{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T12:30:27Z","timestamp":1777897827588,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T00:00:00Z","timestamp":1711497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This study conducts buckling and free vibration analyses of multi-directional functionally graded sandwich plates subjected to various boundary conditions. Two scenarios are considered: a functionally graded (FG) skin with a homogeneous hard core, and an FG skin with a homogeneous soft core. Utilizing refined plate models, which incorporate a parabolic distribution of transverse shear stresses while ensuring zero shear stresses on both the upper and lower surfaces, equations of motion are derived using Hamilton\u2019s principle. Analytical solutions for the buckling and free vibration analyses of multi-directional FG sandwich plates under diverse boundary conditions are developed and presented. The obtained results are validated against the existing literature for both the buckling and free vibration analyses. The composition of metal\u2013ceramic-based FG materials varies longitudinally and transversely, following a power law. Various types of sandwich plates are considered, accounting for plate symmetry and layer thicknesses. This investigation explores the influence of several parameters on buckling and free vibration behaviors.<\/jats:p>","DOI":"10.3390\/computation12040065","type":"journal-article","created":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T14:14:09Z","timestamp":1711548849000},"page":"65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Multi-Directional Functionally Graded Sandwich Plates: Buckling and Free Vibration Analysis with Refined Plate Models under Various Boundary Conditions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3333-5902","authenticated-orcid":false,"given":"Lazreg","family":"Hadji","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret 14000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7377-781X","authenticated-orcid":false,"given":"Vagelis","family":"Plevris","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Qatar University, Doha P.O. Box 2713, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3445-9210","authenticated-orcid":false,"given":"Royal","family":"Madan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Graphic Era (Deemed to be University), Dehradun 248002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hassen","family":"Ait Atmane","sequence":"additional","affiliation":[{"name":"Civil Engineering Department, University of Hassiba Ben Bouali, Chlef 02180, Algeria"},{"name":"Laboratory of Structures, Geotechnics and Risks, University of Hassiba Ben Bouali, Chlef 02180, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1007\/s12540-019-00491-0","article-title":"Review on the Influence of Different Reinforcements on the Microstructure and Wear Behavior of Functionally Graded Aluminum Matrix Composites by Centrifugal Casting","volume":"26","author":"Saleh","year":"2020","journal-title":"Met. 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