Applied Mathematics and Mechanics

, Volume 14, Issue 3, pp 241–246 | Cite as

An approximate solution with high accuracy of transverse bending of thin rectangular plates under arbitrarily distributed loads

  • Zhou Ding
Article
  • 26 Downloads

Abstract

Ritz method is an effective way widely used to analyze the transverse bending of thin rectangular plates. Its accuracy depends completely on the basis functions selected. This paper selects the superposition of sine series with polynomials as the basis functions of thin rectangular plates. The calculating formulae are not only simple and easily programmed, but also have high accuracy. Finally, two numerical results are given and compared with those obtained by the classical method.

Key words

rectangular plate bending small deflection 

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References

  1. [1]
    Chang Fo-van,Elastic Thin Plates, Science Press, Beijing, (1963). (in Chinese)Google Scholar
  2. [2]
    Timoshenko, S., et al., Theory of Plates and Shells, McGraw-Hill (1959).Google Scholar
  3. [3]
    Chang Fo-van, Rectangular plates with two adjacent edges clamped and other two adjacent edges free,Acta Mechanica Solida Sinica, 4 (1981), 491–502. (in Chinese)Google Scholar
  4. [4]
    Chang Fo-van, Bending of uniformly loaded cantilever rectangular plates,Appl. Math. and Mech.,1, 3 (1980), 371–383.CrossRefGoogle Scholar
  5. [5]
    Huang Yan and Yang Ying-yuan, Analytical solution for solving bending problem of orthotropic rectangular plates,Shanghai J. of Mech.,7, 1, (1986), 1–10. (in Chinese)Google Scholar
  6. [6]
    Wang Lei and Li Jia-bao, Approximate solution for bending of rectangular plates Kantorovich-Galerkin's method,Appl. Math. and Mech.,7, 1 (1986), 87–102.CrossRefGoogle Scholar
  7. [7]
    Wang Lei, Solution of spline function of elastic plates,Appl. Math. and Mech.,6, 8 (1985), 777–787.MathSciNetGoogle Scholar
  8. [8]
    Xu Yong-lin and Tang Jin-chun, Analysis of plate bending problems with direct singular method and Green formula method for analysing points outside domain boundary element,Comput. Struct. Mech. and Appl.,3, 2 (1986), 9–17. (in Chinese)Google Scholar
  9. [9]
    Xie Xiu-song, Kantorovich-weighted residuals method,Comput. Struct. Mech. and Appl.,2, 1 (1985). 85–88 (in Chinese)Google Scholar
  10. [10]
    Chien, Wei-zang,Variational Method and Finite Element, Science Press (1980). (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1993

Authors and Affiliations

  • Zhou Ding
    • 1
  1. 1.East China Institute of TechnologyNanjing

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