A mortar-finite element formulation for frictional contact problems
2000; Wiley; Volume: 48; Issue: 10 Linguagem: Inglês
10.1002/1097-0207(20000810)48
ISSN1097-0207
AutoresTodd Watters McDevitt, Tod A. Laursen,
Tópico(s)Numerical methods in engineering
ResumoInternational Journal for Numerical Methods in EngineeringVolume 48, Issue 10 p. 1525-1547 Research Article A mortar-finite element formulation for frictional contact problems T. W. McDevitt, T. W. McDevitt Department of Civil and Environmental Engineering, School of Engineering, Duke University, Durham, NC 27708-0287, U.S.A. Assistant Research Professor. Current position: Senior Development Engineer, Mechanical Dynamics, Inc., 2301 Commonwealth Boulevard, Ann Arbor, MI 48105, U.S.A.Search for more papers by this authorT. A. Laursen, Corresponding Author T. A. Laursen [email protected] Department of Civil and Environmental Engineering, School of Engineering, Duke University, Durham, NC 27708-0287, U.S.A. Associate Professor.Department of Civil and Environmental Engineering, School of Engineering, Duke University, PO Box 90287, Durham, NC 27708-0287, U.S.A.Search for more papers by this author T. W. McDevitt, T. W. McDevitt Department of Civil and Environmental Engineering, School of Engineering, Duke University, Durham, NC 27708-0287, U.S.A. Assistant Research Professor. Current position: Senior Development Engineer, Mechanical Dynamics, Inc., 2301 Commonwealth Boulevard, Ann Arbor, MI 48105, U.S.A.Search for more papers by this authorT. A. Laursen, Corresponding Author T. A. Laursen [email protected] Department of Civil and Environmental Engineering, School of Engineering, Duke University, Durham, NC 27708-0287, U.S.A. Associate Professor.Department of Civil and Environmental Engineering, School of Engineering, Duke University, PO Box 90287, Durham, NC 27708-0287, U.S.A.Search for more papers by this author First published: 09 June 2000 https://doi.org/10.1002/1097-0207(20000810)48:10 3.0.CO;2-YCitations: 162 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract In this paper a finite element formulation is developed for the solution of frictional contact problems. The novelty of the proposed formulation involves discretizing the contact interface with mortar elements, originally proposed for domain decomposition problems. The mortar element method provides a linear transformation of the displacement field for each boundary of the contacting continua to an intermediate mortar surface. On the mortar surface, contact kinematics are easily evaluated on a single discretized space. The procedure provides variationally consistent contact pressures and assures the contact surface integrals can be evaluated exactly. Copyright © 2000 John Wiley & Sons, Ltd. REFERENCES 1 Kikuchi N, Oden JT. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM: Philadelphia, PA: 1988. 10.1137/1.9781611970845 Google Scholar 2 Francavilla A, Zienkiewicz OC. A note on numerical computation of elastic contact problems. International Journal for Numerical Methods in Engineering 1975; 9: 913–924. 10.1002/nme.1620090410 Google Scholar 3 Hughes TJR, Taylor RL, Sackman JL, Curnier A, Kanoknukulchai W. A finite element method for a class of contactimpact problems. Computer Methods in Applied Mechanics and Engineering 1976; 8: 249–276. 10.1016/0045-7825(76)90018-9 Google Scholar 4 Hallquist JO, Goudreau GL, Benson DJ. Sliding interfaces with contact-impact in large-scale lagrangian computations. Computer Methods in Applied Mechanics and Engineering 1985; 51: 107–137. 10.1016/0045-7825(85)90030-1 Web of Science®Google Scholar 5 Parisch H. A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis. International Journal for Numerical Methods in Engineering 1989; 28: 1803–1812. 10.1002/nme.1620280807 Web of Science®Google Scholar 6 Wriggers P, Vu Van T, Stein E. Finite element formulation of large deformation impact-contact problems with friction. Computers and Structures 1990; 37: 319–331. 10.1016/0045-7949(90)90324-U Web of Science®Google Scholar 7 Wriggers P, Simo JC. A note on tangent stiffness for fully nonlinear contact problems. Communications in Applied Numerical Methods 1985; 1: 199–203. 10.1002/cnm.1630010503 Web of Science®Google Scholar 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. 