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Graph."],"published-print":{"date-parts":[[2022,10,31]]},"abstract":"<jats:p>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.<\/jats:p>\n          <jats:p>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 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.<\/jats:p>\n          <jats:p>We demonstrate our method on several frame fields produced by the homogenization approach to topology optimization.<\/jats:p>","DOI":"10.1145\/3516522","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T16:42:36Z","timestamp":1645720956000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":20,"title":["Synthesis of Frame Field-Aligned Multi-Laminar Structures"],"prefix":"10.1145","volume":"41","author":[{"given":"Florian Cyril","family":"Stutz","sequence":"first","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4531-7226","authenticated-orcid":false,"given":"Tim Felle","family":"Olsen","sequence":"additional","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeroen Peter","family":"Groen","sequence":"additional","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tuan Nguyen","family":"Trung","sequence":"additional","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Niels","family":"Aage","sequence":"additional","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ole","family":"Sigmund","sequence":"additional","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Justin","family":"Solomon","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA, United States of America"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2583-0660","authenticated-orcid":false,"given":"Jakob Andreas","family":"B\u00e6rentzen","sequence":"additional","affiliation":[{"name":"Technical University of Denmark, Lyngby, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2022,5,13]]},"reference":[{"issue":"7674","key":"e_1_3_3_2_1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1038\/nature23911","article-title":"Giga-voxel computational morphogenesis for structural design","volume":"550","author":"Aage Niels","year":"2017","unstructured":"Niels Aage, Erik Andreassen, Boyan S. 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