Numerical Formulation and Application of Polygonal Finite Elements (2009)
ABSTRACT: In this paper, we develop conforming Galerkin approximations on polygonal elements. A notable contribution is the use of Laplace (natural-neighbor, nn) basis functions on a canonical...
Maximum Entropy Coordinates for Arbitrary Polytopes (2009)
Pierre Alliez, Szymon Rusinkiewicz, K. Hormann, N. Sukumar
Barycentric coordinates can be used to express any point inside a triangle as a unique convex combination of the triangle’s vertices, and they provide a convenient way to linearly interpolate data...
DERIVING THE CONTINUITY OF MAXIMUM-ENTROPY BASIS FUNCTIONS VIA VARIATIONAL ANALYSIS ∗ (2008)
Abstract. In this paper, we prove the continuity of maximum-entropy basis functions using Variational Analysis techniques. The use of information-theoretic variational principles to derive basis...
N. Sukumar, E. Béchet, N. Moës
A numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method and the fast marching method. In...
Received (Day Month Year) (2008)
In this paper, a conforming polygonal finite element method is applied to problems in linear elasticity. Meshfree natural neighbor (Laplace) shape functions are used to construct conforming...
Extended Finite Element Method on (2008)
Quadtree Meshes, A. Tabarraei, N. Sukumar
In this paper, we present mesh-independent modeling of discontinuous fields on polygonal and quadtree finite element meshes. This approach falls within the class of extended and generalized finite...
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2008)
N. Sukumar, N. Moes, B. Moran, T. Belytschko
Extended nite element method for three-dimensional crack modelling
Abstract. In this paper, we prove the continuity of maximum-entropy basis functions using variational analysis techniques. The use of information-theoretic variational principles to derive basis...
170 An element-free Galerkin method for three-dimensional fracture mechanics (2008)
N. Sukumar, B. Moran, T. Black, T. Belytschko
Abstract The application of a coupled ®nite element± element-free Galerkin (EFG) method to problems in threedimensional fracture is presented. The EFG method is based on moving least square (MLS)...
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2008)
N. Sukumar, B. Moran, A. Yu Semenov, V. V. Belikov
Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data tting and smoothing. The numerical implementation of natural neighbour co-ordinates in...
Finite Element-Based Model for Crack Propagation in Polycrystalline Materials ∗ (2008)
In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element...
This paper is an overview of recent developments in the construction of finite element interpolants, which are C 0-conforming on polygonal domains. In 1975, Wachspress proposed a general method for...
J.-B.: Deriving the continuity of maximum-entropy basis functions via variational analysis (2008)
Abstract. In this paper, we prove the continuity of maximum-entropy basis functions using variational analysis techniques. The use of information-theoretic variational principles to derive basis...
Extended finite element method on polygonal and quadtree meshes (2008)
In this paper, we present mesh-independent modeling of discontinuous fields on polygonal and quadtree finite element meshes. This approach falls within the class of extended and generalized finite...
Computational multiscale modelling of heterogeneous material layers (2008)
C. B. Hirschberger, S. Ricker, P. Steinmann, N. Sukumar
A computational homogenization procedure for a material layer that possesses an underlying heterogeneous microstructure is introduced within the framework of finite deformations. The macroscopic...
N. Sukumar, B. Moran, T. Belytschko
International Journal for Numerical Methods in Engineering
N. Sukumar, N. Moes, T. Belytschko
A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (Osher and Sethian,...
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2007)
Ted Belytschko, U Parimi, Nicolas Moes, N. Sukumar, Shuji Usui
Structured extended nite element methods for solids de ned by implicit surfaces
A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the eXtended Finite Element Method (X-FEM) to the Fast Marching Method...
A two-dimensional numerical model for crack propagation through polycrystalline microstructures is proposed. The extended finite element method (X-FEM) [1] is adopted as the computational method of...
