Thermodynamic Topology Optimization of compliant mechanisms including a multi-objective approach to prevent one-node connections

Thermodynamic Topology Optimization of compliant mechanisms including a multi-objective approach to prevent one-node connections | 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 Thermodynamic Topology Optimization of compliant mechanisms including a multi-objective approach to prevent one-node connections Sebastian Wolf, Philipp Junker, Dustin Roman Jantos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7369733/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 We integrate compliant mechanisms into our Thermodynamic Topology Optimization framework. By applying Hamilton’s principle we obtain the governing system of equations for both the physical variables and the design variable, all derived from a single Hamilton functional. In this context, the Helmholtz free energy is modeled by using Betti’s reciprocal theorem taking into account two load cases. The first load case defines the acting force, while the second load case determines the location where displacement should be maximized. Since a pure SIMP approach results in large intermediate material regions, we introduce a Heaviside function in order to enforce binary material states. As a consequence, the topology develops one-node connections. To prevent this, we propose a simple but effective multi-objective approach for their avoidance. Mechanical Engineering topology optimization compliant mechanisms variational calculus multi-objective 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. 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-7369733","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":502375069,"identity":"78c83ab1-2545-467f-a07a-4ae852f63530","order_by":0,"name":"Sebastian Wolf","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYFAC5oYPHwwSwMwDjA0IYTxaGBtnziBZy2wehgQomxgtBscbG5ttCtKiGSRyDx5g3GGXZ87eY/i4gsFaDqeWMwcbm3MMcnIbJPISDjCeSS627DljbHiGId0YlxazG4ntj3MMKoBacgwO/21jTtxwIy1NsoHhcGIDbi2NzRZQLQcY2+pBWtJ/ArXU49XCAHYYWMthoJbkY8BgOJyAy2H2QL809hik5bbxvAFpOZ644czhw5INBumGuGyRbG8+2PDjT3JuP3uO8QfGturEDcAw/NhQYS2PyxY4YEPlGhDUMApGwSgYBaMADwAANq1fDAzSUaAAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0000-9969-7159","institution":"Leibniz University Hannover, Institute of Continuum Mechanics, Hannover, Germany","correspondingAuthor":true,"prefix":"","firstName":"Sebastian","middleName":"","lastName":"Wolf","suffix":""},{"id":502375070,"identity":"ef85e258-4992-4eb4-bd0e-3b8609bf93ff","order_by":1,"name":"Philipp Junker","email":"","orcid":"https://orcid.org/0000-0002-8572-6841","institution":"Leibniz University Hannover, Institute of Continuum Mechanics, Hannover, Germany","correspondingAuthor":false,"prefix":"","firstName":"Philipp","middleName":"","lastName":"Junker","suffix":""},{"id":502375071,"identity":"d69b5b91-e133-4330-81e3-693af45c3da9","order_by":2,"name":"Dustin Roman Jantos","email":"","orcid":"https://orcid.org/0000-0003-1725-7323","institution":"Leibniz University Hannover, Institute of Continuum Mechanics, Hannover, Germany","correspondingAuthor":false,"prefix":"","firstName":"Dustin","middleName":"Roman","lastName":"Jantos","suffix":""}],"badges":[],"createdAt":"2025-08-14 04:42:20","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-7369733/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7369733/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89442083,"identity":"350ccd8a-8c2c-44d8-8124-51cf9ee94163","added_by":"auto","created_at":"2025-08-20 03:41:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1252621,"visible":true,"origin":"","legend":"","description":"","filename":"ThermodynamicTopologyOptimizationofCompliantMechanismsPREPRINT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7369733/v1_covered_28f8c3b6-4a20-400b-aca8-94503542d573.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eThermodynamic Topology Optimization of compliant mechanisms including a multi-objective approach to prevent one-node connections\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[{"identity":"8ece5bd8-d870-4f76-adb7-3b0dc320cc02","identifier":"10.13039/501100001659","name":"Deutsche Forschungsgemeinschaft","awardNumber":"390833453","order_by":0}],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Leibniz University Hannover","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":"topology optimization, compliant mechanisms, variational calculus, multi-objective","lastPublishedDoi":"10.21203/rs.3.rs-7369733/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7369733/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe integrate compliant mechanisms into our Thermodynamic Topology Optimization framework. 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