{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T15:11:13Z","timestamp":1768749073697,"version":"3.49.0"},"reference-count":47,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T00:00:00Z","timestamp":1660867200000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51978150"],"award-info":[{"award-number":["51978150"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52050410334"],"award-info":[{"award-number":["52050410334"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008081","name":"Southeast University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008081","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,9,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Origami tessellations can be folded from a given planar pattern into a three-dimensional object with specific geometric properties, inspiring developments in various fields of science and engineering such as deployable structures, energy absorption devices, reconfigurable robots, and metamaterials. However, the range of existing origami patterns with functional properties such as flat-foldability is rather scant, as analytical solutions to constraint equations arising in the design process are generally highly complicated. In this paper, we tackle the challenging problem of automated design of scalene-faceted flat-foldable origami tessellations using an efficient metaheuristic algorithm. To this end, this study establishes constraint curves based on compatibility conditions for all six-fold (i.e., degree-6) vertices. Subsequently, a graphical method and a particle swarm optimization (PSO) method are adopted to produce optimal origami patterns. Moreover, mountain-valley assignments for the obtained geometric designs are determined using a computational approach based on mixed-integer linear programming. It turns out that the flat-foldable internal vertices of each C2-symmetric unit fragment (UF) exist as C2-symmetric pairs about the centroid of the UF. Furthermore, numerical experiments are carried out to examine the feasibility and compare the accuracy, computational efficiency, and global convergence of the proposed methods. The results of numerical experiments demonstrated that, in comparison with the graphical method, the proposed PSO method has not only a higher accuracy but also a significantly lower computational cost, enabling us to develop an intelligent computational platform to efficiently design scalene-faceted flat-foldable origami tessellations.<\/jats:p>","DOI":"10.1093\/jcde\/qwac082","type":"journal-article","created":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T09:47:44Z","timestamp":1660902464000},"page":"1765-1774","source":"Crossref","is-referenced-by-count":20,"title":["Intelligent computational design of scalene-faceted flat-foldable tessellations"],"prefix":"10.1093","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0924-8945","authenticated-orcid":false,"given":"Yao","family":"Chen","sequence":"first","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University , Nanjing 211189, China"},{"name":"Shaanxi Key Laboratory of Artificially-Structured Functional Materials and Devices, Air Force Engineering University , Xi'an 710051, China"}]},{"given":"Chenhao","family":"Lu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University , Nanjing 211189, China"}]},{"given":"Jiayi","family":"Yan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University , Nanjing 211189, China"}]},{"given":"Jian","family":"Feng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, and National Prestress Engineering Research Center, Southeast University , Nanjing 211189, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1836-2598","authenticated-orcid":false,"given":"Pooya","family":"Sareh","sequence":"additional","affiliation":[{"name":"Creative Design Engineering Lab (Cdel), Department of Mechanical, Materials and Aerospace Engineering, School of Engineering, University of Liverpool , Liverpool, The Quadrangle, Brownlow Hill, L69 3GH, UK"}]}],"member":"286","published-online":{"date-parts":[[2022,8,18]]},"reference":[{"issue":"5","key":"2022092120523862500_bib1","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1177\/0278364908090235","article-title":"Robotic origami folding","volume":"27","author":"Balkcom","year":"2008","journal-title":"The International Journal of Robotics Research"},{"issue":"3","key":"2022092120523862500_bib2","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1038\/nmeth.1570","article-title":"A primer to scaffolded DNA origami","volume":"8","author":"Castro","year":"2011","journal-title":"Nature Methods"},{"key":"2022092120523862500_bib4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijsolstr.2017.05.008","article-title":"Lower-order symmetric mechanism modes and bifurcation behavior of deployable bar structures with cyclic symmetry","volume":"139-140","author":"Chen","year":"2018","journal-title":"International Journal of Solids