Journal ArticleDOI
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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Journal ArticleDOI
Dynamic fracture using element-free galerkin methods
Ted Belytschko,Mazen R. Tabbara +1 more
TL;DR: The element-free Galerkin method for dynamic crack propagation is described and applied to several problems as mentioned in this paper, which facilitates the modelling of growing crack problems because it does not require remeshing; the growth of the crack is modelled by extending its surfaces.
Journal ArticleDOI
A generalized finite element method for the simulation of three-dimensional dynamic crack propagation
TL;DR: In this article, a partition of unity finite element method and hp-cloud method for dynamic crack propagation is presented, where the approximation spaces are constructed using a partition-of-unity (PU) and local enrichment functions.
Journal ArticleDOI
A corrective smoothed particle method for boundary value problems in heat conduction
TL;DR: In this paper, a Corrective Smoothed Particle Method (CSPM) is proposed to solve the problem of particle deficiency at boundaries, which is a shortcoming in Standard Smoothing Particle Hydrodynamics (SSPH).
Journal ArticleDOI
Local maximum-entropy approximation schemes : a seamless bridge between finite elements and meshfree methods
Marino Arroyo,Michael Ortiz +1 more
TL;DR: A one‐parameter family of approximation schemes that bridges continuously two important limits: Delaunay triangulation and maximum‐entropy (max‐ent) statistical inference are presented.
Proceedings ArticleDOI
Meshfree particle method
Huafeng Liu,Pengcheng Shi +1 more
TL;DR: This work presents a new computational paradigm, the meshfree particle method, where the object representation and the numerical calculation are purely based on the nodal points and do not require the meshing of the analysis domain, and can naturally handle large deformation and domain discontinuity issues.
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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