A penalty formulation and numerical approximation of the Reynolds-Hertz problem of elastohydrodynamic lubrication
A new penalty method for the analysis of free boundary problems in elastohydrodynamic lubrication (EHL) is introduced. This class of problems is governed by a pseudomonotone variational inequality for which the existence of solutions was established in an earlier paper [\textit{J. T. Oden} and the author, ibid. 23, 207-216 (1985)]. These earlier results also establish the existence of solutions to a penalized family of regularizations. Convergence of the penalty solutions to the solution of the Reynolds-Hertz problem of EHL is proved. Regularity results for the linear contact case are also established, including the appropriateness of the Reynolds condition, \(dp/dx=0\), on the free boundary. A finite element method based on the penalty formulation is also derived and numerical results obtained for representative problems are in good agreement with available solutions.
application to one-dimensional line contact problems
scientific article; zbMATH DE number 3934481