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Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
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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
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Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws
TL;DR: In this paper, a meshless numerical method, called general particle dynamics (GPD), is proposed to simulate samples of rock-like brittle heterogeneous material containing four preexisting flaws under uniaxial compressive loads.
Journal ArticleDOI
Coupling of soil deformation and pore fluid flow using material point method
Samila Bandara,Kenichi Soga +1 more
TL;DR: In this paper, a numerical procedure based on material point method (MPM) is proposed to solve fully coupled dynamic problems that undergo large deformations in saturated soils, where two sets of Lagrangian material points are used to represent soil skeleton and pore water layers.
Journal ArticleDOI
Moving kriging interpolation and element‐free Galerkin method
TL;DR: In this paper, a new formulation of the element-free Galerkin (EFG) method is presented, which eliminates this shortcoming through the moving kriging (MK) interpolation.
Journal ArticleDOI
The meshless finite element method
TL;DR: Idelsohn and Rodolfo as mentioned in this paper presented a model of the Instituto de Desarrollo Tecnologico para la Industria Quimica (ITE-QUIMICA).
Journal ArticleDOI
Adaptivity for structured meshfree particle methods in 2D and 3D
Timon Rabczuk,Ted Belytschko +1 more
TL;DR: In this paper, the implementation of h-adaptivity for mesh-free particle methods within a structured framework is described, where the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions.
References
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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.
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