar 

  • Pedersen P (1972) On the optimal layout of multi-purpose trusses. Comput Struct 2:659–712

    Article  Google Scholar 

  • Rozvany GIN, Bendsøe MP, Kirsch U (1995) Layout optimization of structures. Appl Mech Rev 48(2):41–119

    Article  Google Scholar 

  • Rozvany GIN (2011) A review of new fundamental principles in exact topology optimization. In: Proceedings of 19th International Conference on Computer Methods in Mechanics, Warsaw

  • Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12(2):555–573

    Article  MATH  MathSciNet  Google Scholar 

  • Topping BHV (1983) Shape optimization of skeletal structures: a review. J Struct Eng ASCE 109(8):1933–1951

    Article  Google Scholar 

  • Vanderplaats GN, Moses F (1972) Automated design of trusses for optimum geometry. J Struct Div 98(3):671–690

    Google Scholar 

  • Wei P, Ma H, Chen T, Wang MY (2010) Stiffness spreading method for layout optimization of truss structures. In: Proceedings of the 6th China-Japan-Korea joint symposium on optimization of structural and mechanical systems, Kyoto

  • Wei P, Shi J, Ma H (2012) Integrated layout optimization design of multi-component systems based on the stiffness spreading method. In: Proceedings of the 7th China-Japan-Korea joint symposium on optimization of structural and mechanical systems, Huangshan

  • Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math 4:389–396

    Article  MATH  MathSciNet  Google Scholar 

  • Wu Z (1995) Multivariate compactly supported positive definite radial functions. Adv Comput Math 4:283–292

    Article  MATH  MathSciNet  Google Scholar 

  • Zegard T, Paulino GH (2013) Truss layout optimization within a continuum. Struct Multidiscip Optim 48(1):1–16

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors are grateful to Prof. Krister Svanberg for providing his MMA codes.

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Authors and Affiliations

  1. State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China

    Peng Wei & Haitao Ma

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China

    Michael Yu Wang

Authors
  1. Peng Wei
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  2. Haitao Ma
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  3. Michael Yu Wang
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Corresponding author

Correspondence to Peng Wei.

Additional information

The research work is supported by The National Science Foundation for Young Scientists of China (Grant Nos. 11002058 and 11002056) and State Key Lab of Subtropical Building Science (SCUT) (Grant Nos. 2010ZA03 and 2012ZC22)

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Wei, P., Ma, H. & Wang, M.Y. The stiffness spreading method for layout optimization of truss structures. Struct Multidisc Optim 49, 667–682 (2014). https://doi.org/10.1007/s00158-013-1005-7

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  • DOI: https://doi.org/10.1007/s00158-013-1005-7

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