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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A numerical method with a posteriori error estimation for determining the path taken by a propagating crack
Thomas J. Stone,Ivo Babuška +1 more
TL;DR: In this paper, the authors proposed a method for predicting the path taken by a propagating crack under general loading in a two-dimensional domain using smooth curves to model the crack, and an a posteriori error estimate for the difference between the computed crack and the true crack is developed.
Journal ArticleDOI
A new SPH-based continuum framework with an embedded fracture process zone for modelling rock fracture
TL;DR: In this article, a new computational approach combining the Smooth Particle Hydrodynamics and a constitutive model that possesses an intrinsic length scale is proposed for modelling rock fracture, where a continuum-based size-dependent constitutive models with an embedded fracture process zone described by a cohesive model is adopted for modelling strain localisation in geomaterials.
Mid-frequency vibro-acoustic modelling: challenges and potential solutions
TL;DR: In this paper, a wave-based prediction technique for (coupled) vibro-acoustic analysis that is being developed at the KULeuven Noise and Vibration Research group is presented.
Journal ArticleDOI
Static, dynamic and buckling analyses of 3D FGM plates and shells via an isogeometric-meshfree coupling approach
TL;DR: In this paper, a mesh-free IGA and mesh free coupling approach is proposed to investigate the static, dynamic and buckling behaviors for plates and shells of functionally graded material (FGM).
Journal ArticleDOI
Meshless Method for Crack Analysis in Functionally Graded Materials with Enriched Radial Base Functions
Pihua Wen,M.H. Aliabadi,Y.W. Liu +2 more
TL;DR: In this paper, the element-free Galerkin method with enriched radial base function was applied to two-dimensional fracture mechanics in functionally graded materials and a significant improvement of accuracy was achieved.
References
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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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