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An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model. (English) Zbl 0879.73044
We prove the existence of solution for a mathematical model governing the displacement of piezoviscous thin fluid films between elastic and rigid surfaces. The hydrodynamic part is governed by the Reynolds lubrication equation combined with the cavitation free-boundary model of Elrod-Adams and with the Barus law for piezoviscous fluids. The elastic deformation of one of the lubricated surfaces is modelled by the hinged plate biharmonic equation where the fluid pressure is treated as an external force. An iterative algorithm is suggested which decouples the hydrodynamic and elastic parts. The method also includes finite element approximations and upwind technique to discretize the lubrication model.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K20 Plates
76D08 Lubrication theory
35Q72 Other PDE from mechanics (MSC2000)
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