The paper describes an algorithm for generation of locally regular computational nodes with variable density for interiors of 2D, 3D or higher-dimensional domains. The generated distributions are suitable for use with the RBF-FD meshless method, as demonstrated by solving the Poisson's and convection-diffusion equation. Besides that, minimal spacing guarantees are proven for both uniform and variable distributions. The presented algorithm takes O(N) time to generate N points for uniform distributions, and O(N log N) time for variable density distributions. The agorithm is compared with existing algorithms in terms of node quality, time complexity, execution time, and PDE solution accuracy.
COBISS.SI-ID: 32782887
A strong form numerical meshless method based on a local Weighted Least Squares approximation is used to solve the Cauchy-Navier equation for steady state linear elasticity problems. Advantages, such as its generality in terms of approximation setup and positions of computational nodes of the employed numerical approach, are explored. Two irregular cases are considered, first a drilled cantilever beam, where an irregular domain is treated with an original nodal positioning algorithm, and a Hertzian contact problem, where a refinement algorithm is used to extensively refine discretization under the contact area. The main contribution of the paper is demonstration that the strong form meshless methods can be used to effectively solve difficult problems with irregular geometry or high local stress concentrations.
COBISS.SI-ID: 31107623
V članku je predstavljen numeričen izračun napetosti pod pogoji drsnega utrujanja. Navier-Cauchyjeve enačbe, ki opisujejo problem, rešimo v močni in šibki obliki z brezmrežnimi numeričnimi metodami. Rezultate primerjamo z rešitvijo, dobljeno s programskim paketom ABAQUS, ki uporablja klasično metodo končnih elementov (FEM). Pokazano je, da se brezmrežne metode, ki rešujejo problem v šibki obliki, obnašajo podobno kot FEM, medtem ko v tem primeru brezmrežne metode, ki rešujejo enačbo v močni obliki, bolje opišejo vrh napetostnega profila. Ravno ta vrh je pomemben pri drsnem utrujanju, saj neposredno vpliva na položaj začetka razpoke. Rezultati so prikazani v obliki površinskih profilov napetosti, konvergenčnih grafov za vse metode in konturnih diagramov von Misesove napetosti.
COBISS.SI-ID: 32424999
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 applications 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 3D Boussinesq's problem of the concentrated normal traction acting on an isotropic half-space.
COBISS.SI-ID: 32230439
Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. This paper analyses finite element models to reproduce results of recent laboratory studies. Specifically, it observes if any singularities are present under the contact zone and analyses convergence rates in terms of contact width and coefficient of friction. Recommendations for mesh sizes for analyses of fretting problems are proposed as a result of this research.
COBISS.SI-ID: 29649703