Non-conforming multi-patch isogeometric topology optimization for plate and shell structures based on Nitsche’s method

Non-conforming multi-patch isogeometric topology optimization for plate and shell structures based on Nitsche’s 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 Non-conforming multi-patch isogeometric topology optimization for plate and shell structures based on Nitsche’s method Can liu, Shuting Wang, Xianda Xie This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8674307/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract This paper presents a multi-patch isogeometric topology optimization (MITO) method for plates and shells based on Nitsche’s method, which can effectively address compliance minimization problems of complex structures comprised of non-conforming multiple NURBS patches. 5-DOFs Reissner-Mindlin (RM) degenerate elements are used to discretize complex plate and shell structures. Meanwhile, NURBS-based isogeometric analysis (IGA) can accurately described the geometry of the mid-surfaces of both RM plates and shells, where Nitsche’s method is used to couple different patches for several typical interface formulations, with a broader parameter stability domain in penalty factor than traditional penalty method. In addition, the tensor-product decomposed explicit filter is employed to substitute traditional sensitivity filter in our presented MITO approach. Several benchmark examples are presented to verify the effectiveness and robustness of the proposed MITO method for thin wall structures. Compared to the traditional sensitivity filter, the compliance value and design variable update time obtained by the tensor-product decomposed explicit filter are maximumly reduced by 14.8% and 50.6%, respectively. In summary, the proposed MITO method is an effective tool of performing innovative design for complex thin wall structures. Isogeometric analysis ‧ Plate and shell structures ‧ Reissner-Mindlin theory ‧ Topology optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 27 Apr, 2026 Reviews received at journal 02 Apr, 2026 Reviews received at journal 30 Mar, 2026 Reviewers agreed at journal 12 Mar, 2026 Reviewers agreed at journal 07 Mar, 2026 Reviewers agreed at journal 04 Mar, 2026 Reviewers agreed at journal 02 Mar, 2026 Reviewers invited by journal 02 Mar, 2026 Editor assigned by journal 23 Jan, 2026 Submission checks completed at journal 23 Jan, 2026 First submitted to journal 22 Jan, 2026 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-8674307","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":600369140,"identity":"3722fbaf-9e29-499c-a628-a3527890a1d0","order_by":0,"name":"Can liu","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Can","middleName":"","lastName":"liu","suffix":""},{"id":600369142,"identity":"f8c0dc18-276d-4a23-b6a9-11f7ef706557","order_by":1,"name":"Shuting Wang","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Shuting","middleName":"","lastName":"Wang","suffix":""},{"id":600369144,"identity":"728cf412-3118-41d1-9326-e3399fa55cdc","order_by":2,"name":"Xianda Xie","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYDACZiDmMbDh4UdwidJSkSYn2UC0FhDgOXPY2OAAsVoMjjMfk3jbxpy4+XbzMwmGCuvEBvazB/BqkWxmSzac28aWuO3OMTMJhjPpiQ08eQl4tfAz8xg+5m3jSdx2I4dNgrHtcGKDBI8BXi1szPwfDvO2SSRungHS8o8ILUBbGB/znDEwNpAAaWkgQgvQL8aGcyoS5CRupBlbJBxLN27jycGvxeD84WcSbwz+8/DPSH5440ONtWw/+xn8WlBBAsh3JKgfBaNgFIyCUYADAABoVz3dyhkUFQAAAABJRU5ErkJggg==","orcid":"","institution":"Nanchang University","correspondingAuthor":true,"prefix":"","firstName":"Xianda","middleName":"","lastName":"Xie","suffix":""}],"badges":[],"createdAt":"2026-01-23 02:53:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8674307/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8674307/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104401576,"identity":"a055c5bb-3397-4b27-8f1a-c540b604ebed","added_by":"auto","created_at":"2026-03-11 12:13:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1884564,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8674307/v1_covered_9d520708-7a63-4291-9694-d9a0bfea900c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Non-conforming multi-patch isogeometric topology optimization for plate and shell structures based on Nitsche’s method","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"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":"Isogeometric analysis ‧ Plate and shell structures ‧ Reissner-Mindlin theory ‧ Topology optimization","lastPublishedDoi":"10.21203/rs.3.rs-8674307/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8674307/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper presents a multi-patch isogeometric topology optimization (MITO) method for plates and shells based on Nitsche\u0026rsquo;s method, which can effectively address compliance minimization problems of complex structures comprised of non-conforming multiple NURBS patches. 5-DOFs Reissner-Mindlin (RM) degenerate elements are used to discretize complex plate and shell structures. 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