Reproducing Kernel Particle Method Numerical Modeling of Thin Sheet Superplastic Tension Forming

2007 ◽  
Vol 551-552 ◽  
pp. 303-308 ◽  
Author(s):  
Hong Sheng Liu ◽  
Yu Ying Yang ◽  
Chun Feng Li
Keyword(s):  
Meshless Method ◽  
Reproducing Kernel ◽  
Thin Sheet ◽  
Superplastic Forming ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Forming Process ◽  
Essential Boundary Condition ◽  
Reproducing Kernel Particle ◽  
Superplastic Tension

Superplastic forming has emerged as an important manufacturing process, large deformation always occurs during superplastic forming, time-consuming remeshing is necessary while the finite element method (FEM) is used to analyze metal forming process. Meshless methods with no meshes can avoid this problem and overcome those problems in FEM. In this paper a meshless method based on the reproducing kernel particle method (RKPM) is applied to analyze Magnesium Alloy (MB15) thin sheet superplastic tension forming. A superplastic meshless method modeling program is set up, and background cells are used to compute the integrations in weak form equations and the mixed transformation method (MTM) is used to impose the essential boundary condition exactly. Numerical example demonstrates the effectiveness of the method in superplastic forming.

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.

scholarly journals Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Lei Mu ◽  
Zhi-hong He ◽  
Shi-kui Dong
Keyword(s):  
Heat Transfer ◽  
Meshless Method ◽  
Radiative Heat ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Scattering Medium ◽  
Residual Function ◽  
Participating Media ◽  
Reproducing Kernel Particle

The reproducing kernel particle method (RKPM), which is a Lagrangian meshless method, is employed for the calculation of radiative heat transfer in participating media. In the present method, for each discrete particle (i.e., spatial node) within a local support domain, the approximate formulas of the radiative intensity and its derivatives are constructed by the reproducing kernel interpolation function, and the residual function is obtained when these parameters are substituted into the radiative transfer equation. Then the least-squares point collocation technique (LSPCT) is introduced by minimizing the summation of residual function. Five test cases are considered and quantified to verify the meshless method, including isotropic scattering medium, first-order forward scattering medium, pure absorbing medium, absorbing scattering medium, and absorbing, scattering emitting medium. The results are in good agreement with the benchmark methods, showing the reproducing kernel particle method is an efficient, accurate, and stable method for the calculation of radiative transfer in participating media.

Interpolating Smoothed Particle Method for Elastic Axisymmetrical Problem

2017 ◽  
Vol 09 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Yi Xiao Qin ◽  
Qi Yu Li ◽  
Hong Xiu Du
Keyword(s):  
Meshless Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Energy Principle ◽  
Smoothed Particle ◽  
Minimum Potential ◽  
Reproducing Kernel Particle ◽  
Minimum Potential Energy Principle ◽  
Elastic Mechanics

The interpolating reproducing kernel particle method is a meshless method with discrete points interpolation character. Coupling this method with the minimum potential energy principle of space axisymmetrical problems of elastic mechanics, the interpolating smoothed particle method (ISPM) is formed. The ISPM, which is a meshless method with discrete points interpolation character, can refrain from quadric error of fitting calculation in stress post-processing by obtaining global domain continuous stress fields directly. This method not only has the advantage in directly exerting boundary conditions just like the finite element method, but is also a new numerical method which has greater computational efficiency and precision than it in solving space axisymmetrical problems of elastic mechanics. Numerical examples are given to show the validity of the new meshless method in the paper.

scholarly journals Level set topology optimization with nodally integrated reproducing kernel particle method

2021 ◽  
Vol 385 ◽  
pp. 114016
Author(s):  
Andreas Neofytou ◽  
Tsung-Hui Huang ◽  
Sandilya Kambampati ◽  
Renato Picelli ◽  
Jiun-Shyan Chen ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Reproducing Kernel Particle
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