Skip to main content
SpringerLink
Log in

A method for shape and topology optimization of truss-like structure

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

Abstract

We present a method for the shape and topology optimization of truss-like structure. First, an initial design of a truss-like structure is constructed by a mesh generator of the finite element method because a truss-like structure can be described by a finite element mesh. Then, the shape and topology of the initial structure is optimized. In order to ensure a truss-like structure can be easily manufactured via intended techniques, we assume the beams have the same size of cross-section, and a method based on the concept of the SIMP method is used for the topology optimization. In addition, in order to prevent intersection of beams and zero-length beams, a geometric constraint based on the signed area of triangle is introduced to the shape optimization. The optimization method is verified by several 2D examples. Influence on compliance of the representative length of beams is investigated.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

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  MATH  Google Scholar 

  • Ben-Tal A, Kočvara M, Zowe J (1993) Two nonsmooth approaches to simultaneous geometry and topology design of trusses. In: Bendsøe M, Soares CM (eds) Topology optimization of structures. Kluwer Academic, Dordrecht, pp 31–42

    Google Scholar 

  • 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 

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

    Google Scholar 

  • Chiras S, Mumm DR, Evans AG, Wicks N, Hutchinson JW, Dharmasena K, Wadley HNG, Fichter S (2002) The structural performance of near-optimized truss. Int J Solids Struct 39:4093–4115

    Article  Google Scholar 

  • Coelho PG, Fernandes PR, Guedes JM, Rodrigues HC (2008) A hierarchical model for concurrent material and topology optimisation of three-dimensional structures. Struct Multidisc Optim 35:107–115

    Article  Google Scholar 

  • Dems K, Gatkowski W (1995) Optimal design of a truss configuration under multiloading conditions. Struct Optim 9:262–265

    Article  Google Scholar 

  • Deshpande VS, Fleck NA, Ashby MF (2001) Effective properties of the octet-truss lattice material. J Mech Phys Solids 49:1747–1769

    Article  MATH  Google Scholar 

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

    Google Scholar 

  • Dutta D, Prinz FB, Rosen D, Weiss L (2001) Layered manufacturing: current status and future trends. ASME J Comput Inf Sci Eng 1:60–71

    Article  Google Scholar 

  • Fletcher R (1975) An ideal penalty function for constrained optimization. J Inst Math Appl 15:319–342

    Article  MathSciNet  MATH  Google Scholar 

  • Imai K, Schmit LA (1982) Configuration optimization of trusses. In: Proc. ASCE, vol 107 (ST5), pp 745–756

  • Kočvara M, Zowe J (1995) How to optimize mechanical structures simultaneously with respect to geometry and topology. In: Olhoff N, Rozvany GIN (eds) First world congress of structural and multidisciplinary optimization. Pergamon, Oxford, pp 135–140

    Google Scholar 

  • Kwon YW, Bang H (2000) The finite element method using MATLAB. CRC Press, Boca Raton

    Google Scholar 

  • Lin JH, Che WY, Yu YS (1982) Structural optimization on geometrical configuration and element sizing with statical and dynamical constraints. Comput Struct 15(5):507–515

    Article  MATH  Google Scholar 

  • Liu L, Yan J, Cheng GD (2008) Optimum structure with homogeneous optimum truss-like material. Comput Struct 86:1417–1425

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Persson P, Strang G (2004) A simple mesh generator in MATLAB. SIAM Rev 46(2):329–345

    Article  MathSciNet  MATH  Google Scholar 

  • Rodrigues H, Guedes JM, Bendsøe MP (2002) Hierarchical optimization of material and structure. Struct Multidisc Optim 24:1–10

    Article  Google Scholar 

  • Rozvany GIN (1992) Shape and layout optimization of structural systems and optimality criteria methods. Springer, Berlin

    MATH  Google Scholar 

  • Sigmund O (2001) A 99 line topology optimization code written in MATLAB. Struct Multidisc Optim 21(2):120–127

    Article  Google Scholar 

  • Su W, Liu ST (2010) Size-dependent optimal microstructure design based on couple-stress theory. Struct Multidisc Optim 42:243–254

    Article  Google Scholar 

  • Sypeck DJ, Wadley HNG (2001) Multifunctional microtruss laminates: textile synthesis, and properties. J Mater Res 16(3):890–897

    Article  Google Scholar 

  • Takano N, Zako M (2000) Integrated design of graded microstructures of heterogeneous materials. Arch Appl Mech 70:585–596

    Article  MATH  Google Scholar 

  • Wallach JC, Gibson LJ (2001) Mechanical behavior of a three-dimensional truss material. Int J Solids Struct 38:7181–7196

    Article  MATH  Google Scholar 

  • Wang H (2005) A unit cell approach for lightweight structure and compliant mechnism. PhD thesis, Georgia Institute of Technology, Atlanta, GA

  • Wang B, Cheng GD (2005) Design of cellular structures for optimum efficiency of heat dissipation. Struct Multidisc Optim 30:447–458

    Article  Google Scholar 

  • Wang XM, Wang MY, Guo DM (2004) Structural shape and topology optimization in a level-set framework of region representation. Struct Multidisc Optim 27:1–19

    Article  Google Scholar 

  • Wang H, Cheng Y, Rosen DW (2005) A hybrid geometric modeling method for large scale conformal cellular structures. In: The ASME international design engineering technical conferences & computers and information in engineering conference, Long Beach, CA. Paper No. DETC2005-85366

  • Wicks N, Hutchinson JW (2001) Optimal truss plates. Int J Solids Struct 38:5165–5183

    Article  MATH  Google Scholar 

  • Yan J, Cheng GD, Liu ST, Liu L (2006) Comparison of prediction on effective elastic property and shape optimization of truss material with periodic microstructure. Int J Mech Sci 48:400–413

    Article  MATH  Google Scholar 

  • Zhang WH, Sun SP (2006) Scale-related topology optimization of cellular materials and structures. Int J Numer Methods Eng 68(9):993–1011

    Article  MATH  Google Scholar 

  • Zhang WH, Domaszewski M, Fleury C (1998) A new mixed convex approximation method with applications for truss configuration optimization. Struct Optim 15:237–241

    Article  Google Scholar 

  • Zhou M, Rozvany GIN (1991) The coc algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:197–224

    Article  Google Scholar 

Download references

Acknowledgments

This research work is partly supported by the National Key Basic Research Special Fund of China (Grant No. 2009CB724204), the National Natural Science Foundation of China (Grant No. 51105159), Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110142120091), and the Fundamental Research Funds for the Central Universities, HUST (Grant No. 2011QN033), which the authors gratefully acknowledge. The insightful comments of the reviewers’ are cordially appreciated.

Author information

Authors and Affiliations

  1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China

    Qi Xia & Tielin Shi

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

    Michael Yu Wang

Authors
  1. Qi Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Yu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tielin Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tielin Shi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, Q., Wang, M.Y. & Shi, T. A method for shape and topology optimization of truss-like structure. Struct Multidisc Optim 47, 687–697 (2013). https://doi.org/10.1007/s00158-012-0844-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-012-0844-y

Keywords

Search

Navigation