High-accuracy discretization methods for solid mechanics
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TL;DR: Novel high-accuracy computational techniques for solid mechanics problems are presented, including fourth-order and arbitrary-order finite difference methods based on Pade-type differencing formulas and a meshless method which uses radial basis functions in a "finite difference" mode.
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Abstract: Novel high-accuracy computational techniques for solid mechanics problems are presented. They include fourth-order and arbitrary-order finite difference methods based on Pade-type differencing formulas and a meshless method which uses radial basis functions in a "finite difference" mode. Some results illustrating high performance of the suggested numerical methods are displayed.
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Citations
Scattered node compact finite difference-type formulas generated from radial basis functions
Grady B. Wright,Bengt Fornberg +1 more
TL;DR: The generalization of compact FD formulas that are proposed for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil nodes small without a similar reduction in accuracy.
356
Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations
Scott A. Sarra
- 01 Jan 2009
TL;DR: This monograph differs from other recent books on meshfree methods in that it focuses only on the MQ RBF while others have focused on meshless methods in general.
Radial basis functions-finite differences collocation and a Unified Formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami's zig-zag theory
TL;DR: In this article, the analysis of static deformations, free vibrations and buckling loads on laminated composite plates is performed by local collocation with radial basis functions in a finite differences framework.
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A local radial basis functions—Finite differences technique for the analysis of composite plates
TL;DR: In this paper, a radial basis function is used to predict the static behavior of thin and thick composite plates, which can be used to solve large engineering problems without the issue of ill-conditioning.
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Numerical methods based on radial basis function-generated finite difference (RBF-FD) for solution of GKdVB equation
TL;DR: The two meshless collocation methods based on radial basis function-generated finite difference (RBF-FD) and global RBF(GRBF) methods to solve the non-linear generalized Korteweg-de Vries-Burgers (GKdVB) equation are developed.
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