{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:50:03Z","timestamp":1760143803637,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT, Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia, through IDMEC, under LAETA","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>An analysis of the influence of applied loads on free vibrations of plate and shell panels made of functionally graded materials is analyzed in the present work. Formulations for the static analysis considering geometrically nonlinear behavior, as well as linear buckling and free vibrations analyses are considered. A calculation of the through-thickness stress distribution is also performed. The finite element model is based on a higher order shear deformation theory using a non-conforming flat triangular plate\/shell element with three nodes, and eight degrees of freedom per node is used in the numerical implementation. The results obtained with this numerical model are presented, discussed, and compared with alternative solutions published by other authors in some benchmark applications.<\/jats:p>","DOI":"10.3390\/app14051993","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T09:26:17Z","timestamp":1709112377000},"page":"1993","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Influence of Applied Loads on Free Vibrations of Functionally Graded Material Plate\u2013Shell Panels"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2529-583X","authenticated-orcid":false,"given":"Jos\u00e9 Sim\u00f5es","family":"Moita","sequence":"first","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5159-5361","authenticated-orcid":false,"given":"Victor Franco","family":"Correia","sequence":"additional","affiliation":[{"name":"ENIDH\u2014Escola Superior N\u00e1utica Infante D. Henrique, Av. Eng. Bonneville Franco, 2770-058 Pa\u00e7o de Arcos, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4645-138X","authenticated-orcid":false,"given":"Crist\u00f3v\u00e3o Mota","family":"Soares","sequence":"additional","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7409","DOI":"10.1016\/S0020-7683(01)00048-8","article-title":"Nonlinear analysis of functionally graded plates and shallow shells","volume":"38","author":"Woo","year":"2001","journal-title":"Int. J. Solids Struct."},{"key":"ref_2","unstructured":"Reddy, J.N., and Arciniega, R.A. (2006). Analysis and Design of Plated Structures: Dynamics, Woodhead Publishing."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2036","DOI":"10.1016\/j.ijsolstr.2006.08.035","article-title":"Large deformation analysis of functionally graded shells","volume":"44","author":"Arciniega","year":"2007","journal-title":"Int. J. Solids Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1177\/0021998307086211","article-title":"Geometrically nonlinear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element","volume":"42","author":"Kim","year":"2008","journal-title":"J. Compos. Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.ijmecsci.2008.12.004","article-title":"Geometrically nonlinear analysis of functionally graded shells","volume":"51","author":"Zhao","year":"2009","journal-title":"Int. J. Mech. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.compositesb.2013.02.045","article-title":"Isogeometric analysis of functionally graded plates using higher-order shear deformation theory","volume":"51","author":"Tran","year":"2013","journal-title":"Compos. Part B Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.compstruct.2012.08.025","article-title":"A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates","volume":"96","author":"Thai","year":"2013","journal-title":"Compos. 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Mech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.jsv.2008.03.056","article-title":"Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation","volume":"318","author":"Pradyumna","year":"2008","journal-title":"J. Sound Vib."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.euromechsol.2012.05.005","article-title":"Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations","volume":"37","author":"Neves","year":"2013","journal-title":"Eur. J. Mech. 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