10.1016/0045-7825(92)90061-N Web of Science®Google Scholar 9 Simo JC, Wriggers P, Taylor RL. A perturbed lagrangian formulation for the finite element solution of contact problems. Computer Methods in Applied Mechanics and Engineering 1985; 50: 163–180. 10.1016/0045-7825(85)90088-X Web of Science®Google Scholar 10 Gallego FJ, Anza JJ. A mixed finite element model for the elastic contact problem. International Journal for Numerical Methods in Engineering 1989; 28: 1249–1264. 10.1002/nme.1620280603 Web of Science®Google Scholar 11 Bernardi C, Maday Y, Patera AT. A new nonconforming approach to domain decomposition: the mortar element method. In Nonlinear Partial Differential Equations and Their Applications, H Brezia, JL Lions (eds). Pitman and Wiley: London, New York, 1992; 13–51. Google Scholar 12 Farhat C. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering 1991; 32: 1205–1227. 10.1002/nme.1620320604 Web of Science®Google Scholar 13 Park Jr. KC, Justino MR, Felippa CA. An algebraically partitioned feti method for parallel structural analysis: algorithm description. International Journal for Numerical Methods in Engineering 1997; 40: 2717–2737. 10.1002/(SICI)1097-0207(19970815)40:15 3.0.CO;2-B Web of Science®Google Scholar 14 Justino Jr. MR, Park KC, Felippa CA. An algebraically partitioned feti method for parallel structural analysis: performance evaluation. International Journal for Numerical Methods in Engineering 1997; 40: 2739–2758. 10.1002/(SICI)1097-0207(19970815)40:15 3.0.CO;2-0 Web of Science®Google Scholar 15 Maday Y, Mavriplis C, Patera AT. Nonconforming mortar element methods: application to spectral discretization. In Domain Decomposition Methods, T Chan, R Glowinski, J Periaux, OB Widlund. (editors). SIAM: Philadelphia, PA, 1989; 392–418. Google Scholar 16 Anagnostou G, Maday Y, Mavriplis C, Patera AT. On the mortar element method: generalizations and implementations. In Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, T Chan, R Glowinski, J Periaux, OB Widlund. (eds). SIAM: Philadelphia, PA, 1990; 157–173. Web of Science®Google Scholar 17 Achdou Y. The mortar element method for convection diffusion problems. Comptes Rendus De L'Académie Des Sciences 1995; 321: 117–123. Web of Science®Google Scholar 18 Belhachmi Z, Bernardi C. Resolution of fourth-order problems by the mortar element method. Computer Methods in Applied Mechanics and Engineering 1994; 116: 53–58. 10.1016/S0045-7825(94)80007-3 Web of Science®Google Scholar 19 Belhachm Z. Nonconforming mortar element methods for the spectral discretization of two-dimensional fourth-order problems. SIAM Journal for Numerical Analysis 1997; 34: 1545–1573. 10.1137/S0036142995284363 Web of Science®Google Scholar 20 Belgacem FB, Maday Y. A spectral element methodology tuned to parallel implementations. Computer Methods in Applied Mechanics and Engineering 1994; 116: 59–67. 10.1016/S0045-7825(94)80008-1 Web of Science®Google Scholar 21 Arbogast T, Yotov I. A non-mortar mixed finite element for elliptic problems on non-matching multiblock grids. Computer Methods in Applied Mechanics and Engineering 1997; 149: 255–265. 10.1016/S0045-7825(97)00054-6 Web of Science®Google Scholar 22 Belgacem FB, Hild P, Laborde P. Approximation of the unilateral contact problem by the mortar finite element method. Comptes Rendus De L'Acadéemie Des Sciences 1991; 324: 123–127. 10.1016/S0764-4442(97)80115-2 Google Scholar 23 Aminpour MA, Ransom JB, McCleary SL. A coupled analysis method for structures with independently modelled finite element sub-domains. International Journal for Numerical Methods in Engineering 1995; 38: 3695–3718. 10.1002/nme.1620382109 Web of Science®Google Scholar 24 Rixen D, Farhat C, Géradin M. A two-step, two-field hybrid method for the static and dynamic analysis of substructure problems with conforming and non-conforming interfaces. Computer Methods in Applied Mechanics and Engineering 1998; 154: 229–264. 10.1016/S0045-7825(97)00128-X Web of Science®Google Scholar 25 Giannakopoulos, AE. The return mapping method for the integration of friction constitutive relations. Computers and Structures 1989; 32: 157–167. 10.1016/0045-7949(89)90081-3 Web of Science®Google Scholar 26 Mindlin RD. Compliance of elastic bodies in contact. Transactions of the ASME, Series E Journal of Applied Mechanics 1949; 16: 259–268. Web of Science®Google Scholar Citing Literature Volume48, Issue1010 August 2000Pages 1525-1547 ReferencesRelatedInformation
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