Affiliations: Centro de Matematica e Aplicações Fundamentais, C.M.A.F.-I.N.I.C., Instituto de Fisica e Matematica, Av. Prof Gama Pinto2, 1699 Lisboa Codex, Portugal | Departamento de Matematica Aplicada, Facultad de Matematicas, Universidad de Santiago de Compos tela, 15706 Santiago de Compostela, España
Note: [] This work was performed while the authors were staying at the Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris, France.
Abstract: This work is a continuation of an earlier work by Bermudez and Viaño (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.
