Acta Mechanica Solida Sinica

, Volume 31, Issue 3, pp 349–356 | Cite as

Topology Optimization of Perforated Continua Based on Truss-Like Material Model

  • Kemin Zhou


A topology optimization method from truss-like continua to perforated continua is studied, which is based on the concept of force transmission paths. The force transmission paths are optimized utilizing a truss-like material model. In the optimization procedure, parts of the force transmission paths are removed. Finally, perforated optimal continua are formed by further optimizing the material distribution field. No intermediate densities are suppressed; therefore, no additional technique is involved and no numerical instabilities are created. Structural topologies are presented using material distribution fields rather than the ‘existence’ or ‘inexistence’ of elements. More detailed structures are obtained utilizing less dense elements.


Topology optimization Structural optimization Truss-like material Perforated continua 



This work was financially supported by the National Natural Science Foundation of China (No. 11572131).


  1. 1.
    Michell AGM. The limits of economy of material in frame structure. Philos Mag. 1904;8(47):589–97.CrossRefzbMATHGoogle Scholar
  2. 2.
    Zhou K, Li X. Topology optimisation for minimum compliance under multiple loads based on continuous distribution of members. Struct Multidiscip Optim. 2008;37(1):49–56.CrossRefGoogle Scholar
  3. 3.
    Zhou K, Li X. Topology optimisation of truss-like continua with three member model under stress constraints. Struct Multidiscip Optim. 2011;43(4):487–93.CrossRefGoogle Scholar
  4. 4.
    Bendsoe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng. 1988;71(2):197–224.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Xie YM, Steven GP. Evolutionary structure optimisation for dynamic problems. Comput Struct. 1996;58(6):1067–73.CrossRefzbMATHGoogle Scholar
  6. 6.
    Sigmund O. Numerical instabilities in topology optimisation: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscip Optim. 1998;16(1):68–75.CrossRefGoogle Scholar
  7. 7.
    Eschenauer HA, Olhoff N. Topology optimisation of continuum structures: a review. Appl Mech Rev. 2001;54(4):1453–7.CrossRefGoogle Scholar
  8. 8.
    Kocvara M, Stingl M. Free material optimisation for stress constraints. Struct Multidiscip Optim. 2007;33(4–5):323–35.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Pedersen P, Pedersen N. On strength design using free material subjected to multiple load cases. Struct Multidiscip Optim. 2013;47(1):7–17.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hornlein HREM, Kocvara M, Werner R. Material optimisation bridging the gap between conceptual and preliminary design. Aerosp Sci Technol. 2001;5(8):541–54.CrossRefzbMATHGoogle Scholar
  11. 11.
    Rozvany GIN. Partial relaxation of the orthogonality requirement for classical Michell trusses. Struct Multidiscip Optim. 1997;13(4):271–4.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hemp WS. Optimum structure. Oxford: Clarendon Press; 1973.Google Scholar
  13. 13.
    Rozvany GIN. Exact analytical solutions for some popular benchmark problems in topology optimisation. Struct Multidiscip Optim. 1998;15(1):42–8.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Sigmund O. A 99 line topology optimisation code written in Matlab. Struct Multidiscip Optim. 2001;21(2):120–7.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2018

Authors and Affiliations

  1. 1.College of Civil EngineeringHuaqiao UniversityFujianChina

Personalised recommendations