Meshless Additive Manufacturing

  • Soo-Hwa Kim

Student thesis: Doctoral ThesisPhD


Additive manufacturing (AM) processes produce components by adding material in a layer-by-layer fashion. This allows new types of geometries to be feasible, particularly lattice structures. Although lattices are possible to additively manufacture, the modelling capabilities and customisation is greatly limited by the current conventional AM process flow due to their complex topologies. Within the process flow, there are several stages that use mesh-based modelling posing a costly trade-off between computational memory limits and geometric accuracy.

Meshless implicit-based modelling overcomes the bottlenecks arising from mesh-based issues. This approach is ideal for a sub-class of lattices called triply-periodic minimal surfaces (TPMS) that are defined by a single implicit function. These lattices are gaining popularity in industries and the AM community due to their high surface-area-to-volume ratio, infinitely smooth, and non-self intersecting properties. These properties highlight the challenges presented by conventional mesh-based modelling, promoting a need for an alternative implicit-based modelling approach.

The vision in this thesis is to expand design capabilities and customisation of AM lattice structures, specifically focussing on TPMS, without using mesh-based modelling. The approach taken in this thesis is to customise TPMS by altering the implicit functions to design specification and then directly slicing the manipulated functions as infill. As is, TPMS implicit functions define infinitely thin lattices that are not feasible to manufacture. The functions can be manipulated to create lattice structures, however, the resulting geometry from the manipulated functions was not intuitive. As such the first part of this research was to characterise the resulting geometric properties from manipulating the implicit functions.

Once characterised, such that the TPMS can be customised to a certain geometric specification, this can be used in a direct slicing process flow to fabricate customised TPMS structures. The next step was to create an algorithm to generate toolpaths for an AM machine using manipulated TPMS functions. From this, printed TPMS structures could be related using experimental methods to link engineering properties to the geometric properties. This link enables designers to create lattices in a more purposeful way without the need to use CAD.

Resulting from this research, this thesis presents the following novel research contributions. Firstly, a set of numerical methods were established to calculate the volume fraction, surface area, and minimum thickness of manipulated TPMS structures to a known accuracy tolerance. Next by using this set, empirical geometric relationships between the manipulated implicit functions and the geometric properties were established. Finally, a method was developed to AM TPMS structures with tunable geometric or mechanical properties without using mesh-based methods. The developments achieved in this thesis promote the use of implicit-based modelling and TPMS structures in AM.

Date of Award23 Nov 2022
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorJoseph Flynn (Supervisor) & Vimal Dhokia (Supervisor)


  • Additive manufacturing
  • 3D printing
  • Lattices
  • Triply Periodic Minimal Surfaces (TPMS)
  • Modelling

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