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The displacement boundary conditions for Reddy higher-order shear cantilever beam theory

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Abstract

The paper presents the analytical results aimed at studying the deformations of cantilever beams based on Reddy higher-order shear theory. Five different displacement boundary conditions are investigated. The first two conditions are conventional simplified displacement boundary conditions, and the third one is determined by the least squares method. Besides, two new simplified boundary conditions are given by considering the definition of the fixed end of cantilever beams. Compared with the solutions by the finite element method, results by the two new boundary conditions are found to be much better than those by the conventional ones, especially for deep beams. The new boundary conditions which are first presented are not as good as the condition determined by the least squares method, but they are simple and easy to be coded by engineers.

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References

  1. Yang L.Z., Shang L.G., Gao Y., Wang M.Z.: Further study on the refined theory of rectangle deep beams. Acta Mech. 224, 1999–2007 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dym C.L., Shames I.H.: Solid Mechanics: A Vibrational Approach. McGraw-Hill, New York (1973)

    Google Scholar 

  3. Timoshenko S.P.: On the correction for shear of the differential equation for transverse vibration of prismatic bars. Philos. Mag. Ser. 6, 744–746 (1921)

    Article  Google Scholar 

  4. Cowper G.R.: The shear coefficient in Timoshenko’s beam theory. ASME J. Appl. Mech. 33, 335–340 (1966)

    Article  MATH  Google Scholar 

  5. Reddy J.N.: Energy and Vibrational Methods in Applied Mechanics. Wiley, New York (1984)

    Google Scholar 

  6. Reddy J.N.: Simple higher-order theory for laminated composite plates. ASME J. Appl. Mech. 51, 745–752 (1984)

    Article  MATH  Google Scholar 

  7. Wang C.M., Reddy J.N., Lee K.H.: Shear Deformable Beams and Plates. Elsevier Science Ltd, Netherlands (2000)

    MATH  Google Scholar 

  8. Ghugal Y.M., Shimpi R.P.: A review of refined shear deformation theories for isotropic and anisotropic laminated beams. J. Reinf. Plast. Compos. 20, 255–272 (2001)

    Article  Google Scholar 

  9. Timoshenko S.P., Goodier J.C.: Theory of Elasticity. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  10. Timoshenko S.P., Gere J.M.: Mechanics of Materials. Van Nostrand Company, New York (1972)

    Google Scholar 

  11. Huang, W.B.: Problems on the shear deflection of a plane elastic cantilever. Mech. Eng. 19, 61–62 (1997) (in Chinese)

  12. Huang, W.B.: Further study on the problems on the shear deflection of a plane elastic cantilever. Mech. Eng. 20, 65 (1998) (in Chinese)

  13. Wang, M.Z.: About “Problems on the shear deflection of a plane elastic cantilever”. Mech. Eng. 26, 66–68 (2004) (in Chinese)

  14. Doyle P.F., Pavlovic M.N.: Vibration of beams on partial elastic foundations. Earthq. Eng. Struct. Dyn. 10, 663–674 (1982)

    Article  Google Scholar 

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Authors and Affiliations

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

    Zhendong Sun, Lianzhi Yang & Yang Gao

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  1. Zhendong Sun
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  2. Lianzhi Yang
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  3. Yang Gao
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Correspondence to Yang Gao.

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Sun, Z., Yang, L. & Gao, Y. The displacement boundary conditions for Reddy higher-order shear cantilever beam theory. Acta Mech 226, 1359–1367 (2015). https://doi.org/10.1007/s00707-014-1253-7

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  • DOI: https://doi.org/10.1007/s00707-014-1253-7

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