A special focus on 2D formulations for contact problems using a covariant description

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 9, 2006, Pages 1432-1465

  Konyukhov, Alexander ^a   Schweizerhof, Karl ^a  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

Author keywords

Contact problem; Covariant description; Friction

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTATIONAL GEOMETRY; FINITE ELEMENT METHOD; FRICTION;

CONTACT PROBLEM; COVARIANT DESCRIPTION; LINEAR CONTACT ELEMENT;

KINEMATICS;

BOUNDARY ELEMENT METHOD; COMPUTATIONAL GEOMETRY; FINITE ELEMENT METHOD; FRICTION; KINEMATICS;

EID: 33744546126     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1604     Document Type: Article

References (27)

1. Wriggers P, Vu Van, Stein E. Finite element formulation of large deformation impact-contact problems with friction. Computers and Structures 1990; 37:319-331.
2. Parisch H. A consistent tangent stiffness matrix for three-dimensional nonlinear contact analysis. International Journal for Numerical Methods in Engineering 1989; 28:1803-1812.
3. Parisch H, Lübbing Ch. A formulation of arbitrarily shaped surface elements for three-dimensional large deformation contact with friction. International Journal for Numerical Methods in Engineering 1997; 40: 3359-3383.
4. Peric D, Owen DRJ. Computational model for 3-D contact problems with friction based on the penalty method. International Journal for Numerical Methods in Engineering 1992; 35:1289-1309.
5. Laursen TA, Simo JC. A continuum-based finite element formulation for the implicit solution of multibody large deformation frictional contact problems. International Journal for Numerical Methods in Engineering 1993; 35:3451-3485.
6. Wriggers P. Computational Contact Mechanics. Wiley: Chichester, 2002.
7. Laursen TA. Computational Contact and impact Mechanics. Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Springer: Berlin, Heidelberg, New York, 2002.
8. Kikuchi N, Oden JT. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM: Philadelphia, PA, 1988.
9. Konyukhov A, Schweizerhof K. Contact formulation via a velocity description allowing efficiency improvements in frictionless contact analysis. Computational Mechanics 2004; 33:165-173.
10. Konyukhov A, Schweizerhof K. Covariant description for frictional contact problems. Computational Mechanics 2005; 35:190-213.
11. Gray A. Modern Differential Geometry of Curves and Suraces. CRC Press: Boca Raton, FL, 1993.
12. Marsden JE, Hughes TJR. Mathematical Foundations of Elasticity. Dover: New York, 1994.
13. Wriggers P. Finite element algorithms for contact problems. Archives of Computational Methods in Engineering 1995; 2(4):1-49.
14. Zavarise G, Wriggers P. A segment-to-segment contact strategy. Mathematical and Computer Modelling 1998; 28:497-515.
15. Harnau M, Konyukhov A, Schweizerhof K. Algorithmic aspects in large deformation contact analysis using 'solid-shell' elements. Computers and Structures, available online 21 April 2005.
16. McDevitt TW, Laursen TA. A mortar-finite element formulation for frictional contact problems. International Journal for Numerical Methods in Engineering 2000; 48:1525-1547.
17. Puso MA, Laursen TA. A mortar segment-to-segment contact method for large deformation solid mechanics. Computer Methods in Applied Mechanics and Engineering 2004; 193:601-629.
18. Wriggers P, Scherf O. Different a posteriori error estimators and indicators for contact problems. Mathematical and Computer Modelling 1998; 28:437-447.
19. 1 -interpolations for two-dimensional frictional contact problems. International Journal for Numerical Methods in Engineering 2001; 51:1469-1495.
20. Padmanabhan V, Laursen TA. A framework for development of surface smoothing procedures in large deformation frictional contact analysis. Finite Elements in Analysis and Design 2001; 37:173-198.
21. n continuous modeling of smooth contact surfaces using NURBS and application to 2D problems. International Journal for Numerical Methods in Engineering 2003; 57:2177-2203.
22. Puso MA, Laursen TA. A 3D contact smoothing method using Gregory patches. International Journal for Numerical Methods in Engineering 2002; 54:1161-1194.
23. 1 -continuous formulation for 3D finite deformation frictional contact. Computational Mechanics 2002; 29:27-42.
24. Stadler M, Holzapfel GA. Subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3D. International Journal for Numerical Methods in Engineering 2004; 60:1161-1195.
25. Taylor RL. FEAP - A Finite Element Analysis Program. University of California at Berkeley, Berkeley. Schweizerhof K and Coworkers, FEAP - Mechanik - Karlsruhe. Institut für Mechanik, Universität Karlsruhe, 1987.
26. Hauptmann R, Schweizerhof K. A systematic development of 'Solid-shell' element formulations for linear and non-linear analysis employing only displacement degrees of freedom. International Journal for Numerical Methods in Engineering 1998; 42:49-69.
27. Hauptmann R, Dofl S, Haman M, Schweizerhof K. 'Solid-shell' elements with linear and quadratic shape functions at large deformations with nearly incompressible materials. Computers and Structures 2001; 79: 1671-1685.