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

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• 作者：Qian Zhao ; Patrice Cartraud ; Panagiotis Kotronis
• 关键词：Asymptotic expansion method ; Saint ; Venant solutions ; Transverse shear ; Warping ; Beam
• 刊名：Journal of Elasticity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：126
• 期：2
• 页码：245-270
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-2681
• 卷排序：126

文摘

The formal asymptotic expansion method is an attractive mean to derive simplified models for problems exhibiting a small parameter, such as the elastic analysis of beam-like structures. Usually this method is rigorously justified 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-order 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.