A new computational approach to contact mechanics using variable-node finite elements

International Journal for Numerical Methods in Engineering

Volumn 73, Issue 13, 2008, Pages 1966-1988

  Kim, Jong Hoon ^a   Lim, Jae Hyuk ^a   Lee, Jun Ho ^a   Im, Seyoung ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Contact; Finite element; MLS based finite elements

Indexed keywords

COMPUTER SIMULATION; CONTACTS (FLUID MECHANICS); LEAST SQUARES APPROXIMATIONS;

CONTACT PATCH TEST; VARIABLE-NODE ELEMENTS;

FINITE ELEMENT METHOD;

COMPUTER SIMULATION; CONTACTS (FLUID MECHANICS); FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS;

EID: 41449115312     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2162     Document Type: Article

References (30)

1. Zhong Z-H. Finite Element Procedures for Contact Impact Problems. Oxford University Press: New York, 1993.
2. Laursen TA. Computational Contact and Impact Mechanics. Springer: Berlin, 2002.
3. Wriggers P. Computational Contact Mechanics. Wiley: New York, 2002.
4. Simo JC, Laursen TA. An augmented Lagrangian treatment of contact problems involving friction. Computers and Structures 1992; 42:97-116.
5. Laursen TA, Simo JC. Algorithmic symmetrization of Coulomb frictional problems using augmented Lagrangians. International Journal for Numerical Methods in Engineering 1993; 108:133-146.
6. Laursen TA, Oancea VG. Automation and assessment of augmented Lagrangian algorithms for frictional contact problems. Journal of Applied Mechanics 1994; 61:956-963.
7. Zavarise G, Wriggers P, Schrefler BA. On augmented Lagrangian algorithms for thermomechanical contact problems with friction. International Journal for Numerical Methods in Engineering 1995; 38:2929-2949.
8. Papadopoulos P, Taylor RL. A mixed formulation for the finite element solution of contact problems. Computer Methods in Applied Mechanics and Engineering 1992; 94:373-389.
9. Rebel G, Park KC, Felippa CA. A contact formulation based on localized Lagrange multipliers: formulation and application to two-dimensional problems. International Journal for Numerical Methods in Engineering 2002; 54:263-297.
10. McDevitt TW, Laursen TA. A mortar-finite element formulation for frictional contact problems. International Journal for Numerical Methods in Engineering 2000; 48:1525-1547.
11. Lim JH, Im S. A (4 + n)-noded MLS (moving least square)-based finite elements for mesh gradation. Structural Engineering and Mechanics 2007; 25:91-106.
12. Lim JH, Im S, Cho Y-S. Variable-node elements for non-matching meshes by means of MLS (moving least-square) scheme. International Journal for Numerical Methods in Engineering 2007; DOI: 10.1002/nme.1988.
13. Lim JH, Im S, Cho Y-S. MLS-based finite elements for three dimensional non-matching meshes and adaptive mesh refinement. Computer Methods in Applied Mechanics and Engineering 2007; 196:2216-2228.
14. Cho Y-S, Jun S, Im S, Kim H-G. An improved interface element with variable nodes for non-matching finite element meshes. Computer Methods in Applied Mechanics and Engineering 2005; 194:3022-3046.
15. Cho Y-S, Im S. MLS-based variable-node elements compatible with quadratic interpolation. Part I: formulation and application for non-matching meshes. International Journal for Numerical Methods in Engineering 2006; 65:494-516.
16. Cho Y-S, Im S. MLS-based variable-node elements compatible with quadratic interpolation. Part II: application for finite crack element. International Journal for Numerical Methods in Engineering 2006; 65:517-547.
17. Malsch EA, Dasgupta G. Shape functions for polygonal domains with interior nodes. International Journal for Numerical Methods in Engineering 2004; 61:1153-1172.
18. Sukumar N, Tabarraei A. Conforming polygonal finite elements. International Journal for Numerical Methods in Engineering 2004; 61:2045-2066.
19. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
20. Chen JS, Yoon S, Wu CT. Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2002; 53:2587-2615.
21. Yoo JW, Moran B, Chen JS. Stabilized conforming nodal integration in the natural-element method. International Journal for Numerical Methods in Engineering 2004; 60:861-890.
22. Lee JH. MLS (moving least square)-based finite elements using a stabilized conforming nodal integration. KAIST Master Thesis, 2007.
23. Yang B, Laursen TA, Meng X. Two-dimensional mortar contact methods for large deformation frictional sliding. International Journal for Numerical Methods in Engineering 2005; 62:1183-1225.
24. Wohlmuth B. A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM Journal on Numerical Analysis 2000; 38:989-1012.
25. Brunssen S, Schmid F, Schäfer M, Wohlmuth B. A fast and robust iterative solver for nonlinear contact problems using a primal-dual active set strategy and algebraic multigrid. International Journal for Numerical Methods in Engineering 2007; 69:524-543.
26. ABAQUS Inc. ABAQUS 6.5 User's Manual, 2004.
27. Mindlin RD. Compliance of elastic bodies in contact. Journal of Applied Mechanics, Series E - Transactions of the ASME 1949; 16:259-268.
28. Lancaster P, Salkauskas K. Surface generated by moving least squares method. Mathematics of Computation 1981; 37:141-158.
29. Liu WK, Li S, Belytschko T. Moving least square reproducing kernel method. Part I: method and convergence. Computer Methods in Applied Mechanics and Engineering 1997; 43:113-154.
30. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106.