and Structures"},{"issue":"9","key":"2022092120523862500_bib5","doi-asserted-by":"crossref","first-page":"91402","DOI":"10.1115\/1.4042791","article-title":"An integrated geometric-graph-theoretic approach to representing origami structures and their corresponding truss frameworks","volume":"141","author":"Chen","year":"2019","journal-title":"Journal of Mechanical Design"},{"issue":"9","key":"2022092120523862500_bib9","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.3390\/sym11091101","article-title":"Geometric and kinematic analyses and novel characteristics of origami-inspired structures","volume":"11","author":"Chen","year":"2019","journal-title":"Symmetry"},{"key":"2022092120523862500_bib3","doi-asserted-by":"crossref","first-page":"106328","DOI":"10.1016\/j.compstruc.2020.106328","article-title":"Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming","volume":"239","author":"Chen","year":"2020","journal-title":"Computers & Structures"},{"issue":"4","key":"2022092120523862500_bib6","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1007\/s00707-019-02586-6","article-title":"A hybrid symmetry-PSO approach to finding the self-equilibrium configurations of prestressable pin-jointed assemblies","volume":"231","author":"Chen","year":"2020","journal-title":"Acta Mechanica"},{"issue":"3","key":"2022092120523862500_bib8","doi-asserted-by":"crossref","first-page":"04020003","DOI":"10.1061\/(ASCE)CP.1943-5487.0000882","article-title":"Feasible prestress modes for cable-strut structures with multiple self-stress states using particle swarm optimization","volume":"34","author":"Chen","year":"2020","journal-title":"Journal of Computing in Civil Engineering"},{"issue":"1","key":"2022092120523862500_bib7","doi-asserted-by":"crossref","first-page":"011703","DOI":"10.1115\/1.4047437","article-title":"Particle swarm optimization-based metaheuristic design generation of non-trivial flat-foldable origami tessellations with degree-4 vertices","volume":"143","author":"Chen","year":"2021","journal-title":"Journal of Mechanical Design"},{"issue":"06","key":"2022092120523862500_bib10","doi-asserted-by":"crossref","first-page":"1250054","DOI":"10.1142\/S021945541250054X","article-title":"Folding of a type of deployable origami structures","volume":"12","author":"Chen","year":"2013","journal-title":"International Journal of Structural Stability and Dynamics"},{"key":"2022092120523862500_bib11","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511735172","volume-title":"Geometric folding algorithms: Linkages, origami, polyhedra","author":"Demaine","year":"2007"},{"issue":"3","key":"2022092120523862500_bib12","doi-asserted-by":"crossref","first-page":"183","DOI":"10.20898\/j.iass.2018.197.010","article-title":"A new hybrid type of deployable structure: Origami-scissor hinged","volume":"59","author":"Drover","year":"2018","journal-title":"Journal of the International Association for Shell and Spatial Structures"},{"issue":"5","key":"2022092120523862500_bib13","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1038\/nmat4540","article-title":"Programming curvature using origami tessellations","volume":"15","author":"Dudte","year":"2016","journal-title":"Nature Materials"},{"issue":"15","key":"2022092120523862500_bib14","doi-asserted-by":"crossref","first-page":"1706311","DOI":"10.1002\/adma.201706311","article-title":"Programmable self-locking origami mechanical metamaterials","volume":"30","author":"Fang","year":"2018","journal-title":"Advanced Materials"},{"issue":"9","key":"2022092120523862500_bib15","doi-asserted-by":"crossref","first-page":"91401","DOI":"10.1115\/1.4030876","article-title":"Origami actuator design and networking through crease topology optimization","volume":"137","author":"Fuchi","year":"2015","journal-title":"Journal of Mechanical Design"},{"issue":"4","key":"2022092120523862500_bib16","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1007\/s11771-020-4349-3","article-title":"Recent research development of energy-absorption structure and application for railway vehicles","volume":"27","author":"Gao","year":"2020","journal-title":"Journal of Central South University"},{"key":"2022092120523862500_bib17","doi-asserted-by":"crossref","DOI":"10.1201\/9781315157030","volume-title":"Twists, tilings, and tessellations: Mathematical methods for geometric origami","author":"Lang","year":"2017"},{"issue":"2","key":"2022092120523862500_bib18","doi-asserted-by":"crossref","first-page":"21004","DOI":"10.1115\/1.4038972","article-title":"Rigidly foldable quadrilateral meshes from angle arrays","volume":"10","author":"Lang","year":"2018","journal-title":"Journal of Mechanisms and Robotics"},{"issue":"5","key":"2022092120523862500_bib20","doi-asserted-by":"crossref","first-page":"1805282","DOI":"10.1002\/adma.201805282","article-title":"Architected origami materials: How folding creates sophisticated mechanical properties","volume":"31","author":"Li","year":"2019","journal-title":"Advanced