Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
Reads0
Chats0
TLDR
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.Abstract:
An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.read more
Citations
More filters
Journal ArticleDOI
hp-Meshless cloud method
TL;DR: The improvements in the methodology, in particular the introduction of spectral degrees of freedom, result in a fast and accurate method, significantly more efficient than the Finite Element Method or Element Free Galerkin Method.
Journal ArticleDOI
Some recent results and proposals for the use of radial basis functions in the BEM
TL;DR: In this article, a survey of radial basis functions (rbfs) for the BEM and related algorithms such as the method of fundamental solutions is presented. And a number of proposals are given for future applications of rbfs for interpolation and the solution of boundary integral equations and the application of Kansa's method to develop new rbf based coupled domain-boundary approximation methods.
Journal ArticleDOI
The method of finite spheres
Suvranu De,Klaus-Jürgen Bathe +1 more
TL;DR: The method of finite spheres as discussed by the authors is a special case of the meshless local Petrov-Galerkin (MLPG) procedure, where the nodes are placed and the numerical integration is performed without a mesh.
Journal ArticleDOI
Fracture modeling using meshless methods and level sets in 3D: Framework and modeling
TL;DR: In this article, a numerical framework is developed for 3D fracture modeling where a meshless method, the element-free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution.
Journal ArticleDOI
A meshfree method based on the local partition of unity for cohesive cracks
Timon Rabczuk,Goangseup Zi +1 more
TL;DR: In this paper, a mesh-free method based on the local partition of unity for cohesive cracks is presented, where cracks are described by a jump in the displacement field for particles whose domain of influence is cut by the crack.
References
More filters
Journal ArticleDOI
Smoothed particle hydrodynamics: Theory and application to non-spherical stars
R. A. Gingold,Joseph J Monaghan +1 more
Journal ArticleDOI
Theory of Elasticity (3rd ed.)
Journal ArticleDOI
Surfaces generated by moving least squares methods
Peter Lancaster,K. Salkauskas +1 more
TL;DR: In this article, an analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented, in particular theorems concerning the smoothness of interpolants and the description of m. l.s. processes as projection methods.
Journal ArticleDOI
Generalizing the finite element method: Diffuse approximation and diffuse elements
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
Related Papers (5)
A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Satya N. Atluri,T. Zhu +1 more