Formulation of Reissner-Mindlin Moderately-Thick/Thin Plate Bending Elements

  • D. P. Chen
  • Y. S. Pan
Conference paper


Nine-node quadrilateral element (HP-9) and twelve-node quadrilateral element (HP-12) are formulated on the basis of Reissner-Mindlin plate bending theory by the assumed-stress type hybrid method. Both are free from spurious kinematic mode and not leading to “locking” phenomenon in thin plate limit. Numerical examples demonstrate improvement in stress and displacement performances when comparing with existing counterparts.


Nodal Pattern Shell Finite Element Direction Cosine Matrix Hybrid Stress Element Assumed Stress Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pian, T.H.H.: Derivation of element stiffness matrices by assumed stress distributions. AIAA J. 2 (1964) 1333–1336.CrossRefGoogle Scholar
  2. 2.
    Pian, T.H.H.: Constraints for stresses in hybrid plate and shell elements. Finite element methods for nonlinear problems. Europe--US Symposium, Trondheim, Norway, Aug. 12–16, 1985.Google Scholar
  3. 3.
    Lee, S.W. and Pian, T.H.H.: Improvement of plate and shell finite element by mixed formulations. AIAA J. 16 (1978) 29–34.ADSMATHCrossRefGoogle Scholar
  4. 4.
    Spilker, R.L. et al: The hybrid-stress model for thin plates. IJNME, 15 (1980) 1239–1260.MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Pan, Y.S.: Master thesis, Southwestern Jiaotong University, Emei, China, (1984–1985).Google Scholar
  6. 6.
    Zhao, Z.: Master thesis, SWJTU, Emei, China, (1984–1985).Google Scholar
  7. 7.
    Pian, T.H.H. and Chen, D.P.: On the suppression of zero energy deformation modes. IJNME, 19 (1983) 1741–1752.ADSMATHCrossRefGoogle Scholar
  8. 8.
    Pugh, E.D. et al: A study of quadrilateral plate bending elements with “reduced integration”. IJNME, 12, No.7, (1978).CrossRefGoogle Scholar
  9. 9.
    Washizu, K.: Variational method in elastisity and plasticity. Pergamon Press, 3rd Edition, 1982.Google Scholar
  10. 10.
    Reissner, E.: The effect of transverse-shear deformation on bending of elastic plates. JAM, 12, No.2, June 1945, 69–77.MathSciNetGoogle Scholar
  11. 11.
    Cook, R.D.: Concepts and applications of finite element analysis. 2nd Edition, John Wiley & Sons, New York, 1981.MATHGoogle Scholar
  12. 12.
    Spilker, R.L. et al: A serendipity cubic-displacement hybrid stress element for thin and moderately thick plates. IJNME, 15 (1980) 1261–1278.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • D. P. Chen
    • 1
  • Y. S. Pan
    • 1
  1. 1.Southwestern Jiaotong UniversityEmei, SichuanChina

Personalised recommendations