Synthesis of Frame Field-Aligned Multi-Laminar Structures

Florian Cyril Stutz*, Tim Felle Olsen, Jeroen Peter Groen, Tuan Nguyen Trung, Niels Aage, Ole Sigmund, Justin Solomon, Jakob Andreas Bærentzen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods. Homogenization can represent microstructures at length scales decoupled from the resolution of the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 laminate. Initially, we investigate where singularities occur in orthogonal rank-3 laminates and show that the laminar parts of the structures we seek are unaffected by the singularities. Based on this observation, we propose a method for generating multi-laminar structures from frame fields that describe rank-3 laminates. Rather than establishing a parametrization of the domain, we compute stream surfaces that align with the frame fields and solve an optimization problem in order to find a well-spaced collection of such stream surfaces. Since our method does not rely on a parametrization, we also do not need a combing of the frame fields to generate this collection. Finally, we provide a method for synthesizing multi-laminar structures from a stream surface collection. This method produces a volumetric solid for each surface and combines these to form the output. We demonstrate our method on several frame fields produced by the homogenization approach to topology optimization.
Original languageEnglish
Article number170
JournalA C M Transactions on Graphics
Issue number5
Number of pages20
Publication statusPublished - 2022


  • Topology optimization
  • Multi-laminar structures
  • Frame-fields
  • Stream surfaces


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