An iterative complementarity approach for elastoplastic analysis involving frictional contact

International Journal of Mechanical Sciences

Volumn 45, Issue 2, 2003, Pages 197-216

  Tin Loi, F ^a   Xia, S H ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Complementarity; Contact; Elastoplastic analysis; Friction; Mathematical programming

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; FRICTION; ITERATIVE METHODS; MATHEMATICAL PROGRAMMING; PLASTICITY; PROBLEM SOLVING;

FRICTIONAL CONTACT;

ELASTOPLASTICITY;

EID: 0037611082     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7403(03)00056-0     Document Type: Article

References (35)

1. Duvaut D., Lions J.L. Inequalities in mechanics and physics. 1976;Springer, Berlin.
2. Kikuchi N., Oden J.T. Contact problems in elasticity: a study of variational inequalities and finite element methods. 1988;SIAM, Philadelphia.
3. Mackerle J. Contact mechanics - finite element and boundary element approaches - a bibliography (1995-1997). Finite Elements in Analysis and Design. 29:1998;275-285.
4. Tin-Loi F., Xia S.H. Nonholonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem. Computer Methods in Applied Mechanics and Engineering. 190:2001;4551-4568.
5. Maier G., Andreuzzi F. Elastic and elasto-plastic analysis of submarine pipelines as unilateral contact problems. Computers and Structures. 8:1978;421-431.
6. Maier G., Andreuzzi F., Giannessi F., Jurina L., Taddei F. Unilateral contact, elastoplasticity and complementarity with reference to offshore pipeline design. Computer Methods in Applied Mechanics and Engineering. 17,18:1979;469-495.
7. Polizzotto C., Zito M. BIEM-based variational principles for elastoplasticity with unilateral contact boundary conditions. Engineering Analysis with Boundary Elements. 21:1998;329-338.
8. Klarbring A. Quadratic programs in frictionless contact problems. International Journal of Engineering Science. 24:1986;1207-1217.
9. Klarbring A. A mathematical programming approach to three-dimensional contact problems with friction. Computer Methods in Applied Mechanics and Engineering. 58:1986;175-200.
10. Björkman G. Complementarity conditions in large and small displacement contact problems. Linköping studies in science and technology. Dissertations, No. 272, Division of Solid Mechanics, Linköping University, 1992.
11. Klarbring A. Mathematical programming in contact problems. Aliabadi M.H., Brebbia C.A. Computational methods in contact mechanics. 1993;233-263 Computational Mechanics Publications, Southampton.
12. Kwak B.M., Lee S.S. A complementarity problem formulation for two-dimensional frictional contact problems. Computers and Structures. 28:1988;469-480.
13. Kwak B.M. Complementarity problem formulation of three-dimensional contact. Journal of Applied Mechanics. 58:1991;134-140.
14. Gakwaya A., Lambert D., Cardou A. A boundary element and mathematical programming approach for frictional contact problems. Computers and Structures. 42:1992;341-553.
15. Kong X.A., Gakwaya A., Cardou A., Cloutier L. A numerical solution of general contact problems by the direct boundary element method and mathematical programming approach. Computers and Structures. 45:1992;95-112.
16. Šimunović S., Saigal S. Frictional contact using quadratic programming. Computational Mechanics. 15:1994;173-187.
17. Dirkse S.P., Ferris M.C. A collection of nonlinear mixed complementarity problems. Optimization Methods and Software. 5:1995;319-345.
18. Cottle R.W., Pang J.S., Stone R.E. The linear complementarity problem. 1992;Academic Press, San Diego.
19. Zhu C. A finite element-mathematical programming method for elastoplastic contact problems with friction. Finite Elements in Analysis and Design. 20:1995;273-282.
20. Zhang H., Zhong W., Gu Y. A combined parametric quadratic programming and iteration method for 3-D elastic-plastic frictional contact problem analysis. Computer Methods in Applied Mechanics and Engineering. 155:1998;307-324.
21. Maier G. A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica. 5:1970;54-66.
22. Corradi L. On compatible finite element models for elastic plastic analysis. Meccanica. 13:1978;133-150.
23. Corradi L. A displacement formulation for the finite element elastic-plastic problem. Meccanica. 18:1983;77-91.
24. Comi C., Maier G., Perego U. Generalized variable finite element modeling and extremum theorems in stepwise holonomic elastoplasticity with internal variables. Computer Methods in Applied Mechanics and Engineering. 96:1992;213-237.
25. Capsoni A., Corradi L. A mixed finite element model for plane strain elastic-plastic analysis. Part I. Formulation and assessment of overall behaviour. Computer Methods in Applied Mechanics and Engineering. 141:1997;67-79.
26. Halphen B., Nguyen Q.S. Sur les matériaux standards généralisés. Journal de Mécanique. 14:1975;39-63.
27. Klarbring A., Pang J.S. The discrete steady sliding problem. Zeitschrift fuer Angewandte Mathematik and Mechanik. 79:1999;75-90.
28. Maier G., Novati G., Cen Z. Symmetric Galerkin boundary element method for quasi-brittle fracture and frictional contact problems. Computational Mechanics. 13:1993;74-89.
29. Tin-Loi F. On the numerical solution of a class of unilateral contact structural optimization problems. Structural Optimization. 17:1999;155-161.
30. Brooke A, Kendrick D, Meeraus A, Raman R. GAMS: a user's guide. Washington DC: Gams Development Corporation, 1998.
31. Dirkse S.P., Ferris M.C. The PATH solver. a non-monotone stabilization scheme for mixed complementarity problems Optimization Methods and Software. 5:1995;123-156.
32. Maier G., Novati G. Extremum theorems for finite-step backward difference analysis of elastic-plastic nonlinearly hardening solids. International Journal of Plasticity. 6:1990;1-10.
33. Feng Z.Q. 2D or 3D frictional contact algorithms and applications in a large deformation context. Communications in Numerical Methods in Engineering. 11:1995;409-416.
34. Martin D., Aliabadi M. A BE hyper-singular formulation for contact problems using non-conforming discretization. Computers and Structures. 69:1998;557-565.
35. Givoli D., Doukhovni I. Finite element-quadratic programming approach for contact problems with geometrical nonlinearity. Computers and Structures. 61:1996;31-41.