{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:48:25Z","timestamp":1777448905544,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[1989,8,1]],"date-time":"1989-08-01T00:00:00Z","timestamp":617932800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[1989,8]]},"abstract":"<jats:p>This work is a continuation of an earlier work by Bermudez and Via\u00f1o (1984) on the same subject. In fact, using the same asymptotic expansion in linear elastic beams we give a complete characterization of displacements, bending moments and shear forces of orders 0, 1 and 2. These results include a characterization of the stress field of order 0 and of the axial and shear stresses of order 1. An appropriate physical interpretation of these results, which is considered elsewhere, will allow us to derive and to justify, from a mathematical point of view, the most well-known classical extension, bending and torsion theories for linear elastic beams, including the Bernoulli-Navier, Saint Venant, Timoshenko and Vlasov models.<\/jats:p>","DOI":"10.3233\/asy-1989-2303","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T18:37:16Z","timestamp":1575052636000},"page":"223-255","source":"Crossref","is-referenced-by-count":24,"title":["Existence and characterization of higher-order terms in an asymptotic expansion method for linearized elastic beams"],"prefix":"10.1177","volume":"2","author":[{"given":"L.","family":"Trabucho","sequence":"first","affiliation":[{"name":"Centro de Matematica e Aplica\u00e7\u00f5es Fundamentais, C.M.A.F.-I.N.I.C., Instituto de Fisica e Matematica, Av. Prof Gama Pinto2, 1699 Lisboa Codex, Portugal"}]},{"given":"J.M.","family":"Via\u00f1o","sequence":"additional","affiliation":[{"name":"Departamento de Matematica Aplicada, Facultad de Matematicas, Universidad de Santiago de Compos tela, 15706 Santiago de Compostela, Espa\u00f1a"}]}],"member":"179","published-online":{"date-parts":[[1989,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-1989-2303","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-1989-2303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:20Z","timestamp":1777379960000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-1989-2303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,8]]}},"alternative-id":["10.3233\/ASY-1989-2303"],"URL":"https:\/\/doi.org\/10.3233\/asy-1989-2303","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,8]]}}}