Non-interior smoothing algorithm for frictional contact problems

Applied Mathematics and Mechanics (English Edition)

Volumn 25, Issue 1, 2004, Pages 47-58

  Zhang, Hong Wu ^a   He, Su Yan ^a   Li, Xing Si ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Aggregate function; Linear complementarity problem; NCP function; Non interior smoothing algorithm; Parametric quadratic programming method; Three dimensional frictional contact problem

Indexed keywords

ALGORITHMS; FRICTION; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; THREE DIMENSIONAL;

AGGREGATE FUNCTION; LINEAR COMPLEMENTARITY PROBLEM; NONINTERIOR SMOOTHING ALGORITHM; NONLINEAR COMPLEMENTARITY PROBLEM FUNCTION; PARAMETRIC QUADRATIC PROGRAMMING METHOD; THREE DIMENSIONAL FRICTIONAL CONTACT PROBLEM;

ELASTICITY;

EID: 2442639178     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02437293     Document Type: Article

References (21)

1. Demyanov V F, Stavroulakis G E, Polyakova L N. Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics[M]. Dordrecht: Kluwer Academic Publishers, 1996.
2. Kikuchi N, Oden J T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods[M]. Philadelphia: SIAM, 1988.
3. ZHONG Wan-xie, ZHANG Hong-wu, WU Cheng-wei. Parametric Variational Principles and Applications in Engineering[M]. Beijing: Science Press, 1997. (in Chinese)
4. CHEN Guo-qing, CHEN Wan-ji, FENG En-min. Nonlinear complementarity principle for three-dimensional contact problem and solution method[J]. Science in China, Ser A, 1995, 25(11): 1181-1190. (in Chinese)
5. LI Xue-wen, CHEN Wan-ji. Nonsmooth method for solving three-dimensional frictional contact problems[J]. Chinese Journal of Computational Mechanics, 2000, 17(1): 43-49. (in Chinese)
6. Christensen P W, Klarbring A, Pang J S, et al. Formulation and comparison of algorithms for frictional contact problems[J]. International Journal for Numerical Methods in Engineering, 1998, 42: 145-173.
7. ZHANG Hong-wu, ZHANG Wan-xie, GU Yuan-xian. A combined parametric quadratic programming and iteration method for 3D elastic-plastic frictional contact problem analysis[J]. Comput. Meths. Appl. Mech. 1998, 155: 307-324.
8. ZHANG Hong-wu. Parametric variational principle for elastic-plastic consolidation analysis of saturated porous media[J]. Int. J. Numer. Anal. Meths. Geomechanics, 1995, 19: 851-867.
9. ZHANG Hong-wu, Schrefler B A. Gradient-dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: one dimensional model[J]. European Journal of Solid Mechanics, A/Solids, 2000, 19(3): 503-524.
10. ZHANG Hong-wu. Galvanetto U, Schrefler B A. Local analysis and global nonlinear behaviour of periodic assemblies of bodies in elastic contact[J]. Computational Mechanics, 1999, 24(4): 217-229.
11. ZHANG Hong-wu, GU Yuan-xian, ZHONG Wan-xie. The finite element analysis for coupled problems between heat transfer and contact processes[J]. Acta Solida Mechanica, 2000, 21(3): 217-224. (in Chinese)
12. Billups S C, Murty K G. Complementarity problems[J]. Journal of Computational and Applied Mathematics, 2000, 124: 303-318.
13. Wright S J. Primal-Dual Interior-Point Methods[M]. Philadelphia: SIAM Publications, 1997.
14. XIU Nai-hua, Gao Zi-you. The new advances in methods for complementarity problems[J]. Advances in Mathematics, 1999, 28(3): 193-210. (in Chinese)
15. Ferris M C, Kanzow C. Complementarity and related problems: A survey[A]. In: Pardalos P M, Resende M G C Eds: Handbook on Applied Optimization[C]. New York: Oxford University Press, 2002, 514-530.
16. CHEN Chun-hui, Mangasarian O L. Smoothing methods for convex inequalities and linear complementarity problems[J]. Mathematical Programming, 1995, 71: 51-69.
17. CHEN Bing-tong, XIU Nai-hua. A Global linear and local quadratic non-interior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions[J]. SIAM Journal on Optimization, 1999, 9: 605-623.
18. Burke J V, XU Song. The global linear convergence of a non-interior path following algorithm for linear complementarity problems[J]. Mathematics of Operations Research, 1998, 23: 719-734.
19. LI Xing-si. An efficient method for non-differentiate optimization problem[J]. Science in China, Ser A, 1994, 24(4): 371-377. (in Chinese)
20. Kanzow C. Some noninterior continuation methods for linear complementarity problems[J]. SIAM J Matrix Anal Appl, 1996, 17(4): 851-868.
21. Buczkowski R, Kleiber M. Elasto-plastic interface model for 3D-frictional orthotropic contact problems[J]. International Journal for Numerical Methods in Engineering, 1997, 40: 599-619.