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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Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes
TL;DR: In this article, a unified implicit stress update algorithm for elastoplastic and elasto-viscoplastic constitutive equations for metals submitted to large deformations is presented.
Journal ArticleDOI
Extended meshfree methods without branch enrichment for cohesive cracks
TL;DR: In this paper, an extended meshless method for both static and dynamic cohesive cracks is proposed, which does not need any crack tip enrichment to guarantee that the crack closes at the tip.
Journal ArticleDOI
Enriched finite elements and level sets for damage tolerance assessment of complex structures
Stéphane Bordas,Brian Moran +1 more
TL;DR: In this article, an extended finite element method (X-FEM) was used to solve complex three-dimensional industrial fracture mechanics problems through combination of an object-oriented (C++) research code and a commercial solid modeling/finite element package (EDS-PLM/I-DEAS®).
Journal ArticleDOI
Stabilized conforming nodal integration in the natural-element method
TL;DR: In this paper, a stabilized conforming nodal integration scheme is implemented in the natural neighbor method in conjunction with non-Sibsonian interpolation, and the shape functions and the integration scheme are defined through use of first-order Voronoi diagrams.
Journal ArticleDOI
Material Point Method for Coupled Hydromechanical Problems
TL;DR: In this paper, a soil-pore fluid coupled MPM algorithm based on Biot's mixture theory is proposed for solving hydromechanical interaction problems that include changes in water table location with time.
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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