Two-dimensional analysis of rolling process using a generalized upper bound approach based on a polynomial velocity field

Two-dimensional analysis of rolling process using a generalized upper bound approach based on a polynomial velocity field | 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 Two-dimensional analysis of rolling process using a generalized upper bound approach based on a polynomial velocity field Antonio Del Prete, Teresa Primo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8980086/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 In order to predict material flow and mechanical loads in a 2D plain strain rolling process, in this work, a mathematical rolling model based on the Upper Bound Method (UBM) was developed. In particular, a family of polynomial kinematically admissible velocity fields is proposed and used. Some of these velocity fields with a low number of parameters are used. Among the infinite values ​​that the velocity field coefficients can take on, the most plausible ones will be those that minimize the function that expresses the power necessary to carry out the rolling process. It is possible to observe that non linear fields of that family give a better approximation than the classic one. Predictions were compared with FEM analysis in terms of rolling loads, and results are in good agreement, especially using high degree polynomial fields. Hot Rolling Upper Bound Method Polynomial velocity fields Inhomogeneous deformation Finite Element Method Full Text 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-8980086","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":605807521,"identity":"034d60f2-b54c-482f-80c9-210e3df36785","order_by":0,"name":"Antonio Del Prete","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Antonio","middleName":"Del","lastName":"Prete","suffix":""},{"id":605807522,"identity":"ff1f763f-b084-47b4-9215-756dcbee31f1","order_by":1,"name":"Teresa Primo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVRIiWNgGAWjYFADZiD+wMDAA2Q1gAXYcCjkQdbCOAMswAjUkgDUgkMPDzKHGcKDasFljT1778OHP2oY8szbuRMf27bdkZFvP9j4uPCHDQOffAN2W3iOGxvzHGMoljnMu9k4t+0Zj8GZxGbjGQlpuB0mkcYmDXRC4gxm3m3SuW2HeQwYEtukeRIO49Yi/4z9549/UC2WQC3y/Q/bf+PVIgGU4W2DamEEamG4kdjGjFfLmTRmad4+iWIJZt7Nhj3ngA678bBZmictjYeNLQGrFvb2Y4wff3yzyZPgP7vxwY+yw/by/ckHP/PY2MjJNx/Abg0ESGAayIOpChVgd8MoGAWjYBSMAhAAAPE8TbkwMBmYAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-3777-454X","institution":"Universita del Salento","correspondingAuthor":true,"prefix":"","firstName":"Teresa","middleName":"","lastName":"Primo","suffix":""}],"badges":[],"createdAt":"2026-02-26 16:42:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8980086/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8980086/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106728782,"identity":"c820f721-be8f-4650-b683-b486cd37b2d8","added_by":"auto","created_at":"2026-04-12 18:45:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1039266,"visible":true,"origin":"","legend":"","description":"","filename":"UBMTPRIMO.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8980086/v1_covered_d5a3384d-0f68-48db-b351-5c8a8225dec4.pdf"}],"financialInterests":"","formattedTitle":"Two-dimensional analysis of rolling process using a generalized upper bound approach based on a polynomial velocity field","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":"Hot Rolling, Upper Bound Method, Polynomial velocity fields, Inhomogeneous deformation, Finite Element Method","lastPublishedDoi":"10.21203/rs.3.rs-8980086/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8980086/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn order to predict material flow and mechanical loads in a 2D plain strain rolling process, in this work, a mathematical rolling model based on the Upper Bound Method (UBM) was developed. 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