Skip to main content
SpringerLink
Log in

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

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chang Fo-van,Elastic Thin Plates, Science Press, Beijing, (1963). (in Chinese)

    Google Scholar 

  2. Timoshenko, S., et al., Theory of Plates and Shells, McGraw-Hill (1959).

  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. Chang Fo-van, Bending of uniformly loaded cantilever rectangular plates,Appl. Math. and Mech.,1, 3 (1980), 371–383.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  7. Wang Lei, Solution of spline function of elastic plates,Appl. Math. and Mech.,6, 8 (1985), 777–787.

    MathSciNet  Google Scholar 

  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. Xie Xiu-song, Kantorovich-weighted residuals method,Comput. Struct. Mech. and Appl.,2, 1 (1985). 85–88 (in Chinese)

    Google Scholar 

  10. Chien, Wei-zang,Variational Method and Finite Element, Science Press (1980). (in Chinese)

Download references

Author information

Authors and Affiliations

  1. East China Institute of Technology, Nanjing

    Zhou Ding

Authors
  1. Zhou Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Hsueh Dah-wei

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, Z. An approximate solution with high accuracy of transverse bending of thin rectangular plates under arbitrarily distributed loads. Appl Math Mech 14, 241–246 (1993). https://doi.org/10.1007/BF02451408

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02451408

Key words

Search

Navigation