{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T14:37:54Z","timestamp":1792075074896,"version":"4.4.0"},"reference-count":51,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T00:00:00Z","timestamp":1569888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Key Program of National Natural Science Foundation of China","award":["11832009"],"award-info":[{"award-number":["11832009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In this study, a lightweight sandwich aircraft spoiler (AS) with a high stiffness-to-weight ratio was designed. Excellent mechanical properties were achieved by the synthetic use of topology optimization (TO), lattice structure techniques, and high-performance materials, i.e., titanium alloy and aluminum alloy. TO was first utilized to optimize the traditional aircraft spoiler to search for the stiffest structure with a limited material volume, where titanium alloy and aluminum alloy were used for key joints and other parts of the AS, respectively. We then empirically replaced the fine features inside the optimized AS with 3D kagome lattices to support the shell, resulting in a lightweight sandwich AS. Numerical simulations were conducted to show that the designed sandwich AS exhibited good mechanical properties, e.g., high bending rigidity, with a reduction in weight by approximately 80% when compared with that of the initial design model. Finally, we fabricated the designed model with photosensitive resin using a 3D printing technique.<\/jats:p>","DOI":"10.3390\/ma12193225","type":"journal-article","created":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T11:11:16Z","timestamp":1569928276000},"page":"3225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Topological Design of a Lightweight Sandwich Aircraft Spoiler"],"prefix":"10.3390","volume":"12","author":[{"given":"Jie","family":"Liu","sequence":"first","affiliation":[{"name":"Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haifeng","family":"Ou","sequence":"additional","affiliation":[{"name":"Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8403-9284","authenticated-orcid":false,"given":"Junfeng","family":"He","sequence":"additional","affiliation":[{"name":"Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guilin","family":"Wen","sequence":"additional","affiliation":[{"name":"Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"730","DOI":"10.2514\/1.C031301","article-title":"Aerodynamic characteristics of high-lift devices with downward deflection of spoiler","volume":"48","author":"Wang","year":"2011","journal-title":"J. Aircr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1007\/s11831-015-9151-2","article-title":"Topology optimization in aircraft and aerospace structures design","volume":"23","author":"Zhu","year":"2016","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s00158-013-0978-6","article-title":"Topology optimization approaches","volume":"48","author":"Sigmund","year":"2013","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00158-010-0487-9","article-title":"A further review of ESO type methods for topology optimization","volume":"41","author":"Huang","year":"2010","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"031015","DOI":"10.1115\/1.4042627","article-title":"Design of planar large-deflection compliant mechanisms with decoupled multi-input-output using topology optimization","volume":"11","author":"Zhu","year":"2019","journal-title":"J. Mech. Robot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.advengsoft.2016.07.017","article-title":"A survey of manufacturing oriented topology optimization methods","volume":"100","author":"Liu","year":"2016","journal-title":"Adv. Eng. Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s00158-015-1274-4","article-title":"Bridging topology optimization and additive manufacturing","volume":"53","author":"Zegard","year":"2016","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.cma.2017.05.003","article-title":"Self-supporting structure design in additive manufacturing through explicit topology optimization","volume":"323","author":"Guo","year":"2017","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.compstruc.2018.10.011","article-title":"Topology optimization considering overhang constraint in additive manufacturing","volume":"212","author":"Zhang","year":"2019","journal-title":"Comput. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1108\/RPJ-10-2017-0213","article-title":"Generating support structures for additive manufacturing with continuum topology optimization methods","volume":"25","author":"Liu","year":"2019","journal-title":"Rapid Prototyp. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.compositesa.2017.07.020","article-title":"A novel fabrication method and mechanical behavior of all-composite tetrahedral truss core sandwich panel","volume":"102","author":"Mei","year":"2017","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.eml.2018.07.001","article-title":"Mechanical responses of titanium 3D kagome lattice structure manufactured by selective laser melting","volume":"23","author":"Wei","year":"2018","journal-title":"Extrem. Mech. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.compstruct.2018.10.013","article-title":"On sound insulation of pyramidal lattice sandwich structure","volume":"208","author":"Liu","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.compstruct.2018.03.050","article-title":"In-plane crashworthiness of bio-inspired hierarchical honeycombs","volume":"192","author":"Yin","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Liu, J., Fan, X., Wen, G., Qing, Q., Wang, H., and Zhao, G. (2018). A novel design framework for structures\/materials with enhanced mechanical performance. Materials, 11.","DOI":"10.20944\/preprints201803.0163.v1"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.compositesb.2018.01.027","article-title":"Review of current trends in research and applications of sandwich structures","volume":"142","author":"Birman","year":"2018","journal-title":"Compos. Part B Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.compstruct.2016.02.036","article-title":"A review on plate and shell theories for laminated and sandwich structures highlighting the Finite Element Method","volume":"156","author":"Caliri","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_18","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. Multidiscip. Optim."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.cam.2012.09.001","article-title":"Structural design of aircraft skin stretch-forming die using topology optimization","volume":"246","author":"Zhu","year":"2013","journal-title":"J. Comput. Appl. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1007\/s00158-015-1281-5","article-title":"H-DGTP\u2014A Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures","volume":"52","author":"Liu","year":"2015","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_21","unstructured":"Krog, L., Tucker, A., Kemp, M., and Boyd, R. (September, January 30). Topology optimisation of aircraft wing box ribs. Proceedings of the 10th AIAA\/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"253","DOI":"10.2514\/1.12802","article-title":"Integrated multidisciplinary topology optimization approach to adaptive wing design","volume":"43","author":"Maute","year":"2006","journal-title":"J. Aircr."