{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:55Z","timestamp":1760060455681,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52375257","24PJD073"],"award-info":[{"award-number":["52375257","24PJD073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Pujiang Program","award":["52375257","24PJD073"],"award-info":[{"award-number":["52375257","24PJD073"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper presents a multi-constraint topology optimization strategy for rudder structures, integrating additive manufacturing (AM)-related overhang angle and flutter-performance considerations. To the best of our knowledge, this is the first study to couple AM overhang control with mass center (flutter) steering in a single density-based formulation for flight control rudder structures. The approach incorporates constraints on structural volume fraction, overhang angle for AM, and mass center positioning to address multi-function design objectives\u2014structural lightweighting, stiffness, aerodynamic stability, and manufacturability. A build-direction-aware projection filter and a smooth Heaviside mass center constraint are introduced to enforce these requirements during every optimization iteration. The resulting layout converges to a sandwich-type rudder with balanced mechanical performance and AM feasibility. Simulation results show that enforcing overhang constraints reduces support material usage by 46.9% and residual deformation by 14.2%, significantly enhancing AM feasibility. Additionally, introducing center-of-mass constraints improves flutter velocity from 3327 m s\u22121 to 3759 m s\u22121, indicating a 6.84% increase over conventional optimization and demonstrating improved dynamic stability. These simultaneous gains in manufacturability and aeroelastic safety, achieved without post-processing, underline the novelty and practical value of the proposed constraint set. The strategy thus offers a practical and efficient design method for high-performance, AM-friendly rudder structures with superior mechanical and aerodynamic characteristics, and it can be readily extended to other mission-critical AM components.<\/jats:p>","DOI":"10.3390\/computation13090208","type":"journal-article","created":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T13:27:44Z","timestamp":1756733264000},"page":"208","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topology Optimization for Rudder Structures Considering Additive Manufacturing and Flutter Effects"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5039-6865","authenticated-orcid":false,"given":"Heng","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Shuaijie","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Xiaohong","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Jiandong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Min","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1007\/s00158-011-0682-3","article-title":"Application of a bi-level scheme including topology optimization to the design of an aircraft pylon","volume":"44","author":"Remouchamps","year":"2011","journal-title":"Struct. 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