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
On generation of lumped mass matrices in partition of unity based methods
Hong Zheng,Yongtao Yang +1 more
TL;DR: In this paper, the authors proposed a lumped mass matrix is strictly diagonal and can yield the results in agreement with the consistent mass matrix, but has more excellent dynamic property than the latter.
Journal ArticleDOI
Meshfree, probabilistic determination of point sets and support regions for meshless computing
TL;DR: New algorithms are presented for the determination of point sets and associated support regions that can then be used in meshless computing methods, which are probabilistic in nature so that they are totally meshfree.
Journal ArticleDOI
Subdomain radial basis collocation method for heterogeneous media
TL;DR: A simple subdomain strong form collocation method, in which the approximation in each subdomain is constructed separately, and it is shown that both Neumann and Dirichlet boundary conditions should be imposed on the interface to achieve the optimum convergence.
Journal ArticleDOI
Vibration analysis of CNT-reinforced functionally graded rotating cylindrical panels using the element-free kp-Ritz method
TL;DR: In this paper, the analysis of free vibration of carbon nanotube reinforced rotating cylindrical panels is performed by using the element-free kernel particle Ritz method or in short the kp-Ritz method.
Journal ArticleDOI
Coupling of the meshfree and finite element methods for determination of the crack tip fields
TL;DR: In this paper, a new concurrent simulation technique was developed to couple the meshfree method with the finite element method (FEM) for the analysis of crack tip fields, which can take advantage of both the mesh-free method and FEM but at the same time can overcome their shortcomings.
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