A penalty formulation and numerical approximation of the Reynolds-Hertz problem of elastohydrodynamic lubrication
type: Item
instance of: scholarly article
title: A penalty formulation and numerical approximation of the Reynolds-Hertz problem of elastohydrodynamic lubrication
zbMATH Open document ID: 0583.73016
DOI: 10.1016/0020-7225(86)90032-7
author: B. George
published in: International Journal of Engineering Science
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74S99
Mathematics Subject Classification ID: 74F10
zbMATH DE Number: 3934481
zbMATH Keywords: highly nonlinear free boundary problem
zbMATH Keywords: elastic bearing
zbMATH Keywords: deforming
zbMATH Keywords: Newtonian lubricant
zbMATH Keywords: cavitation line
zbMATH Keywords: application to one-dimensional line contact problems
zbMATH Keywords: line-contact case
zbMATH Keywords: penalty method
zbMATH Keywords: elastohydrodynamic lubrication
zbMATH Keywords: pseudomonotone variational inequality
zbMATH Keywords: Convergence
zbMATH Keywords: Reynolds-Hertz problem
zbMATH Keywords: Regularity
zbMATH Keywords: finite element method
MaRDI profile type: Publication
full work available at URL: 0020-7225(86)90032-7
OpenAlex ID: W1967185169
cites work: Equivalent Norms for Sobolev Spaces
cites work: Q4140547
cites work: Q3221604
cites work: On a problem of the theory of lubrication governed by a variational inequality
cites work: On the existence of solutions for the fundamental problem of the hydrodynamic lubrication
cites work: On certain nonlinear problems arising in the theory of lubrication
cites work: A Numerical Solution to the Elasto-Hydrodynamic Problem
cites work: Q4723426
cites work: Theory of variational inequalities with applications to problems of flow through porous media
cites work: Existence of solutions of the Reynolds' equation of elastohydrodynamic lubrication
cites work: A variational formulation for a class of free boundary lubrication
cites work: A unified treatment of thick and thin film elastohydrodynamic problems by using higher order element methods
description: scientific article; zbMATH DE number 3934481