A geometrically exact beam element via the gradient-deficient absolute nodal coordinate formulation

A geometrically exact beam element via the gradient-deficient absolute nodal coordinate formulation | 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 A geometrically exact beam element via the gradient-deficient absolute nodal coordinate formulation Baixun Shao, Minggang Wu, Yufeng Wang, Zhenxing Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9279936/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 Dynamic modeling of beam-like structures undergoing large rotations and deformations within the absolute nodal coordinate formulation (ANCF) often requires a large number of gradient-related degrees of freedom, leading to high computational cost. In this paper, a gradient-deficient geometrically exact ANCF beam element is proposed to achieve a more compact kinematic description while retaining the capability to represent essential deformation modes. The proposed formulation interpolates the axial gradient together with a single transverse gradient to construct a local Cartesian coordinate system for cross-sectional representation, thereby eliminating one redundant transverse gradient. Based on this kinematic framework, the elastic force vector and the generalized external force vectors corresponding to applied moments, concentrated forces, and distributed loads are formulated. Several numerical examples involving large-deflection bending, rolling-up deformation, and pure torsional loading are presented. The results indicate that the proposed element provides accuracy comparable to that of existing fully parameterized ANCF beam elements, while reducing the number of degrees of freedom and the overall computational scale. Absolute nodal coordinate formulation gradient-deficient beam element geometrically exact beam degree of freedom reduction Full Text Additional Declarations No competing interests reported. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9279936","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626971286,"identity":"0ca6450a-cf4e-4390-a0bb-4251f4532a4c","order_by":0,"name":"Baixun Shao","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"Baixun","middleName":"","lastName":"Shao","suffix":""},{"id":626971287,"identity":"f0569956-0fb1-4dbe-8a66-3a86b21db18e","order_by":1,"name":"Minggang Wu","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"Minggang","middleName":"","lastName":"Wu","suffix":""},{"id":626971288,"identity":"4dddbdab-f913-4b1f-9883-1060c8ec038a","order_by":2,"name":"Yufeng Wang","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"Yufeng","middleName":"","lastName":"Wang","suffix":""},{"id":626971289,"identity":"3779e4f7-2f0e-452d-9c51-64f18623c0e5","order_by":3,"name":"Zhenxing Shen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYDACCTBpA+HwkKAljXQth0nQIj+7+djDn23nE+fPSGB88LaNQd6ckBaDO8fSDSTO3E7ccCOB2XBuG4PhzgZCWiRyzCQMKoBaJBLYpHnbGBIMDhBy2Iz8bxIJBudADmP/TZQWhhs5bBIHKg4kNtxIYGMmSovBjTQzyYYzycYbzjxslpxzTsJwA2GHJT+T/NlmJzu/PfnghzdlNvKEHQYFjg0MjA0MsGgiCtgTr3QUjIJRMApGHAAA1mQ/5iJ8X44AAAAASUVORK5CYII=","orcid":"","institution":"Yanshan University","correspondingAuthor":true,"prefix":"","firstName":"Zhenxing","middleName":"","lastName":"Shen","suffix":""}],"badges":[],"createdAt":"2026-03-31 12:39:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9279936/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9279936/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107708076,"identity":"5e2fc19d-d537-4694-9a12-d6dacd3d3515","added_by":"auto","created_at":"2026-04-24 09:21:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2632697,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9279936/v1_covered_dd9cc2f4-a930-45c2-9904-4b58a0ba123c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A geometrically exact beam element via the gradient-deficient absolute nodal coordinate formulation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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},"keywords":"Absolute nodal coordinate formulation, gradient-deficient beam element, geometrically exact beam, degree of freedom reduction","lastPublishedDoi":"10.21203/rs.3.rs-9279936/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9279936/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDynamic modeling of beam-like structures undergoing large rotations and deformations within the absolute nodal coordinate formulation (ANCF) often requires a large number of gradient-related degrees of freedom, leading to high computational cost. In this paper, a gradient-deficient geometrically exact ANCF beam element is proposed to achieve a more compact kinematic description while retaining the capability to represent essential deformation modes. The proposed formulation interpolates the axial gradient together with a single transverse gradient to construct a local Cartesian coordinate system for cross-sectional representation, thereby eliminating one redundant transverse gradient. Based on this kinematic framework, the elastic force vector and the generalized external force vectors corresponding to applied moments, concentrated forces, and distributed loads are formulated. Several numerical examples involving large-deflection bending, rolling-up deformation, and pure torsional loading are presented. 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