Skip to main content
SpringerLink
Log in

Bending theories for beams and plates with single generalized displacement

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

Abstract

Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can not be used for long, slender beams and thin plates since the innate relation between rotation angle and deflection is ignored. These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle. Based on several basic assumptions, a new type of theories which not only include the transverse shearing effect is presented, but also the relation between rotation angle and deflection is obtained. Analytical solutions of several simple beams are given. It has been testified by numerical examples that the new theories can be used for either long, slender beams and thin plates or short, stubby beams and thick plates.

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

Refereces

  1. Timoshenko S P. On the correction for shear of the differential equation for transverse vibration of prismatic bars[J].Philosophical Magazine, 1921,41: 744.

    Google Scholar 

  2. Reissner E. On the theory of bending of elastic plates[J].Journal of Mathematics and Physics, 1944,23: 184.

    MATH  MathSciNet  Google Scholar 

  3. Gong Ke. Numerical analysis of the nonlinear effect of curvature and the universal finite element [D]. Master thesis. Changsha: National Defence of Science and Technology, 1986, 36–43. (in Chinese)

    Google Scholar 

  4. GONG Ke. A rectangular finite element with 12-DOF in common use for thin and thick plates[A]. In: Wuxi Association for Mechanics Eds.Scientific Conference of Wuxi Association for Mechanics [C]. Wuxi, 1987 (in Chinese)

  5. Cao Zhi-yuan, Yang Sheng-tian.Dynamic Theory for Thick Plates and Applications [M]. Beijing: Science Press, 1983, 297–383. (in Chinese)

    Google Scholar 

  6. Zhou Ke-jian, Gong Ke. A triangular finite element with 9-DOF in common use for thin and thick plate vibration problems[A]. In:Proceedings of the ICVPE-Xi' an[C]. Xi'an Jiaotong University Press, 1986, 214–219.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wuxi Institute of Engineering Equipment, 214035, Wuxi, P R China

    Gong Ke (Lecturer, Master)

Authors
  1. Gong Ke
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by WU Pei-de

Biography: GONG Ke (1962≈)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ke, G. Bending theories for beams and plates with single generalized displacement. Appl Math Mech 21, 1091–1098 (2000). https://doi.org/10.1007/BF02459320

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02459320

Key words

CLC numbers

Search

Navigation