On a variational inequality on elasto-hydrodynamic lubrication

We consider the problem of a deformable surface moving over a flat plane. The surfaces are separated by a small gap filled by a lubricant fluid. The mathematical model consists of the Reynolds variational inequality with nonlocal coefficients given by an integral operator which depends on the fluid...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011, Vol.383 (2), p.597-607
Main Authors: Ciuperca, Ionel Sorin, Tello, J. Ignacio
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Elasto-hydrodynamic lubrication
Euler–Bernoulli beam equation
Exact sciences and technology
Global analysis, analysis on manifolds
Hertz elastic operator
Integral equations
Inverse problems
Mathematical analysis
Mathematics
Operator theory
Reynolds variational inequality
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We consider the problem of a deformable surface moving over a flat plane. The surfaces are separated by a small gap filled by a lubricant fluid. The mathematical model consists of the Reynolds variational inequality with nonlocal coefficients given by an integral operator which depends on the fluid pressure. The nonlocal operator represents the deformation of the lubricated surfaces. The problem considers the vertical displacement of the elastic surface from its reference configuration. The goal of the paper is to obtain the range of these admissible displacements. We present general results for nonlocal coefficients with applications to particular problems in elasto-hydrodynamic lubrication.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.05.047