A comprehensive investigation of the bending and vibration behavior of size- dependent functionally graded nanoplates via an enhanced first order shear deformation theory and nonlocal finite element analysis

A comprehensive investigation of the bending and vibration behavior of size- dependent functionally graded nanoplates via an enhanced first order shear deformation theory and nonlocal finite element analysis | 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 comprehensive investigation of the bending and vibration behavior of size- dependent functionally graded nanoplates via an enhanced first order shear deformation theory and nonlocal finite element analysis Mohamed-Ouejdi Belarbi, Soufiane Benounas, Abdelhak Khechai, Pham Van Vinh, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4008300/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 research paper conducts a comprehensive investigation into the bending and free vibration of size-dependent functionally graded (FG) nanoplates, using an improved first-order shear deformation theory (IFSDT). The IFSDT, proposed in this study, offers an enhanced representation and precise computation of normal and shear stresses across the thickness of the nanoplate. Notably, it not only ensures compliance with free conditions on both upper and lower surfaces but also eliminates the need for a conventional correction factor commonly employed in FSDT. The material properties of the FG nanoplate undergo continuous grading throughout the thickness direction using a power-law function. To transcend the assumptions of classical continuum mechanics and address the impacts of small sizes in discrete nanoplates, Eringen's nonlocal elasticity theory is applied. The formulation of the governing equation for bending and free vibration analyses of the FG nanoplate is achieved through the application of Hamilton’s principle. The proposed IFSDT is implemented with a computationally efficient C 0 -continuous quadrilateral element, tackling large-scale discrete numerical problems. The model's performance is showcased through a comparative evaluation against literature predictions, highlighting its high accuracy and rapid convergence. Additionally, the research scrutinizes various parameters such as plate thickness, boundary conditions, aspect ratio, nonlocal parameter, different material compositions, and power-law index. The thorough examination and discussion of these parameters provide insights into their influence on the deflection, stresses, and natural frequency of FG nanoplates. The results underscore the significant impact of size-dependent effects on the bending and vibration behaviors of nanoplates, emphasizing the necessity of incorporating these effects in the design and analysis of FG nanoplates. Ultimately, the developed nonlocal finite element model serves as a valuable predictive tool for understanding the bending and vibration behavior of size-dependent functionally graded nanoplates. Functionally graded Composite nano-plates Static and free vibration finite element Nonlocal elasticity theory Shear deformation theory 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-4008300","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":276227458,"identity":"7875ec63-12c4-4381-9d35-a29e9f4f0583","order_by":0,"name":"Mohamed-Ouejdi Belarbi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIie2QsWrDMBCGrwikRSWrg8kjFM4IYkxDnyUi0LUeAylERpAsobO3vkKnQLcYQbz4AQpdUgydO4UOoUTyLtNsGfQNx0n8HycdQCBwnVCAHAAJ2dnqGiDu+kb1Kl2STi9VgGN3tLVfuVsrevjBh6eU8WOc5wZSxloxf4bRq8cZNzuWlDjL3vXtNi7RQKa5kM0eROFTPqY05kgQjVU4Pi7fDCeVoiC152GdcsKlVfi3UwANayv1B3LVp9iYU9y4ie1ByGIFcuNTmmqdbLDGTFNx7xT3l6R4iUTpU2q9P/zOF5gOzNcnP0WQDup2qI4T78a8+498+UAgEAj8gzNekE4QAM29NAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Biskra","correspondingAuthor":true,"prefix":"","firstName":"Mohamed-Ouejdi","middleName":"","lastName":"Belarbi","suffix":""},{"id":276227459,"identity":"c083149d-f70c-455e-ab54-5a910e5a82f2","order_by":1,"name":"Soufiane Benounas","email":"","orcid":"","institution":"University of Biskra","correspondingAuthor":false,"prefix":"","firstName":"Soufiane","middleName":"","lastName":"Benounas","suffix":""},{"id":276227460,"identity":"7e026a81-7e71-4426-8e69-09c7055527fb","order_by":2,"name":"Abdelhak Khechai","email":"","orcid":"","institution":"University of Biskra","correspondingAuthor":false,"prefix":"","firstName":"Abdelhak","middleName":"","lastName":"Khechai","suffix":""},{"id":276227461,"identity":"fdaa0fc0-428e-4cbd-b235-4f2b89b9ff12","order_by":3,"name":"Pham Van Vinh","email":"","orcid":"","institution":"Le Quy Don Technical University","correspondingAuthor":false,"prefix":"","firstName":"Pham","middleName":"Van","lastName":"Vinh","suffix":""},{"id":276227462,"identity":"cc01af09-f3b8-4fa4-80af-1b90c9c2d1b3","order_by":4,"name":"Eugenio