Partition Of Unity Enrichment For Bimaterial (2007)
Interface Cracks Sukumar, N. Sukumar, Z. Suo, Z. Y. Huang
References
Sukumar And Moran, N. Sukumar, B. Moran
Natural neighbor coordinates (Sibson, 1980) are optimum weighted-average measures for an irregular arrangement of nodes in R . Farin (1990b) used the notion of B'ezier simplices in natural...
In this paper, an overview of the construction of meshfree basis functions is presented, with particular emphasis on moving least-squares approximants, natural neighbour-based polygonal interpolants,...
Quadtree is a hierarchical data structure that is well-suited for h-adaptive mesh refinement. Due to the presence of hanging nodes, classical shape functions are non-conforming on quadtree meshes. In...
Deriving the continuity of maximum-entropy basis functions via variational analysis (2007)
In this paper, we prove the continuity of maximum-entropy basis functions using variational analysis techniques. The use of information-theoretic variational principles to derive basis functions is a...
In this paper, an overview of the construction of meshfree basis functions is presented, with particular emphasis on moving least-squares approximants, natural neighbour-based polygonal interpolants,...
Adaptive computations on conforming quadtree meshes (2005)
In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is...
Irregular lattice model for quasistatic crack propagation (2005)
An irregular lattice model is proposed for simulating quasistatic fracture in softening materials. Lattice elements are defined on the edges of a Delaundy tessellation of the medium. The dual...
Adaptive computations on conforming quadtree meshes (2005)
In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is...
Finite element-based model for crack propagation in polycrystalline materials (2004)
In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element...
POLYGONAL INTERPOLANTS: CONSTRUCTION AND ADAPTIVE COMPUTATIONS ON QUADTREE MESHES (2004)
N. Sukumar, A. Tabarraei, N. Sukumar, A. Tabarraei
Abstract. In this paper, recent advances in meshfree approximations, computational geometry, and computer graphics are described towards the development of polygonal interpolants. A particular and...
Conforming polygonal finite elements (2004)
In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid...
Construction of polygonal interpolants: A maximum entropy approach (2004)
In this paper, we establish a link between maximizing (information-theoretic) entropy and the construction of polygonal interpolants. The determination of shape functions on n-gons (n>3) leads to...
The extended finite element method (X-FEM) is a numerical method for modeling strong (displacement) as well as weak (strain) discontinuities within a standard finite element framework. In the X-FEM,...
Meshless Methods and Partition of Unity Finite Elements (2003)
In this paper, meshless methods and partition of unity based finite element methods are reviewed. In meshless methods, the approximation is built without the explicit connectivity information between...
In Part I (Sukumar and Prevost 2003), we described the implementation of the extended finite element method (X-FEM) within Dynaflow , a standard finite element package. In our implementation, we...
Meshless methods and partition of unity finite elements (2003)
N. Sukumar, J. Dolbow, A. Devan, J. Yvonnet, F. Chinesta, D. Ryckelynck, ...
ABSTRACT. This paper encompasses the main conclusions obtained in the mini-symposium New and Advanced Numerical Strategies in Forming Processes Simulation, held during the 6th International ESAFORM...
Partition of unity enrichment for bimaterial interface cracks (2003)
N. Sukumar, Z. Y. Huang, Z. Suo
Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two-dimensional near-tip asymptotic displacement functions are added to the...
Meshless methods and partition of unity finite elements (2003)
ABSTRACT: In this paper, meshless methods and partition of unity based finite element methods are reviewed. In meshless methods, the approximation is built without the explicit connectivity...
Partition of unity enrichment for bimaterial interface cracks (2003)
N. Sukumar, Z. Y. Huang, Z. Suo
Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two-dimensional near-tip asymptotic displacement functions are added to the...
this paper, we focus on the Laplace interpolant with a two-fold objective: #rst, to unify the previous developments related to the Laplace interpolant and to indicate its ties to some well-known...
Brittle fracture in polycrystalline microstructures with the extended finite element method (2002)
N. Sukumar, D. J. Srolovitz, T. J. Baker, John Wiley
extended nite element method
Natural neighbor galerkin methods (2001)
N. Sukumar, B. Moran, A. Yu Semenov, V. V. Belikov
Natural neighbor coordinates (Sibson coordinates) is a well-known interpolation scheme for multivariate data fitting and smoothing. The numerical implementation of natural neighbor coordinates in a...