Materials"},{"issue":"2","key":"2022092120523862500_bib19","doi-asserted-by":"crossref","first-page":"71","DOI":"10.20898\/j.iass.2021.008","article-title":"Computational modeling and energy absorption behavior of thin-walled tubes with the Kresling origami pattern","volume":"62","author":"Li","year":"2021","journal-title":"Journal of the International Association for Shell and Spatial Structures"},{"issue":"3","key":"2022092120523862500_bib23","doi-asserted-by":"crossref","first-page":"31008","DOI":"10.1115\/1.4026509","article-title":"A novel method to design and optimize flat-foldable origami structures through a genetic algorithm","volume":"14","author":"McAdams","year":"2014","journal-title":"Journal of Computing and Information Science in Engineering"},{"issue":"7","key":"2022092120523862500_bib21","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1002\/adfm.201102978","article-title":"Elastomeric origami: Programmable paper-elastomer composites as pneumatic actuators","volume":"22","author":"Martinez","year":"2012","journal-title":"Advanced Functional Materials"},{"key":"2022092120523862500_bib22","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.engstruct.2014.03.012","article-title":"Honeycomb core sandwich panels for origami-inspired deployable shelters: Multi-objective optimization for minimum weight and maximum energy efficiency","volume":"69","author":"Martinez-Martin","year":"2014","journal-title":"Engineering Structures"},{"issue":"1","key":"2022092120523862500_bib24","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1299\/jsmec.45.364","article-title":"Modelling of folding patterns in flat membranes and cylinders by origami","volume":"45","author":"Nojima","year":"2002","journal-title":"JSME International Journal Series C"},{"issue":"3","key":"2022092120523862500_bib25","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1089\/soro.2016.0023","article-title":"Design and analysis of a soft pneumatic actuator with origami shell reinforcement","volume":"3","author":"Paez","year":"2016","journal-title":"Soft Robotics"},{"issue":"1","key":"2022092120523862500_bib26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms15477","article-title":"Self-folding origami at any energy scale","volume":"8","author":"Pinson","year":"2017","journal-title":"Nature Communications"},{"issue":"12","key":"2022092120523862500_bib27","doi-asserted-by":"crossref","first-page":"3592","DOI":"10.1002\/anie.201408941","article-title":"Reversible reconfiguration of DNA origami nanochambers monitored by single-molecule FRET","volume":"54","author":"Sacc\u00e0","year":"2015","journal-title":"Angewandte Chemie International Edition"},{"key":"2022092120523862500_bib28","doi-asserted-by":"crossref","first-page":"108128","DOI":"10.1016\/j.matdes.2019.108128","article-title":"The least symmetric crystallographic derivative of the developable double corrugation surface: Computational design using underlying conic and cubic curves","volume":"183","author":"Sareh","year":"2019","journal-title":"Materials & Design"},{"issue":"22","key":"2022092120523862500_bib29","doi-asserted-by":"crossref","first-page":"h5228","DOI":"10.1126\/scirobotics.aah5228","article-title":"Rotorigami: A rotary origami protective system for robotic rotorcraft","volume":"3","author":"Sareh","year":"2018","journal-title":"Science Robotics"},{"key":"2022092120523862500_bib30","doi-asserted-by":"crossref","first-page":"105881","DOI":"10.1016\/j.ijmecsci.2020.105881","article-title":"Intrinsic non-flat-foldability of two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals","volume":"185","author":"Sareh","year":"2020","journal-title":"International Journal of Mechanical Sciences"},{"issue":"2","key":"2022092120523862500_bib31","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1260\/0266-3511.30.2.141","article-title":"A framework for the symmetric generalisation of the Miura-ori","volume":"30","author":"Sareh","year":"2015","journal-title":"International Journal of Space Structures"},{"issue":"8","key":"2022092120523862500_bib32","doi-asserted-by":"crossref","first-page":"85001","DOI":"10.1088\/0964-1726\/24\/8\/085001","article-title":"Design of isomorphic symmetric descendants of the Miura-ori","volume":"24","author":"Sareh","year":"2015","journal-title":"Smart Materials and Structures"},{"issue":"8","key":"2022092120523862500_bib33","doi-asserted-by":"crossref","first-page":"85002","DOI":"10.1088\/0964-1726\/24\/8\/085002","article-title":"Design of non-isomorphic symmetric descendants of the Miura-ori","volume":"24","author":"Sareh","year":"2015","journal-title":"Smart Materials and Structures"},{"issue":"4","key":"2022092120523862500_bib34","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1038\/nmat4232","article-title":"Origami structures with a critical transition to bistability arising from hidden degrees of freedom","volume":"14","author":"Silverberg","year":"2015","journal-title":"Nature