Minimum length scale constraints in multi-scale topology optimisation for additive manufacturing

Jikai Liu*, Yufan Zheng, Rafiq Ahmad, Jinyuan Tang, Yongsheng Ma

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


This paper performs a combined numerical and experimental study to explore the role of minimum length scale constraints in multi-scale topology optimisation. Multi-scale topology optimisation is generally performed without considering the actual unit cell size, while an arbitrary value considerably smaller than the part is selected afterwards. However, this procedure would be problematic if including geometric constraints, e.g. minimum length scale constraints, since geometric constraints cannot be applied without knowing the unit cell dimensions. To address this issue, unit cell size should be defined beforehand, and guidelines will be provided in this work through a thorough numerical exploration, i.e. compliance minimisation multi-scale topology optimisation with different unit cell sizes and a consistent minimum length scale limit will be performed. The numerical results indicate that selecting the unit cell size considerably smaller than the part and larger than the length scale limit would be recommended. Then, experiments are conducted to explore the effect of minimum length scale limit on the stiffness and strength of the multi-scale design. It is observed that increasing the minimum length scale limit would reduce the structural mechanical performance in both aspects.

Original languageEnglish
Pages (from-to)229-241
Number of pages13
JournalVirtual and Physical Prototyping
Issue number3
Publication statusPublished - 3 Jul 2019
Externally publishedYes


  • Multi-scale
  • additive manufacturing
  • length scale
  • topology optimisation
  • unit cell size

Cite this