VoroTO: Multiscale Topology Optimization of Voronoi Structures using Surrogate Neural Networks

VoroTO: Multiscale Topology Optimization of Voronoi Structures using Surrogate Neural Networks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article VoroTO: Multiscale Topology Optimization of Voronoi Structures using Surrogate Neural Networks Krishnan Suresh, Rahul Padhy, Aaditya Chandrasekhar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4339435/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Oct, 2024 Read the published version in Engineering with Computers → Version 1 posted 9 You are reading this latest preprint version Abstract ellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers have proposed Voronoi multi-scale designs for a wide variety of engineering applications. However, designing such structures can be computationally prohibitive due to the multi-scale nature of the underlying analysis and optimization.In this work, we propose the use of a neural network (NN) to carry out efficient topology optimization (TO) of multi-scale Voronoi structures. The NN is first trained using Voronoi parameters (cell site locations, thickness, orientation, and anisotropy) to predict the homogenized constitutive properties. This network is then integrated into a conventional TO framework to minimize structural compliance subject to a volume constraint. Special considerations are given for ensuring positive definiteness of the constitutive matrix and promoting macroscale connectivity. Several numerical examples are provided to showcase the proposed method. Topology Optimization Voronoi Structures Neural Network Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Oct, 2024 Read the published version in Engineering with Computers → Version 1 posted Editorial decision: Revision requested 03 Sep, 2024 Reviews received at journal 22 Aug, 2024 Reviews received at journal 03 Jun, 2024 Reviewers agreed at journal 09 May, 2024 Reviewers agreed at journal 07 May, 2024 Reviewers invited by journal 07 May, 2024 Editor assigned by journal 01 May, 2024 Submission checks completed at journal 29 Apr, 2024 First submitted to journal 28 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4339435","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":297680007,"identity":"25a35d9e-1d70-483c-958d-993b6fe9ac6e","order_by":0,"name":"Krishnan Suresh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYBACCQh1QI6BGcxgJl6LMelaEhsYiNUi2X/G7MOHP3fSNxxnf/iBocIaphc3kJbIMZ45s+1Z7obDPMYSDGfSCWuRk+AxZuZtOJy77TAPGwNj22EitPCfMWb+8+dwutlh9mcMjP+I0CLNkGPMzMB2OMHsMIMZA2MDEVokZ6QVM/a2HTbcD/JLwrF0Y4JaJM4f3szw489hecn+4w8/fKixliWoBRUkkKZ8FIyCUTAKRgEuAABGFjzyYETQ9AAAAABJRU5ErkJggg==","orcid":"","institution":"University of Wisconsin–Madison","correspondingAuthor":true,"prefix":"","firstName":"Krishnan","middleName":"","lastName":"Suresh","suffix":""},{"id":297680009,"identity":"8ab29251-8143-466d-a8fc-4a191ed3587e","order_by":1,"name":"Rahul Padhy","email":"","orcid":"","institution":"University of Wisconsin–Madison","correspondingAuthor":false,"prefix":"","firstName":"Rahul","middleName":"","lastName":"Padhy","suffix":""},{"id":297680010,"identity":"084c1dfa-3065-41e9-bf8f-f19540c09c10","order_by":2,"name":"Aaditya Chandrasekhar","email":"","orcid":"","institution":"Northwestern University","correspondingAuthor":false,"prefix":"","firstName":"Aaditya","middleName":"","lastName":"Chandrasekhar","suffix":""}],"badges":[],"createdAt":"2024-04-28 22:53:41","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4339435/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4339435/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00366-024-02077-w","type":"published","date":"2024-10-29T16:20:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":68207260,"identity":"4a486839-bd6b-4fe9-8878-13b6c200de56","added_by":"auto","created_at":"2024-11-04 16:36:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10801552,"visible":true,"origin":"","legend":"","description":"","filename":"VoroTO.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4339435/v1_covered_c7ef9652-926f-4b65-88fd-ee21997df0d4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"VoroTO: Multiscale Topology Optimization of Voronoi Structures using Surrogate Neural Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Topology Optimization, Voronoi Structures, Neural Network","lastPublishedDoi":"10.21203/rs.3.rs-4339435/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4339435/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"ellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. 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