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1002\/nme.2499","article-title":"Integrated layout design of multi-component system","volume":"78","author":"Zhu","year":"2009","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.cma.2012.06.005","article-title":"Sensitivity analysis with the modified Heaviside function for the optimal layout design of multi-component systems","volume":"241","author":"Xia","year":"2012","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.cma.2018.01.021","article-title":"Integrated optimization of actuators and structural topology of piezoelectric composite structures for static shape control","volume":"334","author":"Yang","year":"2018","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Roy, S., Crossley, W.A., Stanford, B., Moore, K.T., and Gray, J.S. (2019, January 7\u201311). A Mixed Integer Efficient Global Optimization Algorithm with Multiple Infill Strategy-Applied to a Wing Topology Optimization Problem. Proceedings of the AIAA Scitech 2019 Forum, San Diego, CA, USA.","DOI":"10.2514\/6.2019-2356"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.2514\/1.J056752","article-title":"Parameterization Framework for the MDAO of Wing Structural Layouts","volume":"56","author":"Dubois","year":"2018","journal-title":"AIAA J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.cad.2018.11.001","article-title":"Design of a Bi-stable Airfoil with Tailored Snap-through Response Using Topology Optimization","volume":"108","author":"Bhattacharyya","year":"2019","journal-title":"Comput. Aided Des."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"081009","DOI":"10.1115\/1.4027609","article-title":"Doing topology optimization explicitly and geometrically\u2014A new moving morphable components based framework","volume":"81","author":"Guo","year":"2014","journal-title":"J. Appl. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1007\/s00158-015-1372-3","article-title":"A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model","volume":"53","author":"Zhang","year":"2016","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1016\/j.cma.2017.05.002","article-title":"Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach","volume":"322","author":"Zhang","year":"2017","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/nme.759","article-title":"Layout optimization with h-adaptivity of structures","volume":"58","author":"Costa","year":"2003","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1002\/cnm.800","article-title":"An adaptive multilevel approach to the minimal compliance problem in topology optimization","volume":"22","author":"Stainko","year":"2006","journal-title":"Commun. Numer. Methods Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.compstruc.2012.11.004","article-title":"An adaptive refinement approach for topology optimization based on separated density field description","volume":"117","author":"Wang","year":"2013","journal-title":"Comput. Struct."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, H., Liu, J., and Wen, G. (2019). An efficient evolutionary structural optimization method with smooth edges based on the game of building blocks. Eng. Optim.","DOI":"10.1080\/0305215X.2018.1562550"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1304","DOI":"10.1002\/nme.6001","article-title":"An adaptive mesh-adjustment strategy for continuum topology optimization to achieve manufacturable structural layout","volume":"117","author":"Wang","year":"2019","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1007\/s00158-018-2114-0","article-title":"An efficient moving morphable component (MMC)-based approach for multi-resolution topology optimization","volume":"58","author":"Liu","year":"2018","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Leader, M.K., Chin, T.W., and Kennedy, G.J. (2019). High-resolution topology optimization with stress and natural frequency constraints. AIAA J.","DOI":"10.2514\/6.2018-4056"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1007\/s00158-018-1904-8","article-title":"An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions","volume":"58","author":"Wei","year":"2018","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1186\/s10033-019-0332-z","article-title":"Topological and shape optimization of flexure hinges for designing compliant mechanisms using the level set method","volume":"32","author":"Zhu","year":"2019","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_41","unstructured":"(2014). ABAQUS User\u2019s Manual, Dassault Syst\u00e8mes Simulia Corp.. version 6.14."},{"key":"ref_42","unstructured":"(2014). SolidWorks User\u2019s Guide, SolidWorks Corp.. version 2014."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1002\/nme.1620240207","article-title":"The method of moving asymptotes\u2014A new method for structural optimization","volume":"24","author":"Svanberg","year":"1987","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00158-016-1513-3","article-title":"Multi-material topology optimization using ordered SIMP interpolation","volume":"55","author":"Zuo","year":"2017","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2098","DOI":"10.1016\/j.engstruct.2013.08.012","article-title":"Topological optimization design of structures under random excitations using SQP method","volume":"56","author":"Rong","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.1007\/s00158-018-2159-0","article-title":"Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming","volume":"59","author":"Long","year":"2019","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s00158-015-1334-9","article-title":"Layout optimization of continuum structures considering the probabilistic and fuzzy directional uncertainty of applied loads based on the cloud model","volume":"53","author":"Liu","year":"2016","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/0045-7949(93)90035-C","article-title":"A simple evolutionary procedure for structural optimization","volume":"49","author":"Xie","year":"1993","journal-title":"Comput. Struct."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s10443-018-9680-6","article-title":"Topology optimization of lightweight lattice structural composites inspired by cuttlefish bone","volume":"26","author":"Hu","year":"2019","journal-title":"Appl. Compos. Mater."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1038\/nature23911","article-title":"Giga-voxel computational morphogenesis for structural design","volume":"550","author":"Aage","year":"2017","journal-title":"Nature"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Xue, X., Pereira, A., Vincze, G., Wu, X., and Liao, J. (2019). Interfacial Characteristics of Dissimilar Ti6Al4V\/AA6060 Lap Joint by Pulsed Nd: YAG Laser Welding. Metals, 9.","DOI":"10.3390\/met9010071"}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/12\/19\/3225\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:26:39Z","timestamp":1760189199000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/12\/19\/3225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,1]]},"references-count":51,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["ma12193225"],"URL":"https:\/\/doi.org\/10.3390\/ma12193225","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,1]]}}}