Refined Meshless Local Strong Form solution of Cauchy–Navier equation on an irregular domain

Slak, J.; Kosec, Gregor

doi:10.1016/j.enganabound.2018.01.001

Cited by 27 publications

(30 citation statements)

References 20 publications

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“…The next case considers Hertzian contact between an elastic cylinder and a half‐plane, as recently used in our other work . The analytical boundary condition on the top boundary is given by the known pressure distribution

p false(x false) = ({, \begin{matrix} array \\ array p_{0} \sqrt{1 - \frac{x^{2}}{a^{2}}}, & array | x | \leq a \\ array 0, & array otherwise \end{matrix}), p_{0} = \sqrt{\frac{P E^{*}}{π R}}, a = 2 \sqrt{\frac{P R}{π E^{*}}},

where P is the pressure force, R is the radius of the cylinder, and the combined Young's modulus E ∗ is given by

\frac{1}{E^{*}} = \frac{1 - ν_{1}^{2}}{E_{1}} + \frac{1 - ν_{2}^{2}}{E_{2}}

, where E 1 , ν 1 and E 2 , ν 2 are the material properties of the cylinder and the half‐plane, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For the choice

R = 1 normalm, P = 543 \frac{N}{m}, E = 72.1 GPa, ν = 0.33

, the contact width a is approximately 0.13 mm. A choice of H = 0.1 m, which is approximately 770 times larger than the phenomenon of interest, is sufficiently large that the truncation error does not present a significant contribution …”

Section: Numerical Resultsmentioning

confidence: 99%

“…The adaptive procedure was run with α = 5, ε = 10 5 , β = 1.5, η = 10 4 and left to run for 6 iterations. The errors measured against a closed‐form solution,8(eqs.54‐56) and the number of nodes over the course of the iterative procedure are shown in Figure . Additionally, data about node refinement for each iteration is shown in Table .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This turns into an underdetermined system, however, it can be solved uniquely by imposing additional condition of minimising the norm ‖ w i ‖ of the weights. The benefit of this approach is that it is less sensitive to perturbations of nodal positions . This modification will be used in this paper.…”

Section: Rbf‐generated Finite Differencesmentioning

confidence: 99%

“…A popular variant among many local meshless methods is the radial basis function–generated finite differences (RBF‐FD) method, which uses finite difference‐like collocation weights on an unstructured set of nodes. The method has been successfully used in several problems and is still actively researched . In the field of solid mechanics, where problems are traditionally tackled with the finite element method (FEM), meshless methods surfaced as a response to the cumbersome meshing of realistic three‐dimensional (3D) domains required by FEM .…”

Section: Introductionmentioning

confidence: 99%

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

Slak

Kosec

2019

Numerical Meth Engineering

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Summary This paper proposes an original adaptive refinement framework using radial basis function–generated finite differences method. Node distributions are generated with a Poisson disc 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. First, a disc under pressure is considered and the computed stress field is compared to the closed‐form solution of the problem to assess the behaviour of the algorithm and the influence of free parameters. Second, a Hertzian contact problem 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 produces results comparable with finite element method without the need for manual refinement or any human intervention. In the last case, generality of the proposed approach is demonstrated by solving a three‐dimensional Boussinesq's problem.

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