Journal ArticleDOI
A natural neighbour-based moving least-squares approach for the element-free Galerkin method
TLDR
In this article, a new concept for the automatic adjustment of nodal influence domains in the EFG method is presented in order to obtain an efficiency similar to the NEM, which is based on the definition of natural neighbours for each meshless node which can be determined from a Voronoi diagram of the nodal set-up.Abstract:
The element-free Galerkin method (EFG) and the natural element method (NEM) are two well known and widely used meshless methods. Whereas the EFG method can represent moving boundaries like cracks only by modifying the weighting functions the NEM requires an adaptation of the nodal set-up. But on the other hand the NEM is computationally more efficient than EFG. In this paper a new concept for the automatic adjustment of nodal influence domains in the EFG method is presented in order to obtain an efficiency similar to the NEM. This concept is based on the definition of natural neighbours for each meshless node which can be determined from a Voronoi diagram of the nodal set-up. In this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction. In the paper we show that this concept leads, especially for problems with grading node density, to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort. Copyright © 2006 John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares
Thomas Most,Christian Bucher +1 more
TL;DR: In this paper, two new concepts for the classical moving least squares (MLS) approach are presented, one is an interpolating weighting function, which leads to MLS shape functions fulfilling the interpolation condition exactly.
Journal ArticleDOI
Mixed meshless local Petrov---Galerkin collocation method for modeling of material discontinuity
TL;DR: In this paper, a mixed meshless local Petrov-Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures.
Journal ArticleDOI
Mixed meshless formulation for analysis of shell-like structures
Jurica Sorić,Tomislav Jarak +1 more
TL;DR: An efficient mixed meshless computational method based on the Local Petrov-Galerkin approach for analysis of plate and shell structures is presented in this paper, allowing the use of complete three-dimensional constitutive equations, and exact shell geometry can be described.
Journal ArticleDOI
Dynamic elastoplastic analysis using the meshless local natural neighbor interpolation method
TL;DR: In this paper, a meshless local natural neighbor interpolation (MLNNI) method was proposed to perform the dynamic analysis of elastoplastic structures under plane stress or plane strain conditions.
Journal ArticleDOI
Mesh free Galerkin method based on natural neighbors and conformal mapping
TL;DR: In this work, a robust mesh free method has been presented for the analysis of two dimensional problems that takes into account the nonuniform nodal discretization in the element free Galerkin formulation.
References
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Book
Finite Element Procedures
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
Book
The stress analysis of cracks handbook
TL;DR: The Stress Analysis of Cracks Handbook as mentioned in this paper provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations, along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more.
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Proceedings ArticleDOI
A two-dimensional interpolation function for irregularly-spaced data
TL;DR: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface as discussed by the authors, and it is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
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A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
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