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Finite element solution of a Reynolds-Koiter coupled problem for the elastic journal-bearing. (English) Zbl 1013.74019

Summary: We present a numerical algorithm for solving a new elastohydrodynamic free boundary problem which models the lubricant pressure behaviour by means of Reynolds equation, jointly with the free boundary model of Elrod-Adams for cavitation and with elastic deformation of the bearing governed by Koiter shell model; a non-local constraint on the pressure is imposed. The proposed algorithm uncouples the hydrodynamic and elastic parts to achieve a fixed point. For two-dimensional problem, we employ a combination of finite element, transport-diffusion and duality methods. For three-dimensional elastic problem, a finite element discretization is applied to a mixed formulation of Koiter model.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76D08 Lubrication theory
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