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The refined theory of deep rectangular beams based on general solutions of elasticity

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Abstract

The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity.

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Authors and Affiliations

  1. College of Science, China Agricultural University, Beijing, 100083, China

    Gao Yang

  2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, China

    Wang Minzhong

Authors
  1. Gao Yang
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  2. Wang Minzhong
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Correspondence to Gao Yang.

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Gao, Y., Wang, M. The refined theory of deep rectangular beams based on general solutions of elasticity. SCI CHINA SER G 49, 291–303 (2006). https://doi.org/10.1007/s11433-006-0291-0

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  • DOI: https://doi.org/10.1007/s11433-006-0291-0

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