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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The effect of thermally grown oxide on multiple surface cracking in air plasma sprayed thermal barrier coating system
TL;DR: In this paper, the effect of TGO thickness on the strain energy release rate (SERR) was investigated in an air plasma sprayed (APS) thermal barrier coating system (TBCs).
Journal ArticleDOI
Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method
Zhijun Wu,Louis Ngai Yuen Wong +1 more
TL;DR: In this paper, the formation of localized deformation band and failure processes of brittle-ductile materials (coarse and medium marbles) containing pre-existing flaws under various loading conditions are simulated numerically.
Journal ArticleDOI
A new weight‐function enrichment in meshless methods for multiple cracks in linear elasticity
TL;DR: In this paper, a new enriched weight function for meshless methods is proposed for the numerical treatment of multiple arbitrary cracks in two dimensions, which allows a more straightforward implementation and simulation of the presence of multiple cracks, crack branching and crack propagation in a meshless framework without using any of the existing algorithms such as visibility, transparency, and diffraction and without using additional unknowns and additional equations for the evolution of the level-sets.
Journal ArticleDOI
A direct fragmentation method with Weibull function distribution of sizes based on finite- and discrete element simulations
TL;DR: In this article, a direct method is proposed to rapidly fragment bodies during impulse-based discrete element method simulations of multiple body interactions, making use of patterns and size distributions obtained both from experiments, and from numerical models that rigorously compute fragmentation by growing fractures explicitly.
Journal ArticleDOI
A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media
TL;DR: In this paper, the edge-based smoothed finite element method (ES-FEM) is extended to fracture problems in anisotropic media using a specially designed five-node singular crack tip (T5) element.
References
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Smoothed particle hydrodynamics: Theory and application to non-spherical stars
R. A. Gingold,Joseph J Monaghan +1 more
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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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