Sibson and non-Sibsonian interpolants for elliptic partial differential equations (2001)
The Natural Element Method (NEM) is a meshless Galerkin method which has shown promise in the area of computational mechanics. In earlier applications of NEM [1--3], natural neighbor (Sibson)...
Biswal, BK, Sukumar, N, Vijayan, M
The structure analyses of orthorhombic lysozyme grown at pH 6.5 and its low-humidity variant are reported. The structures of the same form grown at pH 9.5 and 4.5 and that of the lowhumidity variant...
Biswal, BK, Sukumar, N, Vijayan, M
The structure analyses of orthorhombic lysozyme grown at pH 6.5 and its low-humidity variant are reported. The structures of the same form grown at pH 9.5 and 4.5 and that of the lowhumidity variant...
Dispersive Properties of the Natural Element Method (2000)
D. Bueche, N. Sukumar, B. Moran
The Natural Element Method (NEM) is a mesh-free numerical method for the solution of partial differential equations. In the natural element method, natural neighbor coordinates, which are based on...
An Extended Finite Element Method (x-Fem) For Two- And Three-Dimensional Crack Modeling (2000)
N. Moes, N. Moes, N. Sukumar, N. Sukumar, B. Moran, B. Moran, ...
The finite element method is now well established as a robust and reliable numerical technique in many areas of solid mechanics. There are however problems where the use of the finite element method...
Structures of orthorhombic lysozyme grown at basic pH and its low-humidity variant (1999)
Sukumar, N, Biswal, BK, Vijayana, M
The structures of orthorhombic lysozyme grown at basic pH and its low-humidity variant have been solved and refined at 1.9 and 2.0 \AA resolution, respectively. A comparison of the native structure...
Structures of orthorhombic lysozyme grown at basic pH and its low-humidity variant (1999)
Sukumar, N, Biswal, BK, Vijayana, M
The structures of orthorhombic lysozyme grown at basic pH and its low-humidity variant have been solved and refined at 1.9 and 2.0 \AA resolution, respectively. A comparison of the native structure...
C¹ natural neighbor interpolant for partial differential equations (1999)
Natural neighbor coordinates [20] are optimum weighted-average measures for an irregular arrangement of nodes in Rn. [26] used the notion of Bézier simplices in natural neighbor coordinates Φ to...
Effect of Boundary Conditions on Cellular Automata that Classify Density (1998)
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather...
The Natural Element Method in Solid Mechanics (1998)
N. Sukumar, B. Moran, T. Belytschko
The application of the Natural Element Method (NEM) 1; 2 to boundary value problems in two-dimensional small displacement elastostatics is presented. The discrete model of the domain consists of a...
Delarue, M., Boulé, J.B., Lescar, J., Expert-Bezançon, N., Jourdan, N., Sukumar, N., ...
The crystal structure of the catalytic core of murine terminal deoxynucleotidyltransferase (TdT) at 2.35 Å resolution reveals a typical DNA polymerase β-like fold locked in a closed form. In...
Delarue, M., Boulé, J.B., Lescar, J., Expert-Bezançon, N., Jourdan, N., Sukumar, N., ...
The crystal structure of the catalytic core of murine terminal deoxynucleotidyltransferase (TdT) at 2.35 Å resolution reveals a typical DNA polymerase β-like fold locked in a closed form. In...
Crystal structure of human intrinsic factor: Cobalamin complex at 2.6-Å resolution
Mathews, F. S., Gordon, M. M., Chen, Z., Rajashankar, K. R., Ealick, S. E., Alpers, D. H., ...
The structure of intrinsic factor (IF) in complex with cobalamin (Cbl) was determined at 2.6-Å resolution. The overall fold of the molecule is that of an α6/α6 barrel. It is a two-domain protein,...