A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

An alternative numerical method for solving contact problems for real rough surfaces is proposed. The real area of contact and the contact pressure distribution are determined using a single-loop iteration scheme based on the conjugate gradient method, which converges for arbitrary rough surfaces. The surface deflections and subsurface stresses are computed using an alternative two-dimensional multi-level multi-summation algorithm, which allows the summation error to be kept under the discretization error for any number of contact points. The proposed method is fast: rough contact problems for surface samples with 10(5)-10(6) data points are solved on a personal computer in a few hours. The numerical algorithms are described in full detail so that an interested reader can implement the new contact solver in a computer code. Numerical examples demonstrating the method advantages are presented. The method is compared with other fast contact solvers that have emerged in the last few years. (C) 1999 Elsevier Science S.A. All rights reserved.