Topology optimized metal forming tools: Using Mixed-Integer Programming to design truss-like structures

Topology optimized metal forming tools: Using Mixed-Integer Programming to design truss-like 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 Topology optimized metal forming tools: Using Mixed-Integer Programming to design truss-like structures Julian Mrochen, Jonas Reuter, Apostolos Aslanidis, Peter Frohn-Sörensen, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7021236/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 accelerating megatrends of individualization, neo-ecology, and increased connectivity are fundamentally reshaping the demands placed on modern manufacturing. To sustain economic viability amidst these shifts, industry requires highly flexible production systems capable of rapid adaptation to evolving market and ecological constraints. In this context, the development of adjustable or transformable manufacturing tools emerges as a pivotal strategy, offering significant reductions in resource consumption associated with tooling while simultaneously enabling process reconfigurability and supporting variable, demand-driven production. Historically, the fabrication of highly optimized and articulated structures for such adaptive tools was constrained by the limitations of conventional manufacturing techniques. However, the advent of additive manufacturing has removed many of these barriers, making it feasible to realize complex, resource-efficient designs that were previously unattainable. In this work, we introduce an advanced methodology for truss topology optimization (TTO) based on Mixed Integer Programming (MIP), which systematically generates lightweight, structurally efficient truss-like geometries tailored for application in metal forming tools. We present a comprehensive workflow for integrating TTO with additive manufacturing, culminating in the design and realization of a novel tube bending tool. In a future prospect, the tool demonstrates inherent transformability, allowing for reconfiguration to accommodate different bending radii without necessitating the fabrication of entirely new tooling components. The results underscore a significant mitigation of resource consumption at the level of production equipment and indicate meaningful progress towards more agile, sustainable manufacturing enabled by transformable, additively manufactured tools. Discrete Mathematics Mechanical Engineering Truss Topology Optimization Resource-efficient Design Flexible Manufacturing Systems Lightweight Structures Additive Manufacturing Forming Tools 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-7021236","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511773549,"identity":"c2382bce-b513-47b3-8ab7-015ecccf96e4","order_by":0,"name":"Julian Mrochen","email":"data:image/png;base64,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","orcid":"","institution":"University of Siegen - 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