A dynamic variation principle for elasticfluid contacts, applied to elastohydrodynamic lubrication theory
Abstract
The variational structure underlying elastohydrodynamic lubrication theory is investigated by the study of the variational structure of the line contact problem between an elastic medium and a fluid. Equations for the deformation in the elastic material, and the flow of viscous fluid are determined from an elastic energy and power functional, and a variational formula given for the combined system. Equations expressing the balance of forces on the separating boundary, and equations in the interior of both media, are obtained. Time dependent deformations are considered, where the velocity in the elastic medium vanishes, and the particle acceleration on both sides of the common boundary is equal. The result is applied to a typical problem from elastohydrodynamic theory and resulting expressions are simplified by imposing a common restriction to small deformations and exploiting the characteristic length scales of the problem. The formulation of the approximated system is shown to be a genuine variational principle and to correctly produce the differential expressions. A natural way of generating efficient numerical methods to calculate the deformation of, and the pressure at, the free boundary, if the time variable is descretized, is achieved.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 November 1988
 Bibcode:
 1988STIN...8928782V
 Keywords:

 Approximation;
 Boundary Lubrication;
 Elastohydrodynamics;
 FluidSolid Interactions;
 Formulas (Mathematics);
 Variational Principles;
 Boundary Layer Flow;
 Differential Equations;
 Elastic Deformation;
 Elastic Media;
 Problem Solving;
 Surface Reactions;
 Viscous Fluids;
 Fluid Mechanics and Heat Transfer