Materials"},{"issue":"2200","key":"2022092120523862500_bib35","doi-asserted-by":"crossref","first-page":"20170016","DOI":"10.1098\/rspa.2017.0016","article-title":"Design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns","volume":"473","author":"Song","year":"2017","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"1","key":"2022092120523862500_bib36","doi-asserted-by":"crossref","first-page":"33312","DOI":"10.1038\/srep33312","article-title":"Folding to curved surfaces: A generalized design method and mechanics of origami-based cylindrical structures","volume":"6","author":"Wang","year":"2016","journal-title":"Scientific Reports"},{"issue":"2","key":"2022092120523862500_bib37","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1007\/s11771-020-4321-2","article-title":"Crashworthiness of innovative hexagonal honeycomb-like structures subjected to out-of-plane compression","volume":"27","author":"Wang","year":"2020","journal-title":"Journal of Central South University"},{"issue":"21","key":"2022092120523862500_bib38","doi-asserted-by":"crossref","first-page":"215501","DOI":"10.1103\/PhysRevLett.110.215501","article-title":"Geometric mechanics of periodic pleated origami","volume":"110","author":"Wei","year":"2013","journal-title":"Physical Review Letters"},{"issue":"9","key":"2022092120523862500_bib39","doi-asserted-by":"crossref","first-page":"2763","DOI":"10.1007\/s11771-020-4497-5","article-title":"Crashworthiness design and experimental validation of a novel collision post structure for subway cab cars","volume":"27","author":"Xing","year":"2020","journal-title":"Journal of Central South University"},{"issue":"1","key":"2022092120523862500_bib40","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1093\/jcde\/qwab074","article-title":"Method for solving origami tessellation hole problem using triangle twist folding","volume":"9","author":"Yamamoto","year":"2022","journal-title":"Journal of Computational Design and Engineering"},{"key":"2022092120523862500_bib41","first-page":"277","article-title":"Developing novel patterns for six-fold origami structures using graph theory and optimization algorithms","volume":"43","author":"Yan","year":"2021","journal-title":"Journal of Building Structures (in Chinese)"},{"issue":"18","key":"2022092120523862500_bib42","doi-asserted-by":"crossref","first-page":"185502","DOI":"10.1103\/PhysRevLett.114.185502","article-title":"Reentrant origami-based metamaterials with negative Poisson\u2019s ratio and bistability","volume":"114","author":"Yasuda","year":"2015","journal-title":"Physical Review Letters"},{"issue":"9","key":"2022092120523862500_bib43","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1073\/pnas.1720171115","article-title":"Origami-inspired, on-demand deployable and collapsible mechanical metamaterials with tunable stiffness","volume":"115","author":"Zhai","year":"2018","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2022092120523862500_bib44","doi-asserted-by":"crossref","first-page":"114227","DOI":"10.1016\/j.engstruct.2022.114227","article-title":"Structural symmetry recognition in planar structures using convolutional neural networks","volume":"260","author":"Zhang","year":"2022","journal-title":"Engineering Structures"},{"issue":"4","key":"2022092120523862500_bib45","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.jcde.2018.01.002","article-title":"Approximating 3D surfaces using generalized waterbomb tessellations","volume":"5","author":"Zhao","year":"2018","journal-title":"Journal of Computational Design and Engineering"},{"issue":"2181","key":"2022092120523862500_bib46","doi-asserted-by":"crossref","first-page":"20150407","DOI":"10.1098\/rspa.2015.0407","article-title":"Design of three-dimensional origami structures based on a vertex approach","volume":"471","author":"Zhou","year":"2015","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"1","key":"2022092120523862500_bib47","doi-asserted-by":"crossref","first-page":"11004","DOI":"10.1115\/1.4044737","article-title":"Rigid and flat foldability of a degree-four vertex in origami","volume":"12","author":"Zimmermann","year":"2020","journal-title":"Journal of Mechanisms and Robotics-Transactions of the ASME"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwac082\/45480102\/qwac082.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/9\/5\/1765\/45960691\/qwac082.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/9\/5\/1765\/45960691\/qwac082.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T21:16:06Z","timestamp":1663794966000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/9\/5\/1765\/6671738"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,18]]},"references-count":47,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,9,21]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwac082","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,10]]},"published":{"date-parts":[[2022,8,18]]}}}