On the utilization of the reproducing kernel particle method for the numerical simulation of plane strain rolling

Shangwu, Xiong; Liu, W.K.; Cao, Jian; Rodrigues, J.M.C.; Martins, P.A.F.

doi:10.1016/s0890-6955(02)00134-7

Cited by 20 publications

(26 citation statements)

References 34 publications

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“…1. In order to ensure the incompressibility requirements of the plastic deformation of metals, both complete and reduced Gauss point integration schemes are utilised for the calculation of the domain integral [15][16][17][18][19]. The numerical integration of the boundary integrals is performed by means of a 5 Gauss point quadra- …”

Section: Rkpm Discretization Of the Flow Formulationmentioning

confidence: 99%

“…In what concerns the setting of unknowns and the solution of the non-linear system of Eq. (23), please refer to previously published works on quadrilateral background cells for slightly compressible rigid-plastic materials [15][16][17][18][19][20].…”

Section: Rkpm Discretization Of the Flow Formulationmentioning

confidence: 99%

“…In some finite element [31,40] and meshless computer programs (based on the slightly compressible flow formulation [41]) [15][16][17][18][19][20], the volumetric strain-rate,ε…”

Section: Evaluation Of the Average Stressesmentioning

confidence: 99%

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On background Cells during the Analysis of Bulk Forming Processes by the Reproducing Kernel Particle Method

2006

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The reproducing kernel particle method based on the irreducible flow formulation is utilised to perform the numerical simulation of bulk metal forming processes. Emphasis is given on analysing the influence of employing triangular or quadrilateral background cells on the predictions of material flow, forming load and distribution of strain. A new proposal to smooth the distribution of average stresses during stress computations in the background cells is also included. The effectiveness of the proposed method is discussed by comparing its numerical predictions with a benchmark test case, finite element calculations and experimental data. The benchmark test case is included with the objective of illustrating the influence of several theoretical and numerical subjects such as; order of the basis correction functions, dimension of the compact support and computation of the volume associated to each nodal point. Experimental data was acquired from metal forming controlled laboratory-based tests that were designed so that the proposed method could be tested on its ability to efficiently handle large plastic deformations. It is shown that adaptive arbitrary triangular background cells are capable of efficiently handling large plastic deformations without remeshing.

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Section: Rkpm Discretization Of the Flow Formulationmentioning

confidence: 99%

Section: Rkpm Discretization Of the Flow Formulationmentioning

confidence: 99%

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On background Cells during the Analysis of Bulk Forming Processes by the Reproducing Kernel Particle Method

2006

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“…The calculation steps for radiative transfer are as follows: firstly, the shape function of RKPM is calculated according to the current distribution of discrete particle and substituted into (10a) and (10b); secondly, the matrix coefficient of (13) is obtained by substituting (10a) and (10b) into (14a) and (14b); finally, the radiative intensity for all the discrete particles is calculated and used to solve (13). Due to the scattering effect, the radiative intensity would reiterate the process for all directions until the convergence condition is satisfied.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…So the RKPM can work well over the whole domain. It has wide application in many engineering fields, such as, rolling plane strain problem [13], bucking analysis of thin plates [14], large deformation nonlinear elastic problems [15][16][17][18], metal forming problem [19][20][21][22], elastic-plastic problems [23,24], convection-diffusion problem [25][26][27], