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Article Dans Une Revue Journal of Elasticity Année : 2017

Justification of the Asymptotic Expansion Method for Homogeneous Isotropic Beams by Comparison with De Saint-Venant's Solutions

Résumé

The formal asymptotic expansion method is an attractive mean to derive simpli-fie models for problems exhibiting a small parameter, such as the elastic analysis of beam-like structures. Usually this method is rigorously justifie using convergence theorems Yu and Hodges, 2004. In this paper it is illustrated how the Saint-Venant's solution naturally arises from the lowest order terms of an asymptotic expansion of the elastic state for the case of homogeneous isotropic beams. It is also highlighted that the Saint-Venant solutions corresponding to pure traction, bending and torsion involve the solution of the first-orde microscopic problems, while for the simple bending problem, the solution of the second-order microscopic problems is needed. The second-order problems provide therefore a way to characterize the transverse shear behavior and the cross-sectional warping of the beam.
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Dates et versions

hal-02143835 , version 1 (29-05-2019)

Identifiants

Citer

Qian Zhao, Patrice Cartraud, Panagiotis Kotronis. Justification of the Asymptotic Expansion Method for Homogeneous Isotropic Beams by Comparison with De Saint-Venant's Solutions. Journal of Elasticity, 2017, 126 (2), pp.245-270. ⟨10.1007/s10659-016-9593-2⟩. ⟨hal-02143835⟩
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