Voxel-based support structures for additive manufacture of topologically optimal geometries

  • Martin LearyEmail author
  • Maciej Mazur
  • Marcus Watson
  • Etienne Boileau
  • Milan Brandt


Additive manufacturing (AM) enables the direct manufacture of complex geometries with unique engineering properties. In particular, AM is compatible with topology optimisation (TO) and provides a unique opportunity for optimal structural design. Despite the commercial opportunities enabled by AM, technical requirements must be satisfied in order to achieve robust production outcomes. In particular, AM requires support structures to fabricate overhanging geometry and avoid overheating. Support generation tools exist; however, these are generally not directly compatible with the voxel-based representation typical of TO geometries, without additional computational steps. This research proposes the use of voxel-based Cellular automata (CA) as a fundamentally novel method for the generation of AM support structures. A number of CA rules are proposed and applied with the objective of generating robust support structures for an arbitrary TO geometry. Relevant CA parameters are assessed in terms of structure manufacturability, including sequential and random CA, rotation of the cellular array, and alternate CA boundary rules, including permutations not previously reported. From this research, CA with complex cell arrangements that provide robust AM support for TO geometries are identified and demonstrated by manufacture with selective laser melting (SLM) and fused deposition modelling (FDM). These CA may be automatically applied to enable TO geometries to be directly fabricated by AM, thereby providing a unique, and commercially significant, design for AM (DFAM) capability.


Design for additive manufacture DFAM Optimisation 3D printing Self-supporting Print-ready 



Additive manufacturing


Computer-aided design


Cellular automaton


Design for additive manufacture


Fused deposition modelling


Selective laser melting


Topology optimisation


A discrete element of a volume domain


The status of a cell, either ON or OFF, or undefined (?)



Percentage of manufacturable cells in the CA support structure


Percentage of manufacturable cells in part geometry

Mp, ave

Average percentage of Mp for multiple geometries


Percentage of manufacturable cells in support geometry

Ms, ave

Average percentage of Ms for multiple geometries


Time step


Voxel side length


Set of manufacturable part voxels


Set of manufacturable support voxels


Number of CA permutations


Total number of voxels


O-notation for asymptotic upper bound of computational complexity


Funding information

This study was financially supported by the members of the ARC Training Centre for Lightweight Automotive Structures and from the Australian Research Council (Grant Reference IC160100032).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Martin Leary
    • 1
    • 2
    Email author
  • Maciej Mazur
    • 1
  • Marcus Watson
    • 1
    • 2
  • Etienne Boileau
    • 3
  • Milan Brandt
    • 1
  1. 1.RMIT Centre for Additive ManufactureRMIT UniversityMelbourneAustralia
  2. 2.ARC Training Centre for Lightweight Automotive Structures (ATLAS), Australian Research Council Grant IC160100032Mill ParkAustralia
  3. 3.Institut Français de Mécanique AvancéeClermont-FerrandFrance

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