Journal ArticleDOI
Analysis of thin plates by the element-free Galerkin method
Petr Krysl,Ted Belytschko +1 more
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TLDR
A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented and it is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids.Abstract:
A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of the C
1 continuity requirements are easily met by EFG since it requires only C
1 weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.read more
Citations
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Journal ArticleDOI
Meshless methods: An overview and recent developments
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.
Journal ArticleDOI
A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach
TL;DR: In this paper, a meshless Galerkin finite element method (GFEM) based on Local Boundary Integral Equation (LBIE) has been proposed, which is quite general and easily applicable to non-homogeneous problems.
Journal ArticleDOI
A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method
T. Zhu,Satya N. Atluri +1 more
TL;DR: In this paper, a modified collocation method using the actual nodal values of the trial function uh(x) is presented, to enforce the essential boundary conditions in the element free Galerkin (EFG) method.
Journal ArticleDOI
The boundary node method for potential problems
TL;DR: The Boundary Node Method (BNM) as discussed by the authors uses a nodal data structure on the bounding surface of a body whose dimension is one less than that of the domain itself.
Journal ArticleDOI
A smoothed finite element method for plate analysis
TL;DR: In this paper, a quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed, where the curvature at each point is obtained by a non-local approximation via a smoothing function.
References
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Book
Theory of plates and shells
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: 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.
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.
Journal ArticleDOI
Multiquadrics--a scattered data approximation scheme with applications to computational fluid-dynamics-- ii solutions to parabolic, hyperbolic and elliptic partial differential equations
TL;DR: In this paper, the authors used MQ as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation, and showed that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.
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