Acta Mechanica Sinica

, Volume 6, Issue 4, pp 349–356 | Cite as

Effective numerical methods for elasto-plastic contact problems with friction

  • Wang Xucheng
  • Chang Liangming
  • Cen Zhangzhi


Several effective numerical methods for solving the elasto-plastic contact problems with friction are presented. First, a direct substitution method is employed to impose the contact constraint conditions on condensed finite element equations, thus resulting in a reduction by half in the dimension of final governing equations. Second, an algorithm composed of contact condition probes and elasto-plastic iterations is utilized to solve the governing equation, which distinguishes two kinds of nonlinearities, and makes the solution unique. In addition, Positive-Negative Sequence Modification Method is used to condense the finite element equations of each substructure and an analytical integration is introduced to determine the elasto-plastic status after each time step or each iteration, hence the computational efficiency is enhanced to a great extent. Finally, several test and practical examples are presented showing the validity and versatility of these methods and algorithms.

Key Words

elasto-plasticity contact problem finite element method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Hughes, T.R.J., Taylor, R.L., Sackman, J.L., Curnier, A. and Kanoknukulchai, W. —A finite element method for a class of contact-impact problems.Comput. Meths. Appl. Mech. Engrg.,8(1976), 249zbMATHCrossRefGoogle Scholar
  2. [2]
    Bathe, K.J. and Chaudhary, A., A solution method for planar and axisymmetric contact problems.Int. J. Numer. Methods Eng.,21(1985), 65.zbMATHCrossRefGoogle Scholar
  3. [3]
    Kikuchi, N. and Oden, J.T., Contact problems in elastostatics,Finite Elements: Special Problems in Solid Mechanics, Eds. Oden, J. t. and Carey, G.F., Prentice-Hall, Englewood cliffs, NJ, vol. IV (1984).Google Scholar
  4. [4]
    Wang X. C. and Chang L.M., Adaptive solution of structural system with local nonlinearity,Transactions of 9th SMiRT, B3/4, Lausanne (August, 1987).Google Scholar
  5. [5]
    Wang, X.C. and Chang, L. M., Integration of constitutive equations of hardening material.Res Mechanics,26 (1987) 113.Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1990

Authors and Affiliations

  • Wang Xucheng
    • 1
  • Chang Liangming
    • 1
  • Cen Zhangzhi
    • 1
  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

Personalised recommendations