On the Convergence of the Kriging-Based Finite Element Method

Wong, Foek Tjong; Kanok‐Nukulchai, Worsak

doi:10.1142/s0219876209001784

Cited by 10 publications

(14 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means the elemental piecewise KI is not fully compatible across the interelement boundaries. Its effect on the convergence was studied in the context of 2D elastostatic problems [14,15]. It was found that K-FEM with appropriate choice of correlation function passes the weak patch test and therefore the convergence can be guaranteed.…”

Section: Discussionmentioning

confidence: 99%

Generalization of FEM Using Node-Based Shape Functions

Kanok‐Nukulchai

Wong

Sommanawat

2015

ced

View full text Add to dashboard Cite

In standard FEM, the stiffness of an element is exclusively influenced by nodes associated with the element via its element-based shape functions. In this paper, the authors present a method that can be viewed as a generalization of FEM for which the influence of a node is not limited by a hat function around the node. Shape functions over an element can be interpolated over a predefined set of nodes around the element. These node-based shape functions employ Kriging Interpolations commonly found in geostatistical technique. In this study, a set of influencing nodes are covered by surrounding layers of elements defined as its domain of influence (DOI). Thus, the element stiffness is influenced by not only the element nodes, but also satellite nodes outside the element. In a special case with zero satellite nodes, the method is specialized to the conventional FEM. This method is referred to as Node-Based Kriging FEM or K-FEM. The K-FEM has been tested on 2D elastostatic, Reissner-Mindlin's plate and shell problems. In all cases, exceptionally accurate displacement and stress fields can be achieved with relatively coarse meshes. In addition, the same set of Kringing shape functions can be used to interpolate the mesh geometry. This property is very useful for representing the curved geometry of shells. The distinctive advantage of the K-FEM is its inheritance of the computational procedure of FEM. Any existing FE code can be easily extended to K-FEM; thus, it has a higher chance to be accepted in practice.

show abstract

Section: Discussionmentioning

confidence: 99%

Generalization of FEM Using Node-Based Shape Functions

Kanok‐Nukulchai

Wong

Sommanawat

2015

ced

View full text Add to dashboard Cite

show abstract

“…6, a polynomial basis function and a correlation function should be chosen. Basis functions ranging from polynomial of the degree one up to four have been utilized in the past works on the K-FEM [2][3][4][5][6][7][8][9][10][11].…”

Section: Kriging Interpolation In the K-femmentioning

confidence: 99%

“…Following the previous works [3][4][5][6][7][8][9][10], Gaussian and Quartic Spline correlation function (QS) were chosen. Gaussian correlation function is defined as…”

Section: Kriging Interpolation In the K-femmentioning

confidence: 99%

“…A drawback of the K-FEM is that the interpolation function is discontinuous at the inter-element boundaries (except in 1D problems). In spite of this discontinuity, using appropriate choice of shape function parameters, the K-FEM passes weak patch tests and therefore the convergence is guaranteed [5]. The basic concepts and advances of the K-FEM have been presented in several papers [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Kriging-Based Timoshenko Beam Element for Static and Free Vibration Analyses

Wong

Syamsoeyadi²

2011

ced

View full text Add to dashboard Cite

An enhancement of the finite element method using Kriging interpolation (K-FEM) has been recently proposed and applied to solve one-and two-dimensional linear elasticity problems. The key advantage of this innovative method is that the polynomial refinement can be performed without adding nodes or changing the element connectivity. This paper presents the development of the K-FEM for static and free vibration analyses of Timoshenko beams. The transverse displacement and the rotation of the beam are independently approximated using Kriging interpolation. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. In an attempt to eliminate the shear locking, the selective-reduced integration technique is utilized. The developed beam element is tested to several static and free vibration problems. The results demonstrate the excellent performance of the developed element.

show abstract

“…In other words, the Kriging-based elements are nonconforming. The issue of non-conformity and its effects on the convergence characteristics has been addressed in Reference [4]. It was found that despite the non-conformity, solutions of the K-FEM with a quartic spline correlation function and appropriate Kriging parameters always converge to the exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique

Tjong¹,

Santoso²,

Sutrisno³

2022

ced

View full text Add to dashboard Cite

Kriging-based finite element method (K-FEM) is an enhancement of the conventional finite element method using a Kriging interpolation as the trial solution in place of a polynomial function. In the application of the K-FEM to the Timoshenko beam model, the discrete shear gap (DSG) technique has been employed to overcome the shear locking difficulty. However, the applied DSG was only effective for the Kriging-based beam element with a cubic basis and three element-layer domain of influencing nodes. Therefore, this research examines a modified implementation of the DSG by changing the substitute DSG field from the Kriging-based interpolation to linear interpolation of the shear gaps at the element nodes. The results show that the improved elements of any polynomial degree are free from shear locking. Furthermore, the results of beam deflection, cross-section rotation, and bending moment are very accurate, while the shear force field is piecewise constant.

show abstract

On the Convergence of the Kriging-Based Finite Element Method

Cited by 10 publications

References 18 publications

Generalization of FEM Using Node-Based Shape Functions

Generalization of FEM Using Node-Based Shape Functions

Kriging-Based Timoshenko Beam Element for Static and Free Vibration Analyses

Locking-free Kriging-based Timoshenko Beam Elements using an Improved Implementation of the Discrete Shear Gap Technique

Contact Info

Product

Resources

About