Finite element solution of a Reynolds–Koiter coupled problem for the elastic journal–bearing Original Research Article

The aim of this work is to 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 the elastic deformation of the bearing with the 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 the two-dimensional problem, a combination of finite elements, transport-diffusion and duality methods is performed. For the three-dimensional elastic problem, a finite element discretization is applied to a mixed formulation for the Koiter model.