Skip to main content
Log in

Geometrically nonlinear analysis of mindlin plate using the incompatible bending elements with internal shear strain

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

Abstract

An approach of the incompatible elements with additional internal shear strain is, in the present paper, suggested and applied to geometrically nonlinear analysis of Mindlin plate bending problem. It provides a quite covenient way to avoid the shear locking troubles. An energy consistency condition for this kind of C° elements is offered. The nonlinear element formulations and some numerical results are presented.

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

Access this article

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. Hughes, T. J. R., R. L. Taylor and S. Kanonukulchai, A simple and efficient finite element for bending,nnt. J. Num. Meth. Eng.,11 (1977), 1529–1543.

    Article  MATH  Google Scholar 

  2. Lee, S. W. and T. H. H. Pian, Improvement of plate and shell finite element by mixed formulations,AIAA J.,16 (1978), 29–34.

    Article  MATH  Google Scholar 

  3. Hinton, E. and H. C. Huang, A family of quadrilateral Mindlin plate elements with substitute shear strain fields,Computers & Structures,23 (1986), 409–431.

    Article  Google Scholar 

  4. Papadopoulo, P. and R. L. Taylor, A triangular element based on Reissner-Mindlin plate theory,Int. J. Num. Meth. Eng.,30 (1990), 1029–1049.

    Article  Google Scholar 

  5. Chien Wei-zang,Variational Methods and Finite Elements, Science Press, Beijing (1980). (in Chinese)

    Google Scholar 

  6. Wu Chang-chun, Huang Mao-guang and T. H. H. Pian, Consistency condition and convergence cirteria of incompatible elements: general formulation of incompatible functions and its application.Computers & Structures,27 (1987), 639–644.

    Article  Google Scholar 

  7. Wu Chang-chun and H. Bufler, Multivariable finite elements: consistency and optimization.Science in China, Series A,34 (1991), 284–299.

    Google Scholar 

  8. Pica, A., R. D. Wood and E. Hinton, Finite element analysis of geometrically nonlinear plate behavior using a Mindlin formulation,Computers & Structures,11 (1980), 203–215.

    Article  MATH  MathSciNet  Google Scholar 

  9. Azizan, E. G. and D. J. Dawe, Geometrically nonlinear analysis of rectangular Mindlin plates using the finite strip method.Computers & Structures,21 (1985), 423–436.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project supported by the National Education Committee. Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao-ping, J., Chang-chun, W. & Pian, T.H.H. Geometrically nonlinear analysis of mindlin plate using the incompatible bending elements with internal shear strain. Appl Math Mech 15, 507–516 (1994). https://doi.org/10.1007/BF02450763

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02450763

Key words

Navigation