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We show the strict correspondence between the sandwich beam, sandwich plate, and the analogous composite beam and composite plate problem with partial interaction. The beam problem is governed by a sixth-order differential equation in space for the deflection, whereas the plate problem is governed by a tri-Laplacian equation for the deflection, as first shown by Hoff in 1950 for symmetrical three-layer component (sandwich plate or composite plate theory with partial interaction). It is shown herein that the tri-Laplacian partial differential equation is also valid for general unsymmetrical sandwich plate or partially composite plate. In the limit cases, i.e., for non-composite action and for full-composite action, the beam model reduces into the Euler\u2013Bernoulli beam model and the plate model into the Kirchhoff\u2013Love model. Boundary layer phenomena may be predominant in the asymptotic stiff problem. The nonlocal bending moment\u2013curvature of the sandwich beam (or composite beam with partial interaction) is analysed, and extended to a nonlocal Marcus bending moment\u2013curvature for the composite plate theory. The consistency of the tri-Laplacian plate theory is commented, regarding the bi-Laplacian Reissner sandwich plate theory, which neglects the bending stiffnesses of each face layer. The paper finally presents results for the static bending and vibrations of sandwich beams and plates on simply supported boundary conditions, with a discussion on asymptotic limit cases.<\/jats:p>","DOI":"10.1177\/10812865241289897","type":"journal-article","created":{"date-parts":[[2024,12,21]],"date-time":"2024-12-21T05:14:22Z","timestamp":1734758062000},"page":"1608-1643","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["A historical overview on static and dynamic analyses of sandwich or partially composite beams and plates"],"prefix":"10.1177","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7122-0700","authenticated-orcid":false,"given":"No\u00ebl","family":"Challamel","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Bretagne Sud, IRDL \u2013 UBS \u2013 Lorient, Centre de Recherche, Lorient Cedex, France"}]},{"given":"Seyed Rasoul","family":"Atashipour","sequence":"additional","affiliation":[{"name":"Division of Dynamics, Department of Mechanics and Maritime Sciences (M2), Chalmers University of Technology, Gothenburg, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0336-6433","authenticated-orcid":false,"given":"Ulf Arne","family":"Girhammar","sequence":"additional","affiliation":[{"name":"Division of Wood Science and Engineering, Department of Engineering Sciences and Mathematics, Lule\u00e5 University of Technology, Lule\u00e5, Sweden"}]},{"given":"Viviane Setti","family":"Barroso","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of Coimbra, Coimbra, Portugal"}]},{"given":"An\u00edsio","family":"Andrade","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of Coimbra, Coimbra, Portugal"}]},{"given":"Claude","family":"Boutin","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Lyon, Ecole Nationale des Travaux Publics de l\u2019Etat, LGCB \u2013 CNRS 5513, Vaulx-en-Velin, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8128-3262","authenticated-orcid":false,"given":"Victor A","family":"Eremeyev","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering and Architecture, (DICAAR), University of Cagliari, Cagliari, Italy"}]}],"member":"179","published-online":{"date-parts":[[2024,12,21]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-8935-0"},{"key":"e_1_3_3_3_2","volume-title":"Mechanics of laminated composite plates and shells\u2014Theory and analysis","author":"Reddy JN.","year":"2004","unstructured":"Reddy JN. 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