An improved peridynamics topology optimization formulation for compliance minimization

An improved peridynamics topology optimization formulation for compliance minimization | 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 An improved peridynamics topology optimization formulation for compliance minimization Francisco S. Vieira, Aurélio L. Araújo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4171518/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Aug, 2024 Read the published version in Structural and Multidisciplinary Optimization → Version 1 posted 9 You are reading this latest preprint version Abstract This work proposes an improved peridynamics density-based topology optimization framework for compliance minimization. One of the main advantages of using a peridynamics discretization relies in the fact that it provides a consistent regularization of classical continuum mechanics into a nonlocal continuum, thus containing an inherent length scale called the horizon. Furthermore, this reformulation allows for discontinuities and is highly suitable for treating fracture and crack propagation. Partial differential equations are rewritten as integrodifferential equations and its numerical implementation can be straightforwardly done using meshfree collocation, inheriting its advantages. In the optimization formulation, Solid Isotropic Material with Penalization (SIMP) is used as interpolation for the design variables. To improve the peridynamic formulation and to evaluate the objective function in a energetically consistent manner, surface correction is implemented. Moreover, a detailed sensitivity analysis reveals an analytical expression for the objective function derivatives, different from the one used in the literature, providing an important basis for gradient-based topology optimization with peridynamics. The proposed implementation is studied with two examples illustrating different characteristics of this framework. The analytical expression for the sensitivities is validated against a reference solution, providing an improvement over the existent expression in the literature. Also, the effect of using the surface correction is evidenced. An extensive analysis of the horizon size and sensitivity filter radius indicates that the current method is mesh independent, i.e. a sensitivity filter is redundant since peridynamics intrinsically filters length scales with the horizon. Different optimization methods are also tested for uncracked and cracked structures, demonstrating the capabilities and robustness of the proposed framework. Topology Optimization Peridynamics Sensitivity analysis Mesh-independence Surface correction Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Aug, 2024 Read the published version in Structural and Multidisciplinary Optimization → Version 1 posted Editorial decision: Revision requested 26 Jun, 2024 Reviews received at journal 18 Jun, 2024 Reviewers agreed at journal 18 Jun, 2024 Reviews received at journal 17 Jun, 2024 Reviewers agreed at journal 04 Mar, 2024 Reviewers invited by journal 02 Mar, 2024 Editor assigned by journal 05 Feb, 2024 Submission checks completed at journal 31 Jan, 2024 First submitted to journal 11 Jan, 2024 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-4171518","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":291681457,"identity":"81dcec5c-4e4d-4deb-a134-5f766a9fc20c","order_by":0,"name":"Francisco S. 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