{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T10:24:23Z","timestamp":1785407063071,"version":"3.56.0"},"reference-count":53,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018694","name":"Marie Sklodowska-Curie Actions","doi-asserted-by":"publisher","award":["791235"],"award-info":[{"award-number":["791235"]}],"id":[{"id":"10.13039\/100018694","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015498","name":"Ministry for Innovation and Technology","doi-asserted-by":"publisher","award":["OTKA K-138642"],"award-info":[{"award-number":["OTKA K-138642"]}],"id":[{"id":"10.13039\/501100015498","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,22]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a computer aided design tool that analyses the structural feasibility of interlocking assemblages with orthotropic sliding resistance and automatically adjusts the assemblage shape to remove the infeasibility. First, the static problem of limit analysis is extended to the corrugated interfaces. To model different bond patterns and openings, an assemblage is abstracted to different types of joints representing the dry joints between the blocks, joints inside the blocks, and the excluded joints where the openings are located. This problem is then reformulated to measure the structural infeasibility due to the sliding constraint violation. The so-called sliding infeasibility measure shows how far an infeasible model is to become feasible. This problem is used as the objective function of a shape optimization algorithm that minimizes the sliding infeasibility measure through automated change of the interlocking joints, by which the model becomes structurally feasible. The optimization is validated using the discrete element analysis.<\/jats:p>","DOI":"10.1093\/jcde\/qwac054","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T17:15:14Z","timestamp":1655226914000},"page":"1279-1297","source":"Crossref","is-referenced-by-count":5,"title":["Interlocking joint shape optimization for structurally informed design of block assemblages"],"prefix":"10.1093","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7384-0068","authenticated-orcid":false,"given":"Elham","family":"Mousavian","sequence":"first","affiliation":[{"name":"Department of Structures for Engineering and Architecture, University of Naples Federico II , Via Forno vecchio, 36, 80134 Napoli, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katalin","family":"Bagi","sequence":"additional","affiliation":[{"name":"Department of Structural Mechanics, Budapest University of Technology and Economics , M\u0171egyetem rkp. 3., K. mf. 63, 1111 Budapest, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claudia","family":"Casapulla","sequence":"additional","affiliation":[{"name":"Department of Structures for Engineering and Architecture, University of Naples Federico II , Via Forno vecchio, 36, 80134 Napoli, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"2022072211191366400_bib1","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1016\/j.conbuildmat.2012.08.002","article-title":"Capacity of innovative interlocking blocks under monotonic loading","volume":"37","author":"Ali","year":"2012","journal-title":"Construction and Building Materials"},{"key":"2022072211191366400_bib2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3306346.3323004","article-title":"Surface2Volume: Surface segmentation conforming assemblable volumetric partition","volume":"38","author":"Ara\u00fajo","year":"2019","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib3","doi-asserted-by":"crossref","first-page":"2696","DOI":"10.1016\/j.ijsolstr.2014.03.041","article-title":"When Heyman\u2019s safe theorem for rigid block systems fails: Non-Heymanian collapse modes of masonry structures","volume":"51","author":"Bagi","year":"2014","journal-title":"International Journal of Solids and Structures"},{"key":"2022072211191366400_bib4","first-page":"256","article-title":"A new variable for characterising irregular element geometries in experiments and DEM simulations","volume-title":"Proceedings of the European Council for Modelling and Simulation (ECMS 2020)","author":"Bagi","year":"2020"},{"key":"2022072211191366400_bib5","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.engstruct.2017.01.020","article-title":"Discrete element modelling of the in-plane and out-of-plane behavior of dry-joint masonry wall constructions","volume":"136","author":"Bui","year":"2017","journal-title":"Engineering Structures"},{"key":"2022072211191366400_bib6","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/BF00876528","article-title":"Friction of rocks","volume":"116","author":"Byerlee","year":"1978","journal-title":"Pure and Applied