Reasonable Selection of the Stress Modes in a Hybrid Stress Element

  • Zhao Jingwen
Conference paper


A reasonable condition is suggested to match the displacements and stresses in a hybrid stress element. Based on Hellinger-Reissner principle the displacement and stress modes are assumed to include the complete polynomials in the natural coordinates of an element. The work done by the assumed stresses on the nonconforming strains in an element should vanish. Taking this as a matching condition the dependent stress parameters can be eliminated and a rank sufficient hybrid stress element can be formulated. it contains the minimum number of stress parameters and is invariant for coordinates. Without perturbation a new 4-node (5 stress parameters) plane hybrid stress element has been developed. It can be arranged to satisfy the patch test. To demonstrate the properties of the element the solutions to some example problems are included


Patch Test Stress Parameter ACTA MECHANICA SINICA Stress Mode Element Stiffness Matrix 
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.
    T.H.H.Pian, ‘Derivation of element stiffness matrix by assumed stress distribution’, AIAA, J. 2, 1333–1336 (1964)CrossRefGoogle Scholar
  2. 2.
    T.H.H Pian and Chen Dapeng, ‘Alternative ways for formulation of hybrid stress elements’, Int.J. Mum. Meth. Eng. 18, 1679–1684 (1982)MATHCrossRefGoogle Scholar
  3. 3.
    T.H.H.Pian and K.Sumihara, ‘Rational approach for assumed stress finite elements’, Int. J. Num.Meth. Eng. 20, 1685–1695 (1984)MATHCrossRefGoogle Scholar
  4. 4.
    Wu Changchun and Di Shenglin, ‘The optimum design of a hybrid element’ (in Chinese), KEXUE TONGBAO, (to be published)Google Scholar
  5. 5.
    T.H.H. Pian and P.Tong, ‘Relations between incompatible displacement model and hybrid stress model’, Int. J. Num. Meth. Eng, (to be published)Google Scholar
  6. 6.
    Hu Haichang, ‘On the rational utilization of generalized variational principles for approximate solution’ (in Chinese), ACTA MECHANICA SINICA, 1 (1982)Google Scholar
  7. 7.
    E. L. Wilson, R.L.Taylor, W. P. Doherty and J. Ghaboussi, ‘Incompatible displacement models, in Numerical and Computer Methods in Structural Mechanics (Ed. S.J.Fenves et al), Academic Press, New York, 1973Google Scholar
  8. 8.
    M.Froier, L.Nilsson and A.Samuelsson, ‘The rectangular plane stress element by Turner, Pian and Wilson’, Int.J.Num.Meth. Eng. 8, 433–437 (1974)CrossRefGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • Zhao Jingwen
    • 1
  1. 1.Department of Applied Mathematics and MechanicsHarbin Institute of TechnologyHarbinChina

Personalised recommendations