Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
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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
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Impact Mechanics and High-Energy Absorbing Materials: Review
Pizhong Qiao,Pizhong Qiao,Pizhong Qiao,Mijia Yang,Mijia Yang,Mijia Yang,Florin Bobaru,Florin Bobaru,Florin Bobaru +8 more
TL;DR: A review of impact mechanics and high energy absorbing materials is presented in this paper, which is intended to help the readers in identifying starting points for research in modeling and simulation of impact problems and in designing energy absorbing material and structures.
Comput. Methods Appl. Mech. Engrg.
TL;DR: In this paper, the difference between models (I) and (II) when a(x,x) is a log-normal random process was discussed, and it was shown that the difference is mainly characterized by a scaling factor, which is an exponential function of the degree of perturbation.
Journal ArticleDOI
Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges
TL;DR: In this paper, the free vibration of functionally graded carbon nanotube (FG-CNT) reinforced composite moderately thick rectangular plates with edges elastically restrained against transverse displacements and rotation of the plate cross section is considered.
Journal ArticleDOI
Smooth finite element methods: Convergence, accuracy and properties
TL;DR: In this article, a stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented, where the integration of the stiffness matrix is performed on the boundaries of the finite elements.
Journal ArticleDOI
Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties
TL;DR: In this paper, the local boundary integral formulation for an elastic body with nonhomogeneous material properties is presented, where all nodal points are surrounded by a simple surface centered at the collocation point.
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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