Geophysics"},{"key":"2022072211191366400_bib7","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.scriptamat.2011.12.022","article-title":"Enhancement of sound absorption properties using topologically interlocked elements","volume":"66","author":"Carlesso","year":"2012","journal-title":"Scripta Materialia"},{"key":"2022072211191366400_bib8","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.euromechsol.2018.03.003","article-title":"Corner failure in masonry buildings: An updated macro-modeling approach with frictional resistances","volume":"70","author":"Casapulla","year":"2018","journal-title":"European Journal of Mechanics - A\/Solids"},{"key":"2022072211191366400_bib10","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.compstruc.2019.05.001","article-title":"A digital tool to design structurally feasible semi-circular masonry arches composed of interlocking blocks","volume":"221","author":"Casapulla","year":"2019","journal-title":"Computers and Structures"},{"key":"2022072211191366400_bib9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1617\/s11527-021-01721-x","article-title":"Torsion-shear behaviour at the interfaces of rigid interlocking blocks in masonry assemblages: Experimental investigation and analytical approaches","volume":"54","author":"Casapulla","year":"2021","journal-title":"Materials and Structures"},{"key":"2022072211191366400_bib11","first-page":"1","article-title":"Dapper: Decompose-and-pack for 3D printing","volume":"34","author":"Chen","year":"2015","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib12","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.jcde.2018.10.002","article-title":"Form-finding with robotics: Rapid and flexible fabrication of glass fiber reinforced concrete panels using thermoformed molds","volume":"6","author":"Chen","year":"2019","journal-title":"Journal of Computational Design and Engineering"},{"key":"2022072211191366400_bib13","doi-asserted-by":"crossref","first-page":"108131","DOI":"10.1016\/j.compscitech.2020.108131","article-title":"An analytical model for the bio-inspired nacreous composites with interlocked \u201cbrick-and-mortar\u201d structures","volume":"193","author":"Cui","year":"2020","journal-title":"Composites Science and Technology"},{"key":"2022072211191366400_bib14","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-3-030-11942-3_2","article-title":"Topological interlocking materials","volume-title":"Architectured Materials in Nature and Engineering","author":"Dyskin","year":"2019"},{"key":"2022072211191366400_bib15","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1016\/j.jcde.2018.07.005","article-title":"Towards a multi-criteria framework for stereotomy\u2013Workflows for subtractive fabrication in complex geometries","volume":"6","author":"Fernando","year":"2019","journal-title":"Journal of Computational Design and Engineering"},{"key":"2022072211191366400_bib16","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.engstruct.2017.02.036","article-title":"Minimum thickness of semi-circular skewed masonry arches","volume":"140","author":"Forg\u00e1cs","year":"2017","journal-title":"Engineering Structures"},{"key":"2022072211191366400_bib17","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1016\/j.compstruc.2006.02.005","article-title":"Limit analysis of masonry block structures with non-associative frictional joints using linear programming","volume":"84","author":"Gilbert","year":"2006","journal-title":"Computers and Structures"},{"key":"2022072211191366400_bib18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1680\/eacm.2010.163.3.155","article-title":"Masonry arch analysis using discontinuity layout optimisation","volume":"163","author":"Gilbert","year":"2010","journal-title":"Proceedings of the Institution of Civil Engineers-Engineering and Computational Mechanics"},{"key":"2022072211191366400_bib19","first-page":"2963","article-title":"Design strategy for the rocking stability of horizontally restrained masonry walls","volume-title":"Proceedings of the 6th Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2017)","author":"Giresini","year":"2017"},{"key":"2022072211191366400_bib20","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.soildyn.2019.05.012","article-title":"One-sided rocking analysis of corner mechanisms in masonry structures: Influence of geometry, energy dissipation, boundary conditions","volume":"123","author":"Giresini","year":"2019","journal-title":"Soil Dynamics and Earthquake Engineering"},{"key":"2022072211191366400_bib21","doi-asserted-by":"crossref","first-page":"2265","DOI":"10.1007\/s10518-021-01056-6","article-title":"Experimental estimation of energy dissipation in rocking masonry walls restrained by an innovative seismic dissipator (LICORD)","volume":"19","author":"Giresini","year":"2021","journal-title":"Bulletin