×

Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation. (English) Zbl 1092.74051

Summary: Three-dimensional frictional contact is formulated as linear complementarity problem (LCP) by using the parametric variational principle and quadratic programming method. Two aggregate-function-based algorithms, called respectively self-adjusting interior point algorithm and aggregate function smoothing algorithm, are proposed for the solution of LCP derived from the contact problem. A nonlinear finite element code is developed for numerical analysis of 3D multi-body contact problems. Four numerical examples demonstrate the applicability and computational efficiency of the proposed methods.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Christensen, P.W.; Klarbring, A.; Pang, J.S.; Strömberg, N., Formulation and comparison of algorithms for frictional contact problems, Int. J. numer. methods engng., 42, 145-173, (1998) · Zbl 0917.73063
[2] Tin-Loi, F.; Xia, S.H., Nonholomomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem, Comput. methods appl. mech. engng., 190, 4551-4568, (2001) · Zbl 1059.74063
[3] Mijar, A.R.; Arora, J.S., Review of formulations for elastostatic frictional contact problems, Struct. multiddisc. optim., 20, 167-189, (2000)
[4] Wriggers, P., Computational contact mechanics, (2002), John Wiley New York
[5] Zhong, W.X.; Sun, S.M., A finite element method for elasto-plastic structure and contact problem by parametric quadratic programming, Int. J. numer. meths. engng., 26, 2723-2738, (1988) · Zbl 0673.73056
[6] Zhong, W.X.; Zhang, H.W.; Wu, C.W., Parametric variational principle and its applications in engineering, (1997), Science Press Beijing
[7] Klarbring, A., A mathematical programming approach to three-dimensional contact problems with friction, Comput. methods appl. mech. engng., 58, 175-200, (1986) · Zbl 0595.73125
[8] Klarbring, A.; Björkman, G., A mathematical programming approach to contact problems with friction and varying contact surface, Comput. struct., 30, 1185-1198, (1988) · Zbl 0677.73078
[9] Kwak, B.M., Complementarity problem formulation of three-dimensional frictional contact, ASME J. appl. mech., 58, 134-140, (1991) · Zbl 0756.73086
[10] Park, J.K.; Kwak, B.M., Three-dimensional frictional contact analysis using the homotopy method, ASME J. appl. mech., 61, 703-709, (1994) · Zbl 0825.73651
[11] Ferris, M.C.; Pang, J.S., Engineering and economic applications of complementarity problems, SIAM rev., 37, 669-713, (1997) · Zbl 0891.90158
[12] Leung, A.Y.T.; Chen, G.Q.; Chen, W.J., Smoothing Newton method for solving two- and three-dimensional frictional contact problems, Int. J. numer. methods engng., 41, 1001-1027, (1998) · Zbl 0905.73079
[13] Zhang, H.W.; He, S.Y.; Li, X.S., Non-interior smoothing algorithm for frictional contact problems, Appl. math. mecha., 25, 47-58, (2004) · Zbl 1145.74424
[14] Zhang, H.W.; He, S.Y.; Li, X.S.; Wriggers, P., A new algorithm for numerical solution of 3D elastoplastic contact problems with orthotropic friction law, Comp. mech., 34, 1, 1-14, (2004) · Zbl 1072.74061
[15] Zhang, H.W.; Zhong, W.X.; Gu, Y.X., A combined parametric quadratic programming and iteration method for 3D elastic-plastic frictional contact problem analysis, Comput. methods appl. mech. engng., 155, 307-324, (1998) · Zbl 0964.74072
[16] S.Y. He, Studies on algorithms of complementarity problems and their applications in mechanics, Ph.D. dissertation, Dalian University of Technology, December, 2003.
[17] Pan, S.H.; Li, X.S., A self-adjusting primal dual interior point method for linear programs, Optim. methods soft., 19, 389-397, (2004) · Zbl 1140.90510
[18] Wright, S.J., Primal-dual interior-point methods, (1997), SIAM Publications Philadelphia · Zbl 0863.65031
[19] Peng, J.M.; Roos, C.; Terlaky, T., New and efficient large-update interior-point method for linear optimization, J. comput. technol., 4, 61-80, (2001) · Zbl 0987.90089
[20] Li, X.S., An entropy-based aggregate method for MIN-MAX optimization, Engng. optim., 18, 277-285, (1992)
[21] Burke, J.V.; Xu, S., The global linear convergence of a non-interior path following algorithm for linear complementarity problems, Math. operat. res., 23, 719-734, (1998) · Zbl 0977.90056
[22] Buczkowski, R.; Kleiber, M., Elasto-plastic interface model for 3D-frictional orthotropic contact problems, Int. J. numer. methods engng., 40, 599-619, (1997) · Zbl 0888.73055
[23] Billups, S.C.; Murty, K.G., Complementarity problems, J. comput. appl. math., 124, 303-318, (2000) · Zbl 0982.90058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.