{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:41:27Z","timestamp":1760211687048,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,5,21]],"date-time":"2016-05-21T00:00:00Z","timestamp":1463788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Science Foundation of China","award":["51161120360","91315301-09"],"award-info":[{"award-number":["51161120360","91315301-09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The nonlinear unconditionally stable energy-conserving integration method (ECM) is a new method for solving a continuous equation of motion. To our knowledge, there is still no report about its application on a hybrid test. Aiming to explore its effect on hybrid tests, the nonlinear beam-column element program is developed for computation. The program contains both the ECM and the average acceleration method (AAM). The comparison of the hybrid test results with thesetwo methods validates the effectiveness of the ECM in the hybrid simulation. We found that the energy error of hybrid test by using ECM is less than that of AAM. In addition, a new iteration strategy with reduction factor is presented to avoid the overshooting phenomena during iteration process with the finite element program.<\/jats:p>","DOI":"10.3390\/a9020035","type":"journal-article","created":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T09:05:05Z","timestamp":1464080705000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Application of the Energy-Conserving Integration Method to Hybrid Simulation of a Full-Scale Steel Frame"],"prefix":"10.3390","volume":"9","author":[{"given":"Tianlin","family":"Pan","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China"},{"name":"Key Lab of Structures Dynamic Behavior and Control, Harbin Institute of Technology, Ministry of Education, Harbin 150090, China"}]},{"given":"Bin","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China"},{"name":"Key Lab of Structures Dynamic Behavior and Control, Harbin Institute of Technology, Ministry of Education, Harbin 150090, China"}]},{"given":"Yongsheng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China"},{"name":"Key Lab of Structures Dynamic Behavior and Control, Harbin Institute of Technology, Ministry of Education, Harbin 150090, China"},{"name":"Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China"}]},{"given":"Guoshan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China"},{"name":"Key Lab of Structures Dynamic Behavior and Control, Harbin Institute of Technology, Ministry of Education, Harbin 150090, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1002\/eqe.927","article-title":"Stability of central difference method for dynamic real-time substructure testing","volume":"38","author":"Wu","year":"2009","journal-title":"Earthq. 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