Data-driven and interpretable stiffness modeling of deployable origami structures

Data-driven and interpretable stiffness modeling of deployable origami structures | 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 Data-driven and interpretable stiffness modeling of deployable origami structures Shijun Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9144715/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 Deployable origami structures exhibit highly tunable stiffness characteristics, yet efficient and interpretable modeling across different deployment states remains challenging. This study proposes a data-driven sym bolic learning framework to model the axial and bending stiffness of deployable origami structures based on key geometric parameters, including fold thickness, panel thickness, and fold width. Kolmogorov Arnold Networks are employed to identify explicit analytical expressions directly from data, avoiding the limitations of black-box machine learning approaches. After systematic simplification guided by variable ranges and physical relevance, compact and interpretable stiffness models are obtained. The results re veal that axial stiffness is strongly influenced by fold thickness and panel thickness, reflecting the role of folds as load-transferring and rotational-resisting components. In contrast, bending stiffness is dominated by panel thickness and fold width, while the contribution of fold thickness is negligible due to the panel controlled bending inertia. By introducing deployment ratio as a governing parameter, unified stiffness models valid across multiple deployment states are established. The proposed approach provides an efficient and physically transparent alternative to finite element–based stiffness evaluation. Deployable origami structures Axial and bending stiffness Symbolic learning Kolmogorov Arnold Networks Interpretable modeling Deployment ratio Full Text Additional Declarations The authors declare no competing interests. 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-9144715","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":607352168,"identity":"c77b7d5e-fb9b-4f42-a764-9e8ef4c76090","order_by":0,"name":"Shijun Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYBACeWbmww8+VNjY8TMcPkCcFsP2tjTDGWfSkiUbjyUQac2ZMwbSvG2HGTccPmNAnA7GGWkJhjPY0pgZjp35eOMNg52cbgMBLewSyQcefOCx4WPsObvZcg5DsrHZAaJskUhjZpY4u02ah+FA4jZCWhhu5BhI8xgcZmyTf/OMSC0g7/MkHGbsYTjDRpwWSCAfSEuWYDhmbDnHgAi/gKPy4z8bO/sDhx/eeFNhJ0dQCwqQ4CEyapC1kKpjFIyCUTAKRgQAAD7eSM/p5/EUAAAAAElFTkSuQmCC","orcid":"","institution":"Swinburne University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Shijun","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2026-03-17 06:13:34","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9144715/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9144715/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105033743,"identity":"1be07b38-2731-458f-ac8f-c6d7b10e7ab2","added_by":"auto","created_at":"2026-03-20 07:21:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":341990,"visible":true,"origin":"","legend":"","description":"","filename":"AnalysisusingKAN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9144715/v1_covered_f5347dd4-0c8b-44c4-8f97-653435860685.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eData-driven and interpretable stiffness modeling of deployable origami structures\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Deployable origami structures, Axial and bending stiffness, Symbolic learning, Kolmogorov Arnold Networks, Interpretable modeling, Deployment ratio","lastPublishedDoi":"10.21203/rs.3.rs-9144715/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9144715/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDeployable origami structures exhibit highly tunable stiffness characteristics, yet efficient and interpretable modeling across different deployment states remains challenging. This study proposes a data-driven sym bolic learning framework to model the axial and bending stiffness of deployable origami structures based on key geometric parameters, including fold thickness, panel thickness, and fold width. Kolmogorov Arnold Networks are employed to identify explicit analytical expressions directly from data, avoiding the limitations of black-box machine learning approaches. After systematic simplification guided by variable ranges and physical relevance, compact and interpretable stiffness models are obtained. The results re veal that axial stiffness is strongly influenced by fold thickness and panel thickness, reflecting the role of folds as load-transferring and rotational-resisting components. In contrast, bending stiffness is dominated by panel thickness and fold width, while the contribution of fold thickness is negligible due to the panel controlled bending inertia. 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