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
Cameron, A., Principle of Lubrication. Longmans, London, 1966
Dowson, D. and Taylor, C.M., Cavitation in Bearings. Annual Rev. Fluid Mechanics, 11 (1979): 35–60
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
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
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
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
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
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
Chien, Wei-Zang, Generalized VP, Intelligence Press, Shanghai, 1985
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
Courant R. and Hilbert D., Methods of Mathematical Physics, Vol. I, Interscience, 1953
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
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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
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