Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization

Eduardo Fernández, Kai ke Yang, Stijn Koppen, Pablo Alarcón, Simon Bauduin, Pierre Duysinx

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)


This paper focuses on density-based topology optimization and proposes a combined method to simultaneously impose Minimum length scale in the Solid phase (MinSolid), Minimum length scale in the Void phase (MinVoid) and Maximum length scale in the Solid phase (MaxSolid). MinSolid and MinVoid mean that the size of solid parts and cavities must be greater than the size of a prescribed circle or sphere. This is ensured through the robust design approach based on eroded, intermediate and dilated designs. MaxSolid seeks to restrict the formation of solid parts larger than a prescribed size, which is imposed through local volume restrictions. In the first part of this article, we show that by proportionally restricting the maximum size of the eroded, intermediate and dilated designs, it is possible to obtain optimized designs satisfying, simultaneously, MinSolid, MinVoid and MaxSolid. However, in spite of obtaining designs with crisp boundaries, some results can be difficult to manufacture due to the presence of multiple rounded cavities, which are introduced by the maximum size restriction with the sole purpose of avoiding thick solid members in the structure. To address this issue, in the second part of this article we propose a new geometric constraint that seeks to control the minimum separation distance between two solid members, also called the Minimum Gap (MinGap). Differently from MinVoid, MinGap introduces large void areas that do not necessarily have to be round. 2D and 3D test cases show that simultaneous control of MinSolid, MinVoid, MaxSolid and MinGap can be useful to improve the manufacturability of maximum size constrained designs.

Original languageEnglish
Article number113157
Number of pages31
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2020


  • Filtering
  • Length scale
  • Manufacturing constraints
  • Minimum gap
  • SIMP


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