Adaptive radial basis function–generated finite differences method for contact problems

This paper proposes an original adaptive refinement framework using Radial Basis Functions-generated Finite Differences method. Node distributions are generated with a Poisson Disk Sampling-based algorithm from a given continuous density function, which is altered during the refinement process based on the error indicator. All elements of the proposed adaptive strategy rely only on meshless concepts, which leads to great flexibility and generality of the solution procedure. The proposed framework is tested on four gradually more complex contact problems, governed by the Cauchy-Navier equations. First, a disk under pressure is considered and the computed stress field is compared to the closed form solution of the problem to assess the basic behaviour of the algorithm and the influence of free parameters. Second, a Hertzian contact problem, also with known closed form solution, is studied to analyse the proposed algorithm with an ad-hoc error indicator and to test both refinement and derefinement. A contact problem, typical for fretting fatigue, with no known closed form solution is considered and solved next. It is demonstrated that the proposed methodology can be used in practical application and produces results comparable with FEM without the need for manual refinement or any human intervention. In the last case, generality of the proposed approach is demonstrated by solving a 3-D Boussinesq's problem of the concentrated normal traction acting on an isotropic half-space.