Adaptive Radial Basis Function-generated Finite Differences method for
contact problems
release_fwmkcw3qjnezllfsqiromd73fe
by
Jure Slak, Gregor Kosec
2018
Abstract
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.
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