Interpolating Smoothed Particle Method for Elastic Axisymmetrical Problem

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.101-102.1130 ◽

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.

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

Materials Science Forum ◽

10.4028/www.scientific.net/msf.551-552.303 ◽

2007 ◽

Vol 551-552 ◽

pp. 303-308 ◽

Cited By ~ 2

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.

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

Mathematical Problems in Engineering ◽

10.1155/2015/181536 ◽

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.

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A Simplified Linear Consistency Kernel Function in SPH Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.306-308.595 ◽

2006 ◽

Vol 306-308 ◽

pp. 595-600

Author(s):

Fei Xu ◽

Masanori Kikuchi

Keyword(s):

Kernel Function ◽

Reproducing Kernel ◽

Particle Method ◽

Kernel Functions ◽

Reproducing Kernel Particle Method ◽

Sph Method ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Mode 3 ◽

Reproducing Kernel Particle

Smoothed Particle Hydrodynamics (SPH) is a relatively new technique for simulating the dynamic response of solids, especially for high velocity impact and fracture problem. However, closer examination of SPH reveals some severe problems. The major difficulties are: (1) tensile instability; (2) zero-energy mode; (3) boundary deficiency; (4) less accuracy. One solution to these major difficulties with SPH is to improve the consistency of the kernel function. Based on the Reproducing Kernel Particle Method (RKPM), the concept of the proposed simplified linear consistency is introduced. The most attractive feature of the simplified linear consistency is the ease and cheapness of doing 3D calculation. One contribution of this paper is to show clearly the accuracy of solution gradually improved by increasing the order of the consistency. Simple 3D impacting models are established with different geometries and higher accurate results are obtained by using higher consistency kernel functions. Other features as numerical convergence, computational efficiency, etc. and some considerations of the simplified linear consistency kernel function are also discussed.

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