An explicit solution for the elastic quarter-space problem in matrix formulation

This paper presents a fast and convenient algorithm for the solution of the elastic quarter-space contact problem, which uses discretization to form matrices to realize the overlapping solution process for the elastic quarter-space as developed by Hetenyi [Hetenyi, M., 1970. A general solution for the elastic quarter space, Trans. ASME Journal of Applied Mechanics 37 E(1), 70–76]. This proposed method provides an explicit solution which is as yet absent in existing literatures. The generated matrices are only related to the mesh structure and Poisson’s ratio while unrelated to the loading, such that they can be applied to different loading cases. Hence, the present method offers a possibility for substantially improving the efficiency of those numerical iterative analyses, such as the elastohydrodynamic lubrication of the contact in an elastic quarter-space. Verification of the present method was accomplished by comparison with the existing quarter-space results.