The Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures

The Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures | 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 The Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures Yanze Li, Jiawei Fu, Linfang Qian, Haoyu Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1380355/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 The significance of the nonlinear terms in the governing equations to describe the transiently large deformation of a thin-walled cylindrical shell under impact pressures is discussed in this paper. Firstly, the first P-K stress tensor is adopted to depict the motion equations of the shell with respect to the original configuration. More nonlinear terms are retained when the first P-K stress is transformed into the symmetrical second P-K stress. Moreover, the Green strain tensor is employed in the geometrical equation to describe the nonlinearly large deformation of shell, and the curvature change is expressed to involve large deformation as well. Without considering all these nonlinear terms, the governing equation can degenerate to that in references. The circumferential displacement is kept in the motion equations, and the wall thickness change is taken into account. Dividing these nonlinear terms into two parts according to their affiliations, four groups of governing equations involving different nonlinear terms are obtained. Then, the deformation behavior of a shell subjected to a specified loading is solved using different governing equations and compared with FEM results to reveal the significance of these nonlinear terms. It is found that the nonlinear terms from geometrical equations should be kept while the nonlinear terms in equilibrium equations can be ignored. Nonlinear terms Thin-walled shell Large deformation Impact pressures 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. 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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-1380355","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":89179795,"identity":"72d60996-81fe-4647-aea9-94de4d0c1c34","order_by":0,"name":"Yanze Li","email":"","orcid":"https://orcid.org/0000-0002-6107-7488","institution":"Nanjing University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yanze","middleName":"","lastName":"Li","suffix":""},{"id":89179796,"identity":"2dd5975e-9514-42d9-ad67-39c1cf918d5c","order_by":1,"name":"Jiawei Fu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYBACxgbGBwwfGNggPB7itDAbMM4AaWEjVgsDA7MBM1gl0VqYZySzSdvu4EucPx/oxLdtDPLmBB0G0pJ7hi1xwzEGZsO5bQyGOxsIaZmdf0w6tw2ohY2BTZq3jSHB4ABBLUBbLIFa5rcxsP8mXgsjUEvDMQY2ZuK0zH/MbNnbxma84Vhis+SccxKGGwhpMew5zHjjZ9sx2fnNhw9+eFNmI0/QFsMGMHUMZCGIKUFAPRDIQ6gawipHwSgYBaNg5AIAEts512gRQ3YAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-2638-2468","institution":"Nanjing University of Science and Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jiawei","middleName":"","lastName":"Fu","suffix":""},{"id":89179797,"identity":"0b9dd0dd-af81-4056-94e1-ec67395087f1","order_by":2,"name":"Linfang Qian","email":"","orcid":"","institution":"Northwest Institute of Mechanical and Electrical Engineering","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Linfang","middleName":"","lastName":"Qian","suffix":""},{"id":89179798,"identity":"575b99ba-b7f7-4050-af00-d29f61309ac5","order_by":3,"name":"Haoyu Wang","email":"","orcid":"","institution":"Nanjing University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Haoyu","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2022-02-21 08:50:53","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1380355/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1380355/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":19126241,"identity":"13cb2127-89e9-416a-9399-c5b105183866","added_by":"auto","created_at":"2022-03-11 15:20:26","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":511923,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript2.1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1380355/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eThe Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1380355/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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":"Nonlinear terms, Thin-walled shell, Large deformation, Impact pressures","lastPublishedDoi":"10.21203/rs.3.rs-1380355/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1380355/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe significance of the nonlinear terms in the governing equations to describe the transiently large deformation of a thin-walled cylindrical shell under impact pressures is discussed in this paper. Firstly, the first P-K stress tensor is adopted to depict the motion equations of the shell with respect to the original configuration. More nonlinear terms are retained when the first P-K stress is transformed into the symmetrical second P-K stress. Moreover, the Green strain tensor is employed in the geometrical equation to describe the nonlinearly large deformation of shell, and the curvature change is expressed to involve large deformation as well. Without considering all these nonlinear terms, the governing equation can degenerate to that in references. The circumferential displacement is kept in the motion equations, and the wall thickness change is taken into account. Dividing these nonlinear terms into two parts according to their affiliations, four groups of governing equations involving different nonlinear terms are obtained. Then, the deformation behavior of a shell subjected to a specified loading is solved using different governing equations and compared with FEM results to reveal the significance of these nonlinear terms. It is found that the nonlinear terms from geometrical equations should be kept while the nonlinear terms in equilibrium equations can be ignored.\u003c/p\u003e","manuscriptTitle":"The Significance of Nonlinear Terms in the Governing Equations to Describe the Large Deformation of Thin-Walled Cylindrical Shell Under Transient Pressures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-03-11 15:20:13","doi":"10.21203/rs.3.rs-1380355/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":"6a319290-9706-4246-9c61-b3835397fa60","owner":[],"postedDate":"March 11th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2022-05-17T13:54:06+00:00","versionOfRecord":[],"versionCreatedAt":"2022-03-11 15:20:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1380355","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1380355","identity":"rs-1380355","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}