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 cell-based smoothed radial point interpolation method (CS-RPIM) for static and free vibration of solids
TL;DR: A cell-based smoothed radial point interpolation method (CS-RPIM) based on the generalized gradient smoothing operation is proposed for static and free vibration analysis of solids.
Journal ArticleDOI
Meshfree modeling and homogenization of 3D orthogonal woven composites
L. Li,Pihua Wen,M.H. Aliabadi +2 more
TL;DR: In this article, a mesh-free method for 3D orthogonal woven fabric composite elastic moduli is proposed. But the mesh-based method is not suitable for mesh-only models.
Journal ArticleDOI
Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov–Galerkin method
TL;DR: In this article, a meshless local Petrov-Galerkin (MLPG) method was used to analyze plane strain static thermoelastic deformations of a simply supported functionally graded (FG) plate.
Reference EntryDOI
Damage, Material Instabilities, and Failure
TL;DR: In this article, the authors discuss the implications of strain softening, which starts at a certain level of damage accumulation, as regards important notions such as material stability and ellipticity.
Journal ArticleDOI
Design sensitivity analysis and optimization of nonlinear transient dynamics
Nam H. Kim,Kyung K. Choi +1 more
TL;DR: In this article, a shape design sensitivity analysis (DSA) and optimization of structural transient dynamics are proposed for the finite deformation elastoplastic materials under impact with a rigid surface.
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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