B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method

B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method | 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 B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method Kaixian Liang, Jikai Liu, Shuzhi Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8484746/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Density method and level set method (LSM) stand as the two most prevalent topology optimization approaches. The former boasts strong robustness but suffers from ambiguous boundary geometric information, while the latter describes structural boundaries via implicit functions, enabling accurate high-order boundary information, but suffers from issues of initial guess dependency and incompatibility to standard optimizers. These two approaches have long been isolated with rare mutual compensations. In this paper, we proposed a novel approach that starts from the density field and achieves its transformation to the signed distance function (SDF) by solving design-dependent transient diffusion equation and Poisson equation. The derived SDF maintains geometric equivalence with the original density field. On this foundation, we further developed two B-DGTO (Boundary-fitting Derivable Geodesics-coupled Topology Optimization) frameworks: the density-based B-DGTO and the SDF-based B-DGTO, in supporting the density-level set co-topology optimization. The efficacy of these frameworks is validated through addressing mean curvature constraint and perimeter constraint on the L-brackets and thermal conduction structures. The proposed method provides a systematic framework integrating density method and LSM, holding profound implications for future development. Mechanical Engineering Topology optimization Density method Signed distance function Level set Boundary geometric Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-8484746","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":567537248,"identity":"fc181483-b678-4ed9-9e28-be5c43376595","order_by":0,"name":"Kaixian Liang","email":"","orcid":"","institution":"Shandong university","correspondingAuthor":false,"prefix":"","firstName":"Kaixian","middleName":"","lastName":"Liang","suffix":""},{"id":567537249,"identity":"420213e9-7218-4939-bf4e-a727ff6891a4","order_by":1,"name":"Jikai 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The former boasts strong robustness but suffers from ambiguous boundary geometric information, while the latter describes structural boundaries via implicit functions, enabling accurate high-order boundary information, but suffers from issues of initial guess dependency and incompatibility to standard optimizers. These two approaches have long been isolated with rare mutual compensations. In this paper, we proposed a novel approach that starts from the density field and achieves its transformation to the signed distance function (SDF) by solving design-dependent transient diffusion equation and Poisson equation. The derived SDF maintains geometric equivalence with the original density field. On this foundation, we further developed two B-DGTO (Boundary-fitting Derivable Geodesics-coupled Topology Optimization) frameworks: the density-based B-DGTO and the SDF-based B-DGTO, in supporting the density-level set co-topology optimization. The efficacy of these frameworks is validated through addressing mean curvature constraint and perimeter constraint on the L-brackets and thermal conduction structures. The proposed method provides a systematic framework integrating density method and LSM, holding profound implications for future development.\u003c/p\u003e","manuscriptTitle":"B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-06 02:29:03","doi":"10.21203/rs.3.rs-8484746/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"03d3bd0c-4ede-4bb7-8e60-ffe212b39ab2","owner":[],"postedDate":"January 6th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":60399677,"name":"Mechanical Engineering"}],"tags":[],"updatedAt":"2026-01-06T02:29:03+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-06 02:29:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8484746","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8484746","identity":"rs-8484746","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}