Numerical solution of functionally graded materials based on radial basis reproducing kernel particle method

2020 ◽  
Vol 111 ◽  
pp. 32-43 ◽  
Author(s):  
Zheng Liu ◽  
Gaofeng Wei ◽  
Zhiming Wang
Keyword(s):  
Numerical Solution ◽  
Functionally Graded Materials ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Functionally Graded ◽  
Reproducing Kernel Particle Method ◽  
Graded Materials ◽  
Radial Basis ◽  
Reproducing Kernel Particle

Numerical Analysis of Functionally Graded Materials Using Reproducing Kernel Particle Method

2019 ◽  
Vol 11 (06) ◽  
pp. 1950060 ◽  
Author(s):  
Zheng Liu ◽  
Gaofeng Wei ◽  
Zhiming Wang
Keyword(s):  
Functionally Graded Materials ◽  
Control Parameter ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Functionally Graded ◽  
Reproducing Kernel Particle Method ◽  
Graded Materials ◽  
Node Distribution ◽  
Penalty Factor ◽  
Reproducing Kernel Particle

The reproducing kernel particle method (RKPM) for the elastic mechanical problems of the functionally graded materials (FGM) is proposed in this paper. The corresponding formulae of the RKPM for the FGM are derived. Furthermore, the control parameter of influence domain radius, penalty factor and different node distribution on the calculation accuracy are discussed. The different functional gradient exponents of the FGM are analyzed. The numerical results illustrate that the RKPM is correct and effective to solve the elastic mechanical problems of the FGM.

The Meshless Method for Numerical Solution of Modified Equal Width Wave (MEW) Equation

2011 ◽  
Vol 101-102 ◽  
pp. 1130-1133
Author(s):  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Variational Method ◽  
Numerical Solution ◽  
Meshless Method ◽  
Penalty Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Numerical Examples ◽  
Discrete Equations ◽  
Reproducing Kernel Particle

The reproducing kernel particle method (RKPM) is used in this paper to find the numerical solution of modified equal width wave (MEW) equation. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. The effectiveness of the RKPM for the modified equal width equation is investigated by two numerical examples in this paper.

Meshless Method for the Numerical Solution of a Kind of Linear Hyperbolic Equations

2011 ◽  
Vol 101-102 ◽  
pp. 586-590
Author(s):  
Hai Na Sun ◽  
Rong Jun Cheng ◽  
Hong Xia Ge
Keyword(s):  
Numerical Solution ◽  
Reproducing Kernel ◽  
Hyperbolic Equations ◽  
Particle Method ◽  
Two Dimensional ◽  
Reproducing Kernel Particle Method ◽  
Hyperbolic Problems ◽  
Linear Hyperbolic Equation ◽  
Discrete Equations ◽  
Reproducing Kernel Particle

The present paper deals with the numerical solution of two-dimensional linear hyperbolic equation using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations and the essential boundary conditions that are enforced by the penalty method. The effectiveness RKPM for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.

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