A numerical method has been developed for solving the nonlinear differential equation which arises in the elastohydrodynamic contact of bearing surfaces. This method is based upon the finite element approximation of the governing field equation, the Newton-Raphson algorithm for solving nonlinear systems, and the complementarity formulation of free-boundary problems. The lubricated contact between a sphere and a semi-infinite half-space under dynamic loading is analyzed as an illustrative problem.

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