Skip to main content
SpringerLink
Log in

Mindlin plate finite elements by a modified transverse displacement

  • Published:
KSME Journal Aims and scope Submit manuscript

Abstract

The formulation of 4-node plate bending elements to eliminate the shear locking is presented. The kinematic variables in the Mindlin plate are related through the equilibrium equations; and then the transverse displacement, rotations, and shear strain are expressed in terms of the curvature sum. The elements are formulated by using the modified transverse displacement defined as the transverse displacement subtracted by the curvature sum times the ratio of flexural to shear rigidity. It is shown that the elements describe plate behavior quite correctly without any locking and also that they are applicable to the analysis of both thin 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

References

  • Bathe, K.-J.,Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs. N.J.

  • Bathe, K.-J., Brezzi, F. and Cho, S. W., 1989, “The MITC7 and MITC9 Plate Bending Elements,” Comp. Struct., Vol. 32, pp. 797–814.

    Article  MATH  Google Scholar 

  • Dhatt, G. and Touzot, G., 1984,The Finite Element Method Displayed, John Wiley & Sons, New York.

    MATH  Google Scholar 

  • Hinton, E. and Huang, H. C., 1986, “A Family of Quadrilateral Mindlin Plate Elements with Substitute Shear Strain Fields,” Comp. Struct., Vol. 23, pp. 409–431.

    Article  Google Scholar 

  • Kang, L.-C, 1992, “A Fourier Series Method for Polygonal Domains; Large Element Computation for Plates,” Ph.D. Dissertation, Stanford University.

  • Love, A. E. H., 1944,A Treatise on the Mathematical Theory of Elasticity, 4th edn, Dover Publications, Inc., New York.

    MATH  Google Scholar 

  • Mindlin, R. D., 1951, “Influence of Rotary Inertia on Flexural Motions of Isotropic, Elastic Plates,” J. Appl. Mech., Vol. 18, pp. 31–38.

    MATH  Google Scholar 

  • Pawsey, S. F. and Clough, R. W., 1971, “Improved Numerical Integration of Thick Shell Finite Elements,” Int. J. Numer. Methods Eng., Vol. 3, pp. 575–586.

    Article  MATH  Google Scholar 

  • Prathap, G. and Babu, C. R., 1986, “A Field Consistent Three-noded Quadratic Curved Axisymmetric Shell Element,” Int. J. Numer. Methods Eng., Vol. 23, pp. 711–723.

    Article  MATH  MathSciNet  Google Scholar 

  • Pugh, E. D. L., Hinton, E. and Zienkiewicz, O. C., 1978, “A Study of Quadrilateral Plate Bending Elements with Reduced Integration,” Int. J. Numer. Methods Eng., Vol. 12, pp. 1059–1079.

    Article  MATH  Google Scholar 

  • Timoshenko, S. P. and Woinowsky-Krieger, S., 1959,Theory of Plates and Shells, 2nd edn, McGraw-Hill.

  • Zienkiewicz, O. C. and Taylor, R. L., 1991,The Finite Element Method, 4th edn, Vol. 2, McGraw-Hill.

Download references

Author information

Authors and Affiliations

  1. Institute of Advanced Machinery and Design, Seoul National University, Seoul, Korea

    Pal-Gap Lee

  2. Dept. of Mechanical Design and Production Engineering, Seoul National University, Seoul, Korea

    Hyo-Chol Sin

Authors
  1. Pal-Gap Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hyo-Chol Sin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, PG., Sin, HC. Mindlin plate finite elements by a modified transverse displacement. KSME Journal 8, 19–27 (1994). https://doi.org/10.1007/BF02953239

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02953239

Key Words

Search

Navigation