Topology Optimization Considering Contact- and Stress-Constraints

Topology Optimization Considering Contact- and Stress-Constraints | 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 Topology Optimization Considering Contact- and Stress-Constraints Timo Schmidt, Mirko Keller, Tom Klare, Robert Seifried This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7712248/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 work advances the field of stress-constrained topology optimization by addressing frictionless unilateral contact problems. The approach focuses on minimizing mass of a contact-constrained structure while enforcing stress-constraints using local or global stress measures. Various contact coupling techniques, i.e. node-to-surface and surface-to-surface formulations, are examined and implemented using Lagrange multipliers or penalty methods. The study emphasizes the importance of accurately modeling contact surface geometries as discretization errors at these surfaces can dominate computed stresses and adversely affect optimization outcomes. Blending functions are introduced to mitigate this issue by enabling exact consideration of contact surface geometry without incurring the prohibitive computational costs associated with very fine discretizations. The results demonstrate that surface-to-surface contact methods outperform node-to-segment approaches due to their superior convergence properties and ability to pass the patch test. Additionally, a detailed comparison of augmented Lagrangian and aggregation-based stress-constraint enforcement reveals the superiority of augmented Lagrangian methods for the contact problem. Finally, a weighted augmented Lagrangian approach is proposed to resolve convergence issues in challenging contact scenarios. Mechanical Engineering Topology Optimization Stress-Constraints Node-to-Surface Contact Surface-to-Surface Contact 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-7712248","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":520519270,"identity":"b466136c-bb5d-4974-9853-333156271b73","order_by":0,"name":"Timo Schmidt","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYDACZgiVAGQYMHwAMgwYgAx8gAdJi2HjjARitDDAtDAwGDbzEKPFnp078QHDH7s83Xbm7Y9tfxzOM2dg3vgAv8N4NxswtiUXmx1mK2zOSThcbNnAVozXGqCWbRKMDQcStx3mMQRpSdxwgMdMgqAWhj9QLRYQLeY/CGthg2phgNqCTwcDz2GgXxLbkoFa2Apn9qSlJ244zFaM12Hs/Wc3Pvjwxy5x2/nDGz78sLFO3HC8eeMHvNaAQAIKj5mg+lEwCkbBKBgFhAAAMjZLajKShcoAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-4371-9157","institution":"Hamburg University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Timo","middleName":"","lastName":"Schmidt","suffix":""},{"id":520519271,"identity":"009055b6-6a96-4cce-8f01-b3217f9b3ec8","order_by":1,"name":"Mirko Keller","email":"","orcid":"https://orcid.org/0009-0001-7802-0795","institution":"Hamburg University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Mirko","middleName":"","lastName":"Keller","suffix":""},{"id":520519272,"identity":"539d02b0-aea5-4b1b-a6c5-fd97c69fc2a3","order_by":2,"name":"Tom Klare","email":"","orcid":"","institution":"Hamburg University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Tom","middleName":"","lastName":"Klare","suffix":""},{"id":520519920,"identity":"11f349b1-ce73-4fb7-92f2-d7586273fcb7","order_by":3,"name":"Robert Seifried","email":"","orcid":"https://orcid.org/0000-0001-5795-7610","institution":"Hamburg University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Robert","middleName":"","lastName":"Seifried","suffix":""}],"badges":[],"createdAt":"2025-09-25 11:09:34","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-7712248/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7712248/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92242516,"identity":"1aafcbab-92c6-4174-9241-32334a425588","added_by":"auto","created_at":"2025-09-26 09:03:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":13988751,"visible":true,"origin":"","legend":"","description":"","filename":"snarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7712248/v1_covered_f0de94ac-e80d-4ef0-9f7b-9dde197ef9ec.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eTopology Optimization Considering Contact- and Stress-Constraints\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":"Topology Optimization, Stress-Constraints, Node-to-Surface Contact, Surface-to-Surface Contact","lastPublishedDoi":"10.21203/rs.3.rs-7712248/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7712248/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work advances the field of stress-constrained topology optimization by addressing frictionless unilateral contact problems. The approach focuses on minimizing mass of a contact-constrained structure while enforcing stress-constraints using local or global stress measures. Various contact coupling techniques, i.e. node-to-surface and surface-to-surface formulations, are examined and implemented using Lagrange multipliers or penalty methods. The study emphasizes the importance of accurately modeling contact surface geometries as discretization errors at these surfaces can dominate computed stresses and adversely affect optimization outcomes. Blending functions are introduced to mitigate this issue by enabling exact consideration of contact surface geometry without incurring the prohibitive computational costs associated with very fine discretizations.\u003c/p\u003e\n\u003cp\u003eThe results demonstrate that surface-to-surface contact methods outperform node-to-segment approaches due to their superior convergence properties and ability to pass the patch test. 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