An asymptotic higher-order theory for rectangular beams

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences - Tập 474 Số 2214 - Trang 20180001 - 2018
E.V. Nolde1, A. V. Pichugin1, Julius Kaplunov2
1Department of Mathematics, CEDPS, Brunel University London, Uxbridge UB8 3PH, UK
2School of Computing and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK

Tóm tắt

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.

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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Tập 474 Số 2214

20180001

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