{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:58:03Z","timestamp":1753883883083,"version":"3.41.2"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,5,28]],"date-time":"2012-05-28T00:00:00Z","timestamp":1338163200000},"content-version":"vor","delay-in-days":148,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper investigates different approximation techniques for planar beam column elements in force\u2010based methods. The three fields, introduced in this review, are: curvature\u2010based displacement interpolation (CBDI) used in matrix\u2010based flexibility formulations, linear displacement approximation applied in state space, and higher\u2010order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher\u2010order approximation field in state space.<\/jats:p>","DOI":"10.1155\/2012\/516290","type":"journal-article","created":{"date-parts":[[2012,5,29]],"date-time":"2012-05-29T07:13:52Z","timestamp":1338275632000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Displacement Field Approximations for Force\u2010Based Elements in Large Displacement Analyses"],"prefix":"10.1155","volume":"2012","author":[{"given":"M.","family":"Vahidi","sequence":"first","affiliation":[]},{"given":"V.","family":"Jafari","sequence":"additional","affiliation":[]},{"given":"M. H.","family":"Abyaneh","sequence":"additional","affiliation":[]},{"given":"SH.","family":"Vahdani","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,5,28]]},"reference":[{"key":"e_1_2_6_1_2","unstructured":"CiampiV.andCarlesimoL. A nonlinear beam element for seismic analysis of structures Proceedings of the European Conference on Earthquake Engineering September 1986 Lisbon Portugal 73\u201380."},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7949(95)00103-N"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1999)125:9(994)"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9445(1998)124:6(704)"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-003-0410-y"},{"key":"e_1_2_6_7_2","unstructured":"TaucerF. 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