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

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

doi:10.1243/09544062jmes782

Cited by 11 publications

(14 citation statements)

References 20 publications

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“…This benchmark of meshless analysis has been discussed in-depth in the literature, see Dolbow and Belytschko [15], Liu and Gu [17] or Valencia et al [18]. The boundary where essential conditions are prescribed is a single node; therefore, the displacement at this node can be directly enforced if interpolating MLS shape functions are used.…”

Section: One-dimensional Rod Elastostatic Analysismentioning

confidence: 99%

Global interpolating MLS shape functions for structural problems with discrete nodal essential boundary conditions

Garijo

Valencia²,

Gómez-Escalonilla

2015

Acta Mech

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The moving least squares (MLS)-based element-free Galerkin method (EFGM) has been widely studied, yielding valuable results and becoming a robust mesh-free technique for structural analysis. Due to the non-interpolating nature of MLS shape functions, the EFGM procedure leads to stiffness and mass matrices based on nodal parameters instead of true nodal displacements. The interpolating moving least squares (IMLS) methods with singular weight functions or the weighted nodal least squares (WNLS) methods were proposed in order to arrange the formulation in terms of actual displacements at the nodes. In this work, a later transformation matrix to retrieve the classic stiffness and mass matrices is discussed and numerically tested in problems with discrete prescribed displacements at boundaries, for which a straightforward finite element method (FEM)-type imposition of boundary conditions is possible. Mathematics Subject Classification

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Section: One-dimensional Rod Elastostatic Analysismentioning

confidence: 99%

Global interpolating MLS shape functions for structural problems with discrete nodal essential boundary conditions

Garijo

Valencia²,

Gómez-Escalonilla

2015

Acta Mech

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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%

“…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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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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“…The weak form of the problem's governing equation considering a Galerkin implementation is shown in Valencia et al 13 Z…”

Section: Elastostatic Equations Solved Using Bernstein Shape Functionsmentioning

confidence: 99%

“…Parameter n is increased from 2 to 10. MLS parameter d max to define the size of the domain support 13 is taken 2.0, 2.5, 3.0, 3.5 and 4.0 for each pattern. Four different fixed background meshes for integration are tested, from 2 Â 2 to 8Â 8 cells, with 4 Â 4 integration points per cell.…”

Section: Standard Patch Testmentioning

confidence: 99%

Bernstein–Galerkin approach in elastostatics

Garijo¹,

Valencia²,

Gómez-Escalonilla

et al. 2013

Proceedings of the Institution of Mechanical Engineers, Part C:

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Since 1994, two main meshless methods have been developed and widely used: these are the element free Galerkin method and the meshless local Petrov-Galerkin method. Both methods solve partial differential equations by posing a numerical approximation to the solution using the moving least squares technique. Using Bernstein polynomials as the shape functions of Galerkin weak form-based methods improves the numerical approximation achieved at boundaries without losing accuracy inside the domain.

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

Cited by 11 publications

References 20 publications

Global interpolating MLS shape functions for structural problems with discrete nodal essential boundary conditions

Global interpolating MLS shape functions for structural problems with discrete nodal essential boundary conditions

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

Bernstein–Galerkin approach in elastostatics

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