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
An efficient meshfree method for vibration analysis of laminated composite plates
TL;DR: In this article, a detailed analysis of natural frequencies of laminated composite plates using the mesh-free moving Kriging interpolation method is presented, and the convergence of the method on the natural frequency is also given.
Journal ArticleDOI
Free vibration analysis of thin plates by using a NURBS-based isogeometric approach
TL;DR: In this paper, an isogeometric finite element method is presented for natural frequencies analysis of thin plate problems of various geometries, and the non-uniform rational B-splines (NURBS) basis function is applied for approximation of the thin plate deflection field, as for description of the geometry.
Journal ArticleDOI
Application of essential boundary conditions in mesh-free methods: a corrected collocation method
Gregory J. Wagner,Wing Kam Liu +1 more
Journal ArticleDOI
An enriched finite element method and level sets for axisymmetric two‐phase flow with surface tension
Jack Chessa,Ted Belytschko +1 more
TL;DR: In this paper, a finite element method for axisymmetric two-phase flow problems is presented, which uses an enriched finite element formulation, in which the interface can move arbitrarily through the mesh without remeshing.
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