{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:50:12Z","timestamp":1760151012433,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T00:00:00Z","timestamp":1644710400000},"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":["51822805, 51878147, and U1937202"],"award-info":[{"award-number":["51822805, 51878147, and U1937202"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is necessary to perform the robustness design for the progressive collapse resistance of grid structures. However, there is a lack of a comprehensive index to evaluate the member importance. An evaluation method on element importances is proposed based on the element strain energy and element removal technology. The element importance coefficients can be calculated based on the change of strain energy vectors after the removal of analyzed elements using ANSYS. The influence of the loading pattern, boundary condition, and geometric parameters of square pyramid grid structures are investigated. Moreover, the other three types of spatial grids are introduced to explore the difference in element importance distributions. The considerable difference in element importance coefficient distribution for different grid structures shows that it is essential to establish a general program for rapid model robustness analysis. This principle in this work can be easily integrated into the existing design and analysis platform to make up for this shortcoming.<\/jats:p>","DOI":"10.3390\/sym14020370","type":"journal-article","created":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T20:35:28Z","timestamp":1644784528000},"page":"370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Applications of Energy-Based Evaluation Method of Element Importance to Grid Structures"],"prefix":"10.3390","volume":"14","author":[{"given":"Liwu","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of C & PC Structures of Ministry of Education, National Prestress Engineering Research Center, Southeast University, Nanjing 211189, China"},{"name":"Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China"}]},{"given":"Jian","family":"Feng","sequence":"additional","affiliation":[{"name":"Key Laboratory of C & PC Structures of Ministry of Education, National Prestress Engineering Research Center, Southeast University, Nanjing 211189, China"}]},{"given":"Yixiang","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Aerospace, The University of Nottingham Ningbo China, Ningbo 315100, China"}]},{"given":"Liping","family":"Zhuang","sequence":"additional","affiliation":[{"name":"Key Laboratory of C & PC Structures of Ministry of Education, National Prestress Engineering Research Center, Southeast University, Nanjing 211189, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9784-5787","authenticated-orcid":false,"given":"Qian","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of C & PC Structures of Ministry of Education, National Prestress Engineering Research Center, Southeast University, Nanjing 211189, China"}]},{"given":"Jianguo","family":"Cai","sequence":"additional","affiliation":[{"name":"Key Laboratory of C & PC Structures of Ministry of Education, National Prestress Engineering Research Center, Southeast University, Nanjing 211189, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"04018092","DOI":"10.1061\/(ASCE)CF.1943-5509.0001244","article-title":"Effect of structural redundancy on progressive collapse resistance enhancement in RC frame structures","volume":"33","author":"Ameri","year":"2019","journal-title":"J. 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