Weight Functions Analysis in Elastostatic Problems for Meshless Element Free Galerkin Method

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

doi:10.1007/1-4020-5370-3_531

Cited by 5 publications

(16 citation statements)

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“…Once this point is reached, the way to solve ( 9) only depends on the shape function. In references [15] to [18], MLS-based shape functions are obtained; but such functions lead to a solution with a low accuracy in contours due to the lack of PN property at such boundaries.…”

Section: Bernstein-polynomial-based Efgmmentioning

confidence: 99%

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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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Section: Bernstein-polynomial-based Efgmmentioning

confidence: 99%

“…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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“…Equation (20) in one-dimensional bar axially loaded can be reduced to the formulation as shown in reference [10] by considering a variable stiffness. Therefore, equations (20) to (22), in one-dimensional formulation, become…”

Section: Galerkin Implementation (Efgm)mentioning

confidence: 99%

“…3) is based on a regular 11-node distribution. A linear basis is used, and the function proposed by Valencia et al [20] has been selected as a weight function. The numerical integration of equation ( 23) is performed using a tenth-order Gaussian quadrature, as will be discussed in section 4.4.…”

Section: Accuracy and Computational Cost Of The Efgmmentioning

confidence: 99%

“…Basically, and once ensured the appropriate continuity required by the governing equation of the problem, the most important characteristic of the weight function is its shape, because it will define the relative contribution of each weight function at each integration point. In order to analyse this effect, Valencia et al [20] proposed a modifiable weight function with continuity…”

Section: Shape Of the Weight Functionmentioning

confidence: 99%

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Influence of selectable parameters in element-free Galerkin method: One-dimensional bar axially loaded problem

Valencia

Gómez-Escalonilla²,

Díez

2008

Proceedings of the Institution of Mechanical Engineers, Part C:

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Meshless methods (MMs) have become interesting and promising methods in solving partial differential equations, because of their flexibility in practical applications when compared with the standard finite-element method (e.g. crack propagation, large deformations, and so on). Implementation of these methods requires a good understanding of the influence of some specific selectable parameters. In this article, those parameters are analysed for one of the most popular MMs, the element-free Galerkin method, considering both accuracy and computational cost. Thus, the dependence of the solutions on grid irregularity, order of the polynomial basis, type of weight function, and the support size is investigated, and conclusions are drawn with respect to recommended or ‘optimal’ values for one-dimensional bar problems with applied axial loads.

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