Imposing essential boundary conditions in the natural element method by means of density-scaled?-shapes

Cueto, Elías; Doblaré, M.; Gracia, Luis

doi:10.1002/1097-0207(20001010)49:4<519::aid-nme958>3.0.co;2-0

Cited by 91 publications

(86 citation statements)

References 32 publications

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“…In particular in the Natural Element Method (NEM) [20] the basis functions are constructed using the Delaunay triangulation and the Voronoi diagram of the nodes [21]. These basis functions are non-negative and can be strictly interpolant on the boundary [22]. Thanks to this property the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations, like in FEM implementations.…”

Section: Introductionmentioning

confidence: 99%

A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

et al. 2014

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The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree methods can better handle large deformations and have shown encouraging results. However, viscoplastic flows are nearly incompressible, which poses a challenge to meshfree methods. In this paper we propose a simple model of viscoplasticity, where both the pressure and velocity fields are discretized with maximum entropy approximants. The inf-sup condition is circumvented with a numerically consistent stabilized formulation that involves the gradient of the pressure. The performance of the method is studied in some benchmark problems including metal forming and orthogonal cutting.

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Section: Introductionmentioning

confidence: 99%

A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

et al. 2014

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“…The proposed modification of the shape function computation breaks the duality (only outside the domain) between the Voronoi cells and the triangulation. However, it has been demonstrated that it leads to more accurate results [39], with comparable levels of accuracy on both convex and non-convex domains. For further insight on this topic, consider a situation similar to that in Figure 11.…”

Section: α-Shapes Based Natural Element Methodsmentioning

confidence: 99%

“…In [39], a modification was introduced in the NEM. This modification is based on the concept of α-shapes.…”

Section: α-Shapes Based Natural Element Methodsmentioning

confidence: 99%

“…The α-NEM constructs the model entirely in terms of nodes, and no explicit information (i.e., via a CAD-description) is required for the domain. If the nodes are judiciously placed, which means no more than they can actually reproduce the shape of the domain in the α-shape sense, it has been demonstrated [39] that the shape function is strictly an interpolant along any essential boundary. On the other hand, NEM is based on a PSLG in 2-d. To preserve the Delaunay property, a conforming triangulation is required for non-convex domains which involves the introduction of additional (Steiner) points that are not user-controlled.…”

Section: α-Shapes Based Natural Element Methodsmentioning

confidence: 99%

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Overview and recent advances in natural neighbour galerkin methods

Cueto

Sukumar

Calvo

et al. 2003

ARCO

Self Cite

132

119

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SummaryIn this paper, a survey of the most relevant advances in natural neighbour Galerkin methods is presented. In these methods (also known as natural element methods, NEM), the Sibson and the Laplace (non-Sibsonian) interpolation schemes are used as trial and test functions in a Galerkin procedure. Natural neighbour-based methods have certain unique features among the wide family of so-called meshless methods: a well-defined and robust approximation with no user-defined parameters on non-uniform grids, and the ability to exactly impose essential (Dirichlet) boundary conditions are particularly noteworthy. A comprehensive review of the method is conducted, including a description of the Sibson and the Laplace interpolants in two-and three-dimensions. Application of the NEM to linear and non-linear problems in solid as well as fluid mechanics is studied. Other issues that are pertinent to the vast majority of meshless methods, such as numerical quadrature, imposing essential boundary conditions, and the handling of secondary variables are also addressed. The paper is concluded with some benchmark computations that demonstrate the accuracy and the key advantages of this numerical method.

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“…α-Shape equally offer highly precise linear interpolation over non-convex margins (Cueto, Doblare, & Gracia, 2000). Lately, within the field of image segmentation, boundaries reconstruction from non-optimal or noisy image segmentation has been efficient, courtesy of α-Shape (Meine, Köthe, & Stelldinger, 2009).…”

Section: Alpha Shape (α-Shape)mentioning

confidence: 99%

Hybrid Methodology for Image Segmentation Based on Active Contour Module and Alpha-Shape Theory

Al-Tamimi¹

2016

MAS

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The concept of the active contour model has been extensively utilized in the segmentation and analysis of images. This technology has been effectively employed in identifying the contours in object recognition, computer graphics and vision, biomedical processing of images that is normal images or medical images such as Magnetic Resonance Images (MRI), X-rays, plus Ultrasound imaging. Three colleagues, Kass, Witkin and Terzopoulos developed this energy, lessening "Active Contour Models" (equally identified as Snake) back in 1987. Being curved in nature, snakes are characterized in an image field and are capable of being set in motion by external and internal forces within image data and the curve itself in that order. The present study proposes the use of a hybrid image segmentation technique to acquire precise segmentation outcomes, while engaging "Alpha Shape (α-Shape)" in supposition to derive the original contour, followed by a refining process through engaging a conventional active contour model. Empirical results show high potential in the suggested computational method. Trials indicate that the primary contour is capable of being precisely set next to the objective contour and effectively have these objective contours extracted, devoid of any contour instigation. Some of the benefits associated with the novel hybrid contour include minimized cost of computation, enhanced anti-jamming capability, as well as enlarged utilization array of snake model.

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Imposing essential boundary conditions in the natural element method by means of density-scaled?-shapes

Cited by 91 publications

References 32 publications

A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

Overview and recent advances in natural neighbour galerkin methods

Hybrid Methodology for Image Segmentation Based on Active Contour Module and Alpha-Shape Theory

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