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
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A moving least squares material point method with displacement discontinuity and two-way rigid body coupling
TL;DR: In this article, the Moving Least Squares Material Point Method (MLS-MPM) is used to simulate material cutting, dynamic open boundaries, and two-way coupling with rigid bodies.
Journal ArticleDOI
Data-driven multi-scale multi-physics models to derive process---structure---property relationships for additive manufacturing
Wentao Yan,Stephen Lin,Orion L. Kafka,Yanping Lian,Cheng Yu,Zeliang Liu,Jinhui Yan,Sarah Wolff,Hao Wu,Ebot Ndip-Agbor,Mojtaba Mozaffar,Kornel F. Ehmann,Jian Cao,Gregory J. Wagner,Wing Kam Liu +14 more
TL;DR: In this article, the authors propose data-mining as an effective solution to understand the underlying physical mechanisms of additive manufacturing (AM) processes and material compositions, structures and properties in end-use products with arbitrary shapes.
Journal ArticleDOI
Free mesh method: A new meshless finite element method
Genki Yagawa,Tomonori Yamada +1 more
TL;DR: In this article, a new meshless finite element method, named as the Free Mesh Method, is proposed, where some temporary triangular elements are set around a node, i.e. a current central node.
Engineering Analysis with Boundary Elements
TL;DR: In this paper, a contour integral method is used to convert the nonlinear eigenproblems caused by the boundary element method into ordinary eigen-problems, and all fictitious eigenfrequencies corresponding to the related interior problem are observed.
References
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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.
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