Generalized nodes and high-performance elements

Tian, Rong; Yagawa, Genki

doi:10.1002/nme.1436

Cited by 62 publications

(59 citation statements)

References 40 publications

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“…Duarte et al [14] have shown that quadratic GFEM elements with shape functions (7) are more computationally efficient than classical TET10 elements. These element types are also studied in [60,61]. However, since in Abaqus we are limited to classical finite elements, we adopt TET4 or TET10 elements for all global meshes.…”

Section: Elements Types In Global and Local Discretizationsmentioning

confidence: 99%

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Gupta

Pereira

Kim

et al. 2012

Engineering Fracture Mechanics

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Kim, D J.; Duarte, C A.; and Eason, T, "Analysis of three-dimensional fracture mechanics problems: A nonintrusive approach using a generalized finite element method" (2012 (structural) and local (crack) scale problems. In the approach presented here, an initial global scale problem is solved by a commercial finite element analysis software, local problems containing 3-D fractures are solved by an hp-adaptive GFEM software and an enriched global scale problem is solved by a combination of the FEM and GFEM softwares. The interactions between the solvers are limited to the exchange of load and solution vectors and does not require the introduction of user subroutines to existing FEM software. As a results, the user can benefit from built-in features of available commercial grade FEM software while adding the benefits of the GFEM for this class of problems. Several threedimensional fracture mechanics problems aimed at investigating the applicability and accuracy of the proposed two-solver methodology are presented.

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Section: Elements Types In Global and Local Discretizationsmentioning

confidence: 99%

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Gupta

Pereira

Kim

et al. 2012

Engineering Fracture Mechanics

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“…A clustered POU function is identically equal to one over part of its support as illustrated in Figures 4 and 5. This property can be used to eliminate the well known linear dependence of generalized finite element shape functions [37,56]. The multigrid method is not directly applicable to the linear system when the stiffness matrix is positive semi-definite [28].…”

Section: Gfem Shape Functions With Clustered Poumentioning

confidence: 97%

Clustered generalized finite element methods for mesh unrefinement, non‐matching and invalid meshes

Duarte

Liszka

Tworzydlo

2006

Numerical Meth Engineering

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SUMMARYIn spite of significant advancements in automatic mesh generation during the past decade, the construction of quality finite element discretizations on complex three-dimensional domains is still a difficult and time demanding task.In this paper, the partition of unity framework used in the generalized finite element method (GFEM) is exploited to create a very robust and flexible method capable of using meshes that are unacceptable for the finite element method, while retaining its accuracy and computational efficiency. This is accomplished not by changing the mesh but instead by clustering groups of nodes and elements. The clusters define a modified finite element partition of unity that is constant over part of the clusters. This so-called clustered partition of unity is then enriched to the desired order using the framework of the GFEM.The proposed generalized finite element method can correctly and efficiently deal with: (i) elements with negative Jacobian; (ii) excessively fine meshes created by automatic mesh generators; (iii) meshes consisting of several sub-domains with non-matching interfaces. Under such relaxed requirements for an acceptable mesh, and for correctly defined geometries, today's automated tetrahedral mesh generators can practically guarantee successful volume meshing that can be entirely hidden from the user. A detailed technical discussion of the proposed generalized finite element method with clustering along with numerical experiments and some implementation details are presented.

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“…The displacements that are described by the drilling and strain DOFs are superimposed on the ordinary ones ( u , v ) that are the translational DOFs. In elastic stress problems, GNT3 is known to be as accurate as quadratic element (12) . In addition, GNT3 can easily be extended to the case of three-dimensional tetrahedral finite element.…”

Section: Generalized Finite Element With Drilling and Strain Dofs (Gnt3)mentioning

confidence: 99%

“…In addition, GNT3 can easily be extended to the case of three-dimensional tetrahedral finite element. According to Tian and Yagawa (12) the displacements of GNT3 are written to be: Here, the superscript I indicates node (1, 2 or 3) of triangular element. …”

Section: Generalized Finite Element With Drilling and Strain Dofs (Gnt3)mentioning

confidence: 99%

“…In this paper, to enhance the accuracy of FMM analysis for all crack deformation modes, a VCCM formulation for the generalized finite element with strain DOFs in addition to the drilling DOFs (GNT3: Generalized Node -Triangle of 3 nodes (12) ) is proposed. First, we describe the formulations of GNT3 and of VCCM for an ordinary linear element.…”

Section: Introductionmentioning

confidence: 99%

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A Virtual Crack Closure-Integral Method for Generalized Finite Element with Drilling and Strain Degrees of Freedoms

Kanda

Okada

Iraha

et al. 2009

JCST

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A virtual crack closure-integral method (VCCM) for the generalized finite element with drilling and strain degrees of freedoms (DOFs) is presented in this paper. Free mesh method (FMM) is one of useful methods for fracture mechanics analysis. However, in FMM, quadratic elements with mid-side nodes cannot be employed due to restrictions arising from its local mesh generation rule around each node. Generalized elements with drilling and strain DOFs which have no mid-side nodes may improve the accuracy in fracture mechanics analysis over the conventional constant strain elements. Present authors have proposed a VCCM for two-dimensional generalized elements with drilling DOFs, in their previous papers. In this paper, in order to improve the accuracy in fracture mechanics analysis further, we present a VCCM for generalized finite element with drilling and strain DOFs. Finally, some numerical examples are presented and it is demonstrated that the generalized element with drilling and strain DOFs has superior accuracy over that with drilling DOFs only.

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Generalized nodes and high-performance elements

Cited by 62 publications

References 40 publications

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Clustered generalized finite element methods for mesh unrefinement, non‐matching and invalid meshes

A Virtual Crack Closure-Integral Method for Generalized Finite Element with Drilling and Strain Degrees of Freedoms

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