An asymptotic higher-order theory for rectangular beams

作者：Nolde E; Pichugin A V^*; Kaplunov J

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2018, 474(2214): 20180001.

DOI：10.1098/rspa.2018.0001

• asymptotics
• long waves
• low frequency
• beam theory
• Timoshenko beam theory
• shear correction factor

A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite-element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classical plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions. The implications for the correct choice of the shear correction factor in Timoshenko's beam theory are also discussed.

• 出版日期2018-6