of Earthquake Engineering"},{"key":"2022072211191366400_bib22","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0020-7683(66)90018-7","article-title":"The stone skeleton","volume":"2","author":"Heyman","year":"1966","journal-title":"International Journal of Solids and Structures"},{"key":"2022072211191366400_bib23","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050310","volume-title":"The stone skeleton: Structural engineering of masonry architecture","author":"Heyman","year":"1995"},{"key":"2022072211191366400_bib24","doi-asserted-by":"crossref","first-page":"1635","DOI":"10.1201\/b21889-203","article-title":"Friction on mortar-less joints in semi interlocking masonry","volume-title":"Proceedings of the 16th International Brick and Block Masonry Conference (IBMAC 2016)","author":"Hossain","year":"2016"},{"key":"2022072211191366400_bib25","article-title":"3DEC version 5.2 manual, pp. problem solving with 3dec 3-13","author":"ITASCA","year":"2020"},{"key":"2022072211191366400_bib26","doi-asserted-by":"crossref","first-page":"108347","DOI":"10.1016\/j.matdes.2019.108347","article-title":"Mechanical behaviour of composite structures made of topologically interlocking concrete bricks with soft interfaces","volume":"186","author":"Javan","year":"2020","journal-title":"Materials & Design"},{"key":"2022072211191366400_bib27","first-page":"178","article-title":"Understanding the rigid-block equilibrium method by way of mathematical programming","volume":"174","author":"Kao","year":"2021","journal-title":"Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics"},{"key":"2022072211191366400_bib28","doi-asserted-by":"crossref","first-page":"166","DOI":"10.3390\/ma9030166","article-title":"Cyclic behavior of mortarless brick joints with different interlocking shapes","volume":"9","author":"Liu","year":"2016","journal-title":"Materials"},{"key":"2022072211191366400_bib29","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1002\/nme.1620121207","article-title":"Limit analysis of structures formed from rigid blocks","volume":"12","author":"Livesley","year":"1978","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2022072211191366400_bib30","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF00430042","article-title":"A computational model for the limit analysis of three-dimensional masonry structures","volume":"27","author":"Livesley","year":"1992","journal-title":"Meccanica"},{"key":"2022072211191366400_bib31","doi-asserted-by":"crossref","first-page":"103117","DOI":"10.1016\/j.autcon.2020.103117","article-title":"Free-form structures from topologically interlocking masonries","volume":"113","author":"Loing","year":"2020","journal-title":"Automation in Construction"},{"key":"2022072211191366400_bib32","first-page":"1","article-title":"Two approaches for the analysis of masonry structures: Micro and macro-modeling","volume":"40","author":"Louren\u00e7o","year":"1995","journal-title":"Heron"},{"key":"2022072211191366400_bib33","first-page":"1","article-title":"Chopper: Partitioning models into 3D-printable parts","volume":"31","author":"Luo","year":"2012","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib34","doi-asserted-by":"crossref","first-page":"106079","DOI":"10.1016\/j.cemconres.2020.106079","article-title":"Opportunities and challenges for structural engineering of digitally fabricated concrete","volume":"133","author":"Menna","year":"2020","journal-title":"Cement and Concrete Research"},{"key":"2022072211191366400_bib35","doi-asserted-by":"crossref","first-page":"5258","DOI":"10.1016\/j.ijsolstr.2008.05.019","article-title":"Limit analysis of masonry vaults by means of curved shell finite elements and homogenization","volume":"45","author":"Milani","year":"2008","journal-title":"International Journal of Solids and Structures"},{"key":"2022072211191366400_bib36","doi-asserted-by":"crossref","first-page":"9128","DOI":"10.1073\/pnas.1807272115","article-title":"Simultaneous improvements of strength and toughness in topologically interlocked ceramics","volume":"115","author":"Mirkhalaf","year":"2018","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2022072211191366400_bib37","article-title":"SiDMACIB project. Marie Sk\u0142odowska-Curie individual fellowship","author":"Mousavian","year":"2018"},{"key":"2022072211191366400_bib39","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1093\/jcde\/qwaa038","article-title":"Structurally informed design of interlocking block assemblages using limit analysis","volume":"7","author":"Mousavian","year":"2020","journal-title":"Journal of Computational Design and Engineering"},{"key":"2022072211191366400_bib38","doi-asserted-by":"crossref","first-page":"102898","DOI":"10.1016\/j.advengsoft.2020.102898","article-title":"Quantifiable