Advertisement

Applied Mathematics and Mechanics

, Volume 23, Issue 8, pp 913–921 | Cite as

Unilateral contact problems using quasi-active set strategy

  • Xuan Zhao-cheng
  • Li Xing-si
Article
  • 21 Downloads

Abstract

The unilateral contact problem can be formulated as a mathematical programming with inequality constraints. To resolve the difficulty in dealing with inequality constraints, a quasi-active set strategy algorithm was presented. At each iteration, it transforms the problem into one without contact in terms of the solution obtained in last iteration and initiates the current iteration using the solution of the transformed problem, and updates a group of contact pairs compared with Lemke algorithm that uqdates only one pair of contact points. The present algorithm greatly enhances the efficiency and numerical examples demonstrate the effectiveness and robustness of the proposed algorithm.

Key words

unilateral contact mathematical programming quasi-active set 

CLC number

O175.2 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bisbos C D. A Cholesky condensation method for unilateral contact problems[J].Solid Mechanics Archives, 1985,11(1):1–23.Google Scholar
  2. [2]
    Panagiotopoulos P D. A nonlinear programming approach to the unilateral contact and friction boundary value problem in the theory of elasticity[J].Ingenieur Archiv, 1974,44(3):421–432.MathSciNetGoogle Scholar
  3. [3]
    Kikuchi N, Oden J T.Contact Problems in Elasticity: A Study of Variational Inequalities and FEM[M]. Philadelphia: SIAM, 1988.Google Scholar
  4. [4]
    Zhong W X, Sun S M. A parametric quadratic programming approach to elastic contact problems with friction[J].Comput & Structures, 1989,32(1):37–43.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Xuan Z C, Li X S, Sui Y K. Surrogate dual problem of quadratic programming and the algorithm [J].Chinese J Numer Math Appl, 1999,21(1):45–53.MathSciNetGoogle Scholar
  6. [6]
    Rosen J B, Suzuki S. Construction of nonlinear programming test problems[J].Comm of the ACM, 1965,8(2):113.CrossRefGoogle Scholar
  7. [7]
    Šimunovic S, Saigal S. A linear programming formulation for incremental contact analysis[J].Internat J Numer Methods Engrg, 1995,38(16):2703–2725.CrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Xuan Zhao-cheng
    • 1
  • Li Xing-si
    • 2
  1. 1.School of Mechanical EngineeringDalian University of TechnologyDalianP R China
  2. 2.Research Institute of Engineering MechanicsDalian University of TechnologyDalianP R China

Personalised recommendations