{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T05:55:36Z","timestamp":1770270936422,"version":"3.49.0"},"reference-count":58,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T00:00:00Z","timestamp":1583107200000},"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":["51578133"],"award-info":[{"award-number":["51578133"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["KAKENHI 15KT0109"],"award-info":[{"award-number":["KAKENHI 15KT0109"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.<\/jats:p>","DOI":"10.3390\/sym12030374","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T03:24:20Z","timestamp":1583292260000},"page":"374","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Closed-Form Solutions for the Form-Finding of Regular Tensegrity Structures by Group Elements"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9784-5787","authenticated-orcid":false,"given":"Qian","family":"Zhang","sequence":"first","affiliation":[{"name":"Key Labortary of C &amp; PC Structures of Ministry of Educaiton, National Prestress Engineering Research Center, Southeast University, Nanjing 210096, China"}]},{"given":"Xinyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Labortary of C &amp; PC Structures of Ministry of Educaiton, National Prestress Engineering Research Center, Southeast University, Nanjing 210096, China"}]},{"given":"Jianguo","family":"Cai","sequence":"additional","affiliation":[{"name":"Key Labortary of C &amp; PC Structures of Ministry of Educaiton, National Prestress Engineering Research Center, Southeast University, Nanjing 210096, China"}]},{"given":"Jingyao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Architecture and Architectural Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo, Kyoto 615-8540, Japan"}]},{"given":"Jian","family":"Feng","sequence":"additional","affiliation":[{"name":"Key Labortary of C &amp; PC Structures of Ministry of Educaiton, National Prestress Engineering Research Center, Southeast University, Nanjing 210096, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3741","DOI":"10.1016\/j.ijsolstr.2012.08.008","article-title":"An overview and comparison of structural form finding methods for general networks","volume":"49","author":"Veenendaal","year":"2012","journal-title":"Int. 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