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
Automatic LEFM crack propagation method based on local Lepp-Delaunay mesh refinement
TL;DR: A numerical method for 2D LEFM crack propagation simulation that uses a Lepp-Delaunay based mesh refinement algorithm for triangular meshes which allows both the generation of the initial mesh and the local modification of the current mesh as the crack propagates.
Journal ArticleDOI
Meshless local radial point interpolation (MLRPI) on the telegraph equation with purely integral conditions
TL;DR: In this paper, the meshless local radial point interpolation (MLRPI) method is applied to the one-dimensional telegraph equation with purely integral conditions, which does not require any background integration cells but it requires all integrations be carried out locally over small quadrature domains of regular shapes.
Journal ArticleDOI
Geometric Issues in Computer Aided Design/Computer Aided Engineering Integration
TL;DR: This paper critically examines and compares known mesh-based and meshfree approaches to CAD/CAE integration, focusing on the basic tasks and components required for building fully integrated engineering applications.
Journal ArticleDOI
Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems
TL;DR: In this paper, stable and convergent nodal integration methods are presented and applied to transient and large deformation impact problems, and an eigenvalue analysis of the methods is also provided.
Journal ArticleDOI
Finite deformation elasto-plastic modelling using an adaptive meshless method
Zahur Ullah,Charles E. Augarde +1 more
TL;DR: In this article, an adaptive meshless approach for nonlinear solid mechanics is developed based on the element free Galerkin method, which is extended for linear elasto-static problems.
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