Ruocco","email":"","orcid":"","institution":"University of Campania “L. Vanvitelli”","correspondingAuthor":false,"prefix":"","firstName":"Eugenio","middleName":"","lastName":"Ruocco","suffix":""},{"id":276227463,"identity":"ddd98e60-2def-4734-9735-1703a566938a","order_by":5,"name":"Aman Garg","email":"","orcid":"","institution":"The NorthCap University","correspondingAuthor":false,"prefix":"","firstName":"Aman","middleName":"","lastName":"Garg","suffix":""},{"id":276227464,"identity":"7cd4a58e-9707-421e-8f33-31981bf0c1ee","order_by":6,"name":"Soheil Gohari","email":"","orcid":"","institution":"The University of Melbourne","correspondingAuthor":false,"prefix":"","firstName":"Soheil","middleName":"","lastName":"Gohari","suffix":""}],"badges":[],"createdAt":"2024-03-03 10:46:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4008300/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4008300/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52359689,"identity":"d8db29ff-10dd-4786-a1b0-b07f3956dbe7","added_by":"auto","created_at":"2024-03-10 02:16:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2092211,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4008300/v1_covered_4b72c330-6086-4ae5-a823-4584a36795a4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A comprehensive investigation of the bending and vibration behavior of size- dependent functionally graded nanoplates via an enhanced first order shear deformation theory and nonlocal finite element analysis","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":"Functionally graded, Composite nano-plates, Static and free vibration, finite element, Nonlocal elasticity theory, Shear deformation theory","lastPublishedDoi":"10.21203/rs.3.rs-4008300/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4008300/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research paper conducts a comprehensive investigation into the bending and free vibration of size-dependent functionally graded (FG) nanoplates, using an improved first-order shear deformation theory (IFSDT). The IFSDT, proposed in this study, offers an enhanced representation and precise computation of normal and shear stresses across the thickness of the nanoplate. Notably, it not only ensures compliance with free conditions on both upper and lower surfaces but also eliminates the need for a conventional correction factor commonly employed in FSDT. The material properties of the FG nanoplate undergo continuous grading throughout the thickness direction using a power-law function. To transcend the assumptions of classical continuum mechanics and address the impacts of small sizes in discrete nanoplates, Eringen's nonlocal elasticity theory is applied. The formulation of the governing equation for bending and free vibration analyses of the FG nanoplate is achieved through the application of Hamilton’s principle. The proposed IFSDT is implemented with a computationally efficient C\u003csup\u003e0\u003c/sup\u003e-continuous quadrilateral element, tackling large-scale discrete numerical problems. The model's performance is showcased through a comparative evaluation against literature predictions, highlighting its high accuracy and rapid convergence. Additionally, the research scrutinizes various parameters such as plate thickness, boundary conditions, aspect ratio, nonlocal parameter, different material compositions, and power-law index. The thorough examination and discussion of these parameters provide insights into their influence on the deflection, stresses, and natural frequency of FG nanoplates. The results underscore the significant impact of size-dependent effects on the bending and vibration behaviors of nanoplates, emphasizing the necessity of incorporating these effects in the design and analysis of FG nanoplates. Ultimately, the developed nonlocal finite element model serves as a valuable predictive tool for understanding the bending and vibration behavior of size-dependent functionally graded nanoplates.\u003c/p\u003e","manuscriptTitle":"A comprehensive investigation of the bending and vibration behavior of size- dependent functionally graded nanoplates via an enhanced first order shear deformation theory and nonlocal finite element analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-07 11:17:00","doi":"10.21203/rs.3.rs-4008300/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":"03fce053-ecf6-4888-a382-c5acbcf49fd6","owner":[],"postedDate":"March 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-03-10T02:08:06+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-07 11:17:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4008300","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4008300","identity":"rs-4008300","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}