Extending the BEM for Elastic Contact Problems Beyond the Half-Space Approach

References

• T. Andersson. The boundary element method applied to two-dimensional contact problems with friction. In C. A. Brebbia(Ed.), Proceedings of the 3rd International Seminar, Irvine, California, July 1981, volume 3 of Boundary Elements, pp. 239–258. Springer Berlin Heidelberg, 1981. http://dx.doi.org/10.1007/978-3-662-11270-016.
   Google Scholar
• J.R. Barber. Elasticity. Kluwer, Dordrecht, the Netherlands, 1992.
   Google Scholar
• C. Cattaneo. Sul contatto di due corpi elastici: distribuzione locale degli sforzi. Rendiconti dell'Accademia Nazionale dei Lincei, 27:342–348, 434–436, 474–478, 1938.
   Google Scholar
• J.R. Dydo and H.R. Busby. Elasticity solutions for constant and linearly varying loads applied to a rectangular surface patch on the elastic half-space. Journal of Elasticity, 38(2):153–163, 1995. http://dx.doi.org/10.1007/BF00042496.
   Web of Science ®Google Scholar
• R. Enblom. Deterioration mechanisms in the wheel-rail interface with focus on wear prediction: a literature review. Vehicle System Dynamics, 47(6):661–700, 2009. http://dx.doi.org/10.1080/00423110802331559.
   Web of Science ®Google Scholar
• M.J. Fagan and J. McConnachie. A review and detailed examination of non-layered conformal contact by finite element analysis. The Journal of Strain Analysis for Engineering Design, 36(2):177–195, 2001. http://dx.doi.org/10.1243/0309324011512739.
   Web of Science ®Google Scholar
• S.L. Grassie. Rolling contact fatigue on the British railway system: treatment. Wear, 258(7-8):1310–1318, 2005. http://dx.doi.org/10.1016/j.wear.2004.03.065.
   Web of Science ®Google Scholar
• W. Habchi. A full-system finite element approach to elastohydrodynamic lubrication problems: application to Ultra-Low-Viscosity Fluids. PhD thesis, University of Lyon, France, 2008.
   Google Scholar
• T.A. Harris and M.N. Kotzalas. Rolling Bearing Analysis, volume 3. Wiley, New York, USA, 2001.
   Google Scholar
• H. Hertz. Ü ber die Berührung fester elastischer K¨orper. Journal für die Reine und Angewandte Mathematik, 92:156–171, 1882. http://dx.doi.org/10.1515/crll.1882.92.156.
   Google Scholar
• T.J.R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1987.
   Google Scholar
• K.L. Johnson. Contact Mechanics. Cambridge University Press, UK, 1985.
   Google Scholar
• J.J. Kalker. Three-Dimensional Elastic Bodies in Rolling Contact. Kluwer Academic Publisher, Dordrecht, the Netherlands, 1990.
   Google Scholar
• N. Kikuchi and J.T. Oden. Contact Problems in Elasticity: a Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia, USA, 1988. http://dx.doi.org/10.1137/1.9781611970845.
   Google Scholar
• K. Knothe. History of wheel/rail contact mechanics: from Redtenbacher to Kalker. Vehicle System Dynamics, 46(1-2):9–26, 2008. http://dx.doi.org/10.1080/00423110701586469.
   Web of Science ®Google Scholar
• B.-R. Kucinschi, M. Fillon, J. Frene and M.D. Pascovici. A transient thermoelastohydrodynamic study of steadily loaded plain journal bearings using finite element method analysis. Journal of Tribology, 122(1):219–226, 2000. http://dx.doi.org/10.1115/1.555346.
   Web of Science ®Google Scholar
• T.A. Laursen. Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Springer Science & Business Media, 2002.
   Google Scholar
• J. Li and E.J. Berger. A Boussinesq-Cerruti solution set for constant and linear distribution of normal and tangential load over a triangular area. Journal of Elasticity, 63(2):137–151, 2001. http://dx.doi.org/10.1023/A:1014013425423.
   Web of Science ®Google Scholar
• Z. Li. Wheel-rail rolling contact and its application to wear simulation. PhD thesis, Delft University of Technology, Delft, The Netherlands, 2002.
   Google Scholar
• C.S. Liu, K. Zhang and R. Yang. The FEM analysis and approximate model for cylindrical joints with clearances. Mechanism and Machine Theory, 42(2):183–197, 2007. http://dx.doi.org/10.1016/j.mechmachtheory.2006.02.006.
   Web of Science ®Google Scholar
• S. Liu, Q. Wang and G. Liu. A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses. Wear, 243(1-2):101–111, 2000. http://dx.doi.org/10.1016/S0043-1648(00)00427-0.
   Web of Science ®Google Scholar
• K.W. Man. Contact Mechanics Using Boundary Elements. Computational Mechanics Publisher, Boston MA, 1994.
