{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T04:43:34Z","timestamp":1768797814410,"version":"3.49.0"},"reference-count":17,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T00:00:00Z","timestamp":1702512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The inverse finite element method (iFEM) is a powerful tool for shape sensing and structural health monitoring and has several advantages with respect to some other existing approaches. In this study, a two-dimensional eight-node quadrilateral inverse finite element formulation is presented. The element is suitable for thin structures under in-plane loading conditions. To validate the accuracy and demonstrate the capability of the inverse element, four different numerical cases are considered for different loading and boundary conditions. iFEM analysis results are compared with regular finite element analysis results as the reference solution and very good agreement is observed between the two solutions, demonstrating the capability of the iFEM approach.<\/jats:p>","DOI":"10.3390\/s23249809","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T11:28:07Z","timestamp":1702898887000},"page":"9809","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Two-Dimensional Eight-Node Quadrilateral Inverse Element for Shape Sensing and Structural Health Monitoring"],"prefix":"10.3390","volume":"23","author":[{"given":"Mingyang","family":"Li","sequence":"first","affiliation":[{"name":"Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}]},{"given":"Erkan","family":"Oterkus","sequence":"additional","affiliation":[{"name":"Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow G4 0LZ, UK"}]},{"given":"Selda","family":"Oterkus","sequence":"additional","affiliation":[{"name":"Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow G4 0LZ, UK"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1007\/s12541-012-0281-2","article-title":"Measurement of strain and bending deflection of a wind turbine tower using arrayed FBG sensors","volume":"13","author":"Bang","year":"2012","journal-title":"Int. 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