Solving Elastic Contact Between Rough Surfaces as an Unconstrained Strain Energy Minimization by Using CGM and FFT Techniques

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Abstract
An accurate, robust, and efficient method for elastic contact of rough surfaces is presented. The method converts the contact problem into an unconstrained energy minimization problem. The equality load equilibrium constraint and the inequality complementary constraints are placed in the objective function and enforced simultaneously in search of a feasible solution. Conjugate gradient method is used in conjunction with FFT technique to solve the unconstrained energy minimization problem. To overcome periodical extension error associated with discrete Fourier transform when solving a nonperiodical contact problem, the solution is decomposed into two parts: a smooth part and a fluctuation part. The smooth part is solved analytically and the fluctuation part is solved by the proposed method. The net load or surface traction of the fluctuation part is set to zero to minimize the periodical extension error. Numerical examples demonstrate that the proposed method is accurate, robust, and efficient.