   Google Scholar
• B. Michel, A. Bernard, A. Bietsch, E. Delamarche, M. Geissler, D. Juncker, H. Kind, J.-P. Renault, H. Rothuizen, H. Schmid, P. Schmidt-Winkel, R. Stutz and H. Wolf. Printing meets lithography: soft approaches to high-resolution patterning. IBM Journal of Research and Development, 45(5):697–719, 2001. http://dx.doi.org/10.1147/rd.455.0697.
   Web of Science ®Google Scholar
• I.A. Polonsky and L.M. Keer. Fast methods for solving rough contact problems: a comparative study. Journal of Tribology, 122(1):36–41, 2000. http://dx.doi.org/10.1115/1.555326.
   Web of Science ®Google Scholar
• V.L. Popov. Contact Mechanics and Friction: Physical Principles and Applications. Springer Berlin Heidelberg, Berlin, 2010. http://dx.doi.org/10.1007/978-3-642-10803-7.
   Google Scholar
• E. Rabinowicz. Friction and Wear of Materials, volume 2. Wiley, New York, 1995.
   Google Scholar
• A. Segal. SEPRAN users manual. Ingenieursbureau SEPRA, Den Haag, The Netherlands, 2013. http://ta.twi.tudelft.nl/sepran/sepran.html
   Google Scholar
• H.M. Stanley and T. Kato. An FFT-based method for rough surface contact. Journal of Tribology, 119(3):481–485, 1997. http://dx.doi.org/10.1115/1.2833523.
   Web of Science ®Google Scholar
• A. van der Ploeg, E.F.F. Botta and F.W. Wubs. Nested grids ILU-decomposition (NGILU). Journal of Computational and Applied mathematics, 66(1-2):515–526, 1996. http://dx.doi.org/10.1016/0377-0427(95)00182-4.
   Web of Science ®Google Scholar
• R. Verfürth. A review of a posteriori error estimation techniques for elasticity problems. Computer Methods in Applied Mechanics and Engineering, 176(1-4):419–440, 1999. http://dx.doi.org/10.1016/S0045-7825(98)00347-8.
   Web of Science ®Google Scholar
• S. Vijayakar, H. Busby and L. Wilcox. Finite element analysis of three-dimensional conformal contact with friction. Computers & Structures, 33(1):49–61, 1989. http://dx.doi.org/10.1016/0045-7949(89)90128-4.
   Web of Science ®Google Scholar
• E.A.H. Vollebregt. Refinement of Kalker's rolling contact model. Proceedings of the 8th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Firenze, pp. 149–156, 2009.
   Google Scholar
• E.A.H. Vollebregt. A new solver for the elastic normal contact problem using conjugate gradients, deflation, and an FFT-based preconditioner. Journal of Computational Physics, 257, Part A:333–351, 2014. http://dx.doi.org/10.1016/j.jcp.2013.10.005.
   Google Scholar
• E.A.H. Vollebregt. User's guide for CONTACT, Vollebregt & Kalker's rolling and sliding contact model. Technical Report TR09-03, version 14.1, VORtech BV, The Netherlands, 2014. http://www.kalkersoftware.org/
   Google Scholar
• E.A.H. Vollebregt and A. Segal. Solving conformal wheel–rail rolling contact problems. Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, 52.sup1:455–468, 2014.
   Google Scholar
• Q. Wang. Seizure failure of journal-bearing conformal contacts. Wear, 210(1-2):8–16, 1997. http://dx.doi.org/10.1016/S0043-1648(97)00064-1.
   Web of Science ®Google Scholar
• Q.J. Wang, F. Shi and S.C. Lee. A mixed-lubrication study of journal bearing conformal contacts. Journal of Tribology, 119(3):456–461, 1997. http://dx.doi.org/10.1115/1.2833519.
   Web of Science ®Google Scholar
• P. Wriggers. Computational Contact Mechanics. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-32609-0.
   Google Scholar
• P. Wriggers. Nonlinear Finite Element Methods. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71001-1.
   Google Scholar
• J. Zhao, E.A.H. Vollebregt and C.W. Oosterlee. Multigrid with FFT smoother for a simplified 2D frictional contact problem. Numerical Linear Algebra with Applications, 21(2):256–274, 2014. http://dx.doi.org/10.1002/nla.1923.
   Web of Science ®Google Scholar
• J. Zhao, E.A.H. Vollebregt and C.W. Oosterlee. A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems. Journal of Computational Physics, 288:86–100, 2015. http://dx.doi.org/10.1016/j.jcp.2015.02.016.
   Web of Science ®Google Scholar
• O.C. Zienkiewicz, R.L. Taylor and J.Z. Zhu. The Finite Element Method: its Basis and Fundamentals (Seventh edition). Butterworth-Heinemann, 2013.
   Google Scholar