{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:08:17Z","timestamp":1760242097562,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,16]],"date-time":"2018-12-16T00:00:00Z","timestamp":1544918400000},"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":["51805144"],"award-info":[{"award-number":["51805144"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20170300"],"award-info":[{"award-number":["BK20170300"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a new approach is proposed to identify sectional deformation modes of the doubly symmetric thin-walled cross-section, which are to be employed in formulating a one-dimensional model of thin-walled structures. The approach considers the three-dimensional displacement field of the structure as the linear superposition of a set of sectional deformation modes. To retrieve these modes, the modal analysis of a thin-walled structure is carried out based on shell\/plate theory, with the shell-like deformation shapes extracted. The components of classical modes are removed from these shapes based on a novel criterion, with residual deformation shapes left. By introducing benchmark points, these shapes are further classified into several deformation patterns, and within each pattern, higher-order deformation modes are derived by removing the components of identified ones. Considering the doubly symmetric cross-section, these modes are approximated with shape functions applying the interpolation method. The identified modes are finally used to deduce the governing equations of the thin-walled structure, applying Hamilton\u2019s principle. Numerical examples are also presented to validate the accuracy and efficiency of the new model in reproducing three-dimensional behaviors of thin-walled structures.<\/jats:p>","DOI":"10.3390\/sym10120759","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T02:15:59Z","timestamp":1545099359000},"page":"759","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Identification of Sectional Deformation Modes of Thin-Walled Structures with Doubly Symmetric Cross-Sections Based on the Shell-Like Deformation"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6234-7945","authenticated-orcid":false,"given":"Lei","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aimin","family":"Ji","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weidong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Maryland, Baltimore County, MD 21250, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3499-4037","authenticated-orcid":false,"given":"Liping","family":"Peng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mineral Processing, Beijing General Research Institute of Mining and Metallurgy, Beijing 102600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1016\/j.tws.2018.03.008","article-title":"GBT-based cross-section deformation modes for curved thin-walled members with circular axis","volume":"127","author":"Peres","year":"2018","journal-title":"Thin-Walled Struct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1400298","DOI":"10.1299\/mer.14-00298","article-title":"Recent developments on refined theories for beams with applications","volume":"2","author":"Carrera","year":"2015","journal-title":"Mech. 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