Single Level Fast Multipole Method for frictionless rough contact problems

A perfectly smooth contact surface does not exist in nature and industrial applications. Even a body, that seems perfectly smooth to the naked eye, will show surface roughness at a higher magnification. Due to the roughness of the surface, there are areas of contact and separation, which increases the complexity of the contact calculation. However, this computational complexity increases further due to the multi-scale nature of road surface texture and large contact area in the case of tyre/road interaction. To reduce the computational complexity of this contact problem, the Single Level Fast Multipole Method (SLFMM) is developed within this paper. The contact problem is based on Boussinesq’s contact theory and for the time being, the influence of friction and lateral displacement are neglected. To validate the accuracy and reduction in computational complexity, the SLFMM was applied to rough surfaces of different complexities and compared to a reference method, the so-called Matrix Inversion Method (MIM). Results indicate that the new method computes the pressure distribution and displacement accurately, with a global error of less than 1%. The advantage of the new method compared to the MIM is the multipole expansion, which clusters adjacent contact points to a single center point. As a result, the computational complexity of the contact calculation is reduced. Overall, the Single Level FMM computes the results faster than the reference method. These results demonstrate that the Fast Multipole Method meets the requirements of accuracy and accelerated computation for rough contact problems.