The influence of selectable parameters in the element-free Galerkin method: A one-dimensional beam-in-bending problem

Valencia, O F; Gómez-Escalonilla, F J; López-Díez, J.

doi:10.1243/09544062jmes1198

Cited by 8 publications

(3 citation statements)

References 8 publications

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“…The highlighted limitation is that the numerical accuracy varied with the change of the scaling parameters, i.e., d max , which has been sighted by the numerical studies introduced in the next section and other works. 16,17…”

Section: Mls Approximationmentioning

confidence: 99%

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A modified method to determine the radius of influence domain in element-free Galerkin method

Sheng

Shah

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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The radius of the influence domain is an important parameter in the weight function and plays an essential role in the accuracy of approximations. A modified method was proposed for determining the radius of influence domain. The modification is that the radius of influence domain is prescribed by the desired amount of support nodes for any point of interest. The advantages of this strategy are the regularity of matrix can be ensured in moving least square approximation and the algorithm is simple and practicable. The modified method was validated by thousands of patch tests in the case of regular and irregular node collocations and Timoshenko beam problem with using random node collocation. Results show that the proposed method performs more capability to handle the arbitrary node collocation than the pre-existing methods. This paper provides an alternative way to determine the radius of influence domain.

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Section: Mls Approximationmentioning

confidence: 99%

“…Valencia et al. 16,17 analyzed a one-dimensional (1D) bar axially loaded and a beam under bending to understand the influences of the characteristic parameters on the accuracy and computational effort of the method. Valencia et al.…”

Section: Introductionmentioning

confidence: 99%

A modified method to determine the radius of influence domain in element-free Galerkin method

Sheng

Shah

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…In references [15] to [17], the behaviour of EFGM when varying internal parameters is analysed. However, in all cases, it can be observed that the main contribution to the numerical error of the method is reached in boundaries of the domain.…”

Section: Introductionmentioning

confidence: 99%

Bernstein polynomials in element-free Galerkin method

Valencia

Gómez-Escalonilla

Garijo

et al. 2011

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves, can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

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