rough surfaces and for arbitrary load, it is often impossible to derive a direct result by integration or superposition principle, so numerical methods must be applied. For some special distributed traction, such as the Hertzian contact and cylindrical indenters, analytical solutions exist as well. For the cases of a single concentrated normal or tangential force, the deformations can be calculated with the known analytical solutions. The analytical solutions of stresses and displacements in an elastic half space under a concentrated force or distributed stress are from Boussinesq (1885) and Cerruti (1882) by use of the theory of potential. When the correct state is obtained, the resulting subsurface-stresses can also be evaluated. The most important step in solving these problems is to find a physical combination of surface stresses and surface deformations. Roughness features are flattened out or slide relative to the opposite topography. Non-conforming topographies are brought into contact and deform due to the surface stresses. In many problems in contact mechanics and friction physics, one is primarily concerned with processes and deformations located directly at the surface of the contacting bodies. Keywords: boundary element method, influence matrix, elastic deformation, contact mechanics, dry friction, mixed lubrication
The resulting computer program can be used effectively in iterative schemes also in similar problems, such as mixed lubrication and notably improves the applicability of the boundary element method in contact mechanics. A comprehensive algorithm is given for solving the case of dry Coulomb friction with partial slip.
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We show how to overcome complexity problems by using FFT-based fast convolution. In this paper, we derive the matrixes of influence coefficients for the deformation of an elastic half space, starting from the classical solutions of Boussinesq and Cerruti. However, for every two grid points, influence coefficients have to be employed for every force-displacement combination. The boundary element method as a numerical tool in contact mechanics is widely used and allows for surface roughness to be investigated with very fine grids. Technische Universität Berlin, Berlin, 10623, Germany Complete boundary element formulation for normal and tangential contact problems