On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus

On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus | 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 On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus Luobin Lin, Fuquan Chen, Xianhai Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2875273/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 This paper provides two parallel generalized solutions on a fundamental mixed boundary value problem that a unit annulus is subjected to a partially fixed outer periphery and an arbitrary traction acting along the inner periphery by using the complex variable method. The mixed problem is transformed into two parallel Riemann-Hilbert problems with respective sets of different mathematically rigorous boundary conditions, which are solved by successive approximation method with the Lanczos filtering technique to obtain numerically equivalent stress and displacement results. Four typical numerical cases coded by FORTRAN are carried out and compared to the same cases performed on ABAQUS to validate these two parallel solutions. Based on the case results, the detailed reasons of numerically equivalence between these two parallel solutions are analytically elaborated and several insights of the application of the complex variable method are revealed. Mixed boundary value problem Annulus Riemann-Hilbert problem Mutually numerical equivalence 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-2875273","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":196228904,"identity":"44d1eea9-21c6-4cbe-963c-e3e82c33a1f9","order_by":0,"name":"Luobin Lin","email":"","orcid":"","institution":"Fujian University of Techonology","correspondingAuthor":false,"prefix":"","firstName":"Luobin","middleName":"","lastName":"Lin","suffix":""},{"id":196228905,"identity":"99443d68-a813-4b98-a5d1-95098e248d9f","order_by":1,"name":"Fuquan Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYDACCQYDZiAlx94A4rGRoMWY5wCpWhJ7iNZiLt288XNBxZ30Hv4zBgwfyg4z8M9uwK/Fcs6xYukZZ57l9jCcMWCcce4wg8SdA/i1GNzIMWPmbTucu5+xxwDEYDCQSCBGy7/D6TzMPAbMf4nX0nA4gYcNqIWRGC2WM9KKpXmOHTbs4WErONhzLp1H4gYBLeYSyRs/89QclufhP7zxwY8yazn+GYQchsw5AMQ8+NWjaxkFo2AUjIJRgBUAAPlfPmS4rReZAAAAAElFTkSuQmCC","orcid":"","institution":"Fuzhou University","correspondingAuthor":true,"prefix":"","firstName":"Fuquan","middleName":"","lastName":"Chen","suffix":""},{"id":196228906,"identity":"da42c699-8078-41c1-a6fa-bf01e36fc7d5","order_by":2,"name":"Xianhai Huang","email":"","orcid":"","institution":"Fujian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Xianhai","middleName":"","lastName":"Huang","suffix":""}],"badges":[],"createdAt":"2023-04-29 05:59:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2875273/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2875273/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":36961556,"identity":"f599994b-1c4a-40e8-a641-1b03b7459ed2","added_by":"auto","created_at":"2023-05-12 15:29:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1253976,"visible":true,"origin":"","legend":"","description":"","filename":"fe398e6f21f847e9b543274e208ebfcf.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2875273/v1_covered_90c0c2e5-d755-449d-b943-7ec5da35db82.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus","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":"Mixed boundary value problem, Annulus, Riemann-Hilbert problem, Mutually numerical equivalence","lastPublishedDoi":"10.21203/rs.3.rs-2875273/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2875273/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper provides two parallel generalized solutions on a fundamental mixed boundary value problem that a unit annulus is subjected to a partially fixed outer periphery and an arbitrary traction acting along the inner periphery by using the complex variable method. The mixed problem is transformed into two parallel Riemann-Hilbert problems with respective sets of different mathematically rigorous boundary conditions, which are solved by successive approximation method with the Lanczos filtering technique to obtain numerically equivalent stress and displacement results. Four typical numerical cases coded by FORTRAN are carried out and compared to the same cases performed on ABAQUS to validate these two parallel solutions. Based on the case results, the detailed reasons of numerically equivalence between these two parallel solutions are analytically elaborated and several insights of the application of the complex variable method are revealed.","manuscriptTitle":"On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-05-03 03:57:33","doi":"10.21203/rs.3.rs-2875273/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":"932369b2-b079-4e2c-85d6-a17bd76f87fb","owner":[],"postedDate":"May 3rd, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-05-12T15:29:21+00:00","versionOfRecord":[],"versionCreatedAt":"2023-05-03 03:57:33","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2875273","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2875273","identity":"rs-2875273","version":["v1"]},"buildId":"2u56kwukJI3zHK-uzyFNs","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}