feasibility check of masonry assemblages composed of interlocking blocks","volume":"149","author":"Mousavian","year":"2020","journal-title":"Advances in Engineering Software"},{"key":"2022072211191366400_bib40","doi-asserted-by":"crossref","first-page":"4558860","DOI":"10.23967\/sahc.2021.031","article-title":"Assemblability constraints in the limit analysis of 3D masonry interlocking blocks","volume-title":"12th International Conference on Structural Analysis of Historical Constructions, SAHC 2021","author":"Mousavian","year":"2021"},{"key":"2022072211191366400_bib41","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.engstruct.2016.02.002","article-title":"Assessment of masonry structures subjected to foundation settlements using rigid block limit analysis","volume":"113","author":"Portioli","year":"2016","journal-title":"Engineering Structures"},{"key":"2022072211191366400_bib42","article-title":"Funicular shell design: Geometric approaches to form finding and fabrication of discrete funicular structures","author":"Rippmann","year":"2016"},{"key":"2022072211191366400_bib43","doi-asserted-by":"crossref","first-page":"2461","DOI":"10.1098\/rspa.2006.1788","article-title":"Application of discontinuity layout optimization to plane plasticity problems","volume":"463","author":"Smith","year":"2007","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"2022072211191366400_bib44","doi-asserted-by":"crossref","first-page":"3602","DOI":"10.1002\/eqe.3524","article-title":"Fragility curves and seismic demand hazard analysis of rocking walls restrained with elasto-plastic ties","volume":"50","author":"Solarino","year":"2021","journal-title":"Earthquake Engineering & Structural Dynamics"},{"key":"2022072211191366400_bib45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2366145.2366147","article-title":"Recursive interlocking puzzles","volume":"31","author":"Song","year":"2012","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib46","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.cad.2017.05.006","article-title":"Automatic decomposition of 3D solids into contractible pieces using reeb graphs","volume":"90","author":"Strodthoff","year":"2017","journal-title":"Computer-Aided Design"},{"key":"2022072211191366400_bib47","first-page":"1","article-title":"Design and structural optimization of topological interlocking assemblies","volume":"38","author":"Wang","year":"2019","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib48","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.autcon.2016.05.014","article-title":"Topological interlocking in buildings: A case for the design and construction of floors","volume":"72","author":"Weizmann","year":"2016","journal-title":"Automation in Construction"},{"key":"2022072211191366400_bib49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1618452.1618458","article-title":"Procedural modeling of structurally-sound masonry buildings","volume":"28","author":"Whiting","year":"2009","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib50","article-title":"Design of structurally-sound masonry buildings using 3D static analysis","author":"Whiting","year":"2012"},{"key":"2022072211191366400_bib51","doi-asserted-by":"crossref","first-page":"10503","DOI":"10.1016\/j.tust.2020.103503","article-title":"A novel non-planar interlocking element for tubular structures","volume":"103","author":"Xu","year":"2020","journal-title":"Tunnelling and Underground Space Technology"},{"key":"2022072211191366400_bib52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3072959.3054740","article-title":"Interactive design and stability analysis of decorative joinery for furniture","volume":"36","author":"Yao","year":"2017","journal-title":"ACM Transactions on Graphics"},{"key":"2022072211191366400_bib53","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1115\/1.4003038","article-title":"Topology synthesis of multicomponent structural assemblies in continuum domains","volume":"133","author":"Yildiz","year":"2011","journal-title":"Journal of Mechanical Design"}],"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\/qwac054\/44062594\/qwac054.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/9\/4\/1279\/45047716\/qwac054.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/9\/4\/1279\/45047716\/qwac054.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T06:10:15Z","timestamp":1675836615000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/9\/4\/1279\/6608361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,14]]},"references-count":53,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,7,22]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwac054","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,8]]},"published":{"date-parts":[[2022,6,14]]}}}