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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Reference EntryDOI
Finite Element Methods for Elasticity with Error‐controlled Discretization and Model Adaptivity
Erwin Stein,Marcus Rüter +1 more
TL;DR: The main objective of this chapter is the systematic treatment of error estimation procedures and adaptivity for the linearized and finite elasticity problem covering both global and goal-oriented a posteriori error estimators.
Journal ArticleDOI
Numerical manifold method based on the method of weighted residuals
TL;DR: In this article, the governing equations of the numerical manifold method (NMM) can be derived from a more general method of weighted residuals, which leads to the same result as that derived from the minimum potential energy principle.
Journal ArticleDOI
A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics
TL;DR: In this paper, an enriched Boundary Element Method (BEM) and dual boundary element method (DBEM) approach for accurate evaluation of stress intensity factors (SIFs) in crack problems is presented.
Journal ArticleDOI
On the C1 continuous discretization of non-linear gradient elasticity: A comparison of NEM and FEM based on Bernstein-Bézier patches
TL;DR: In gradient elasticity, the appearance of strain gradients in the free energy density leads to the need of C1 continuous discretization methods, and the isoparametric elements and the NEM show a significantly better performance than the triangular elements.
Journal ArticleDOI
Application of the edge-based gradient smoothing technique to acoustic radiation and acoustic scattering from rigid and elastic structures in two dimensions
TL;DR: In this article, the edge-based smoothed finite element method (ES-FEM) was proposed to solve the exterior structural acoustic problems in unbounded domains, and the well-known Dirichlet-to-Neumann (DtN) map was used to prevent the possible reflections from the far-field.
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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