×

A novel finite element formulation for frictionless contact problems. (English) Zbl 0834.73067

Summary: This article advocates a new methodology for the finite element solution of contact problems involving bodies that may undergo finite motions and deformations. The analysis is based on a decomposition of the two-body contact problem into two simultaneous sub-problems, and results naturally in geometrically unbiased discretization of the contacting surfaces. A proposed two-dimensional contact element is specifically designed to unconditionally allow for exact transmission of constant normal traction through interacting surfaces.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
Full Text: DOI

References:

[1] Conry, J. Appl. Mech. 38 pp 387– (1971) · doi:10.1115/1.3408787
[2] Chan, Int. J. Mech. Sci. 13 pp 615– (1971)
[3] Zhong, Eng. Comp. 9 pp 3– (1992)
[4] Hughes, Comput. Methods Appl. Mech. Eng. 8 pp 249– (1976)
[5] NIKE2D: A Vectorized, Implicit Finite Deformation, Finite Element Code for Analyzing Static and Dynamic Response of 2-D Solids, Lawrence Livermore National Laboratories, University of California, UCID-19677 (rev. 1) edn, 1986.
[6] and , ’An augmented Lagrangian formulation for the finite element solution of contact problems’, SESM Rep. 85/09, University of California at Berkeley, 1985.
[7] Hallquist, Comput. Methods Appl. Mech. Eng. 51 pp 107– (1985)
[8] Simo, Comput. Methods Appl. Mech. Eng. 50 pp 163– (1985)
[9] Papadopoulos, Comput. Methods Appl. Mech. Eng. 94 pp 373– (1992)
[10] ’Numerical integration applied to finite element methods’, in Proc. Conf. on Use of Digital Computers in Structural Engineering, University of Newcastle, 1966.
[11] and , ’The classical field theories’, in (ed.), Handbuch der Physik 111/1, Springer, Berlin, 1960, pp. 226-793.
[12] Introduction to Numerical Linear Algebra and Optimization, Cambridge University Press, Cambridge, 1989.
[13] and , ’An interface interpolation scheme for quadratic convergence in the finite element analysis of contact problems’, in and , (eds.), Nonlinear Computational Mechanics, Springer, Berlin, 1991, pp. 703-715.
[14] and , ’Discrete LBB-conditions for RIP-finite element methods’, TICOM Rep. 80-7, The University of Texas at Austin, 1980.
[15] ’Exterior penalty methods for contact problems in elasticity’, in and (eds.), Europe-US Workshop: Nonlinear Finite Element Analysis in Structural Mechanics, Springer, Berlin, 1980.
[16] and , ’A patch test for contact problems in two dimensions’, in and , (eds.), Nonlinear Computational Mechanics, Springer, Berlin, 1991, pp. 690-702.
[17] and , The Finite Element Method: Basic Formulation and Linear Problems, Vol. 1, 4th edn, McGraw-Hill, London, 1989.
[18] and , The Finite Element Method; Solid and Fluid Mechanics, Dynamics and Non-linearity, Vol. 2, 4th edn, McGraw-Hill, London, 1991.
[19] Hertz, J. Rein. Ang. Math. 92 pp 156– (1882)
[20] Contact Mechanics, Cambridge University Press, Cambridge, 1987.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.