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Dual Variational Principles for the Free-Boundary Problem of Cavitated Bearing Lubrication

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Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 6))

Abstract

The free-boundary problem in cavitated bearing lubrication is handled in a systematic way via the powerful mathematical tool — the functional variation with variable domain, resulting in a pair of dual variational principle families for it. In this way, a new rigorous and sound theoretical foundation for the finite element analysis of the cavitated bearing lubrication problem is founded.

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References

  1. Cameron, A., Principle of Lubrication. Longmans, London, 1966

    Google Scholar 

  2. Dowson, D. and Taylor, C.M., Cavitation in Bearings. Annual Rev. Fluid Mechanics, 11 (1979): 35–60

    Article  ADS  Google Scholar 

  3. Capriz, G. & Cimatti, G., Free boundary problems in the theory of hydrodynamic lubrication: A survey. Free boundary problems: Theory and applications, Vol. II, Fasano, A. and Primicesio, M. (eds), Pitman, Boston, 1983 (Research Notes in Maths. 79 ) 613–635

    Google Scholar 

  4. Cuvelier, C., A free boundary problem in hydrodynamic lubrication including surface tension. Proc. 6th Intl. Conf. Num. Methods in Fluid Dynamics, Cabannes, H. et al. (eds.), Springer, Berlin, 1979 (Lecture Notes in Physics 90 ) 143–148

    Chapter  Google Scholar 

  5. Liu, Gao-Lian. Variable-domain variational finite element method: A general approach to free/moving boundary problems in heat and fluid flow, Nonlinear Analysis, 30 (1997) 5229–5239

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, Gao-Lian, Variational principles (VP) and generalized VP for fully 3-D transonic flow with shocks in a turbo-rotor (I), Acta Mechanica, 95 (1992): 117–130

    Article  MATH  Google Scholar 

  7. Liu, Gao-Lian and Yan, Shan, A unified variable-domain variational approach to hybrid problems of compressible blade-to-blade flow. Intl. J. Turbo and Jet Engines, 10 (1993): 273–284

    Google Scholar 

  8. Liu, Gao-Lian, Derivation and transformation of VP with emphasis on inverse and hybrid problems in fluid dynamics: A systematic approach, Acta Mechanica, 140 (2000): 73–89

    Article  MATH  Google Scholar 

  9. Chien, Wei-Zang, Generalized VP, Intelligence Press, Shanghai, 1985

    Google Scholar 

  10. Rohde, S.M. and McAllister, G.T., A variational formulation for a class of free boundary problems arising in hydrodynamic lubrication. Int. J. Engrg. Sci., 13 (1975): 841–850

    Article  MATH  Google Scholar 

  11. Courant R. and Hilbert D., Methods of Mathematical Physics, Vol. I, Interscience, 1953

    Google Scholar 

  12. Liu, Gao-Lian, Variable-domain variational formulation of free-boundary problem in bearing lubrication with cavitation, Pt. I, Computational Fluid Dynamics Journal, 10 (2002) 539–541

    Google Scholar 

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© 2004 Springer Science+Business Media New York

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Liu, GL. (2004). Dual Variational Principles for the Free-Boundary Problem of Cavitated Bearing Lubrication. In: Complementarity, Duality and Symmetry in Nonlinear Mechanics. Advances in Mechanics and Mathematics, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9577-0_10

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  • DOI: https://doi.org/10.1007/978-90-481-9577-0_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-015-7119-7

  • Online ISBN: 978-90-481-9577-0

  • eBook Packages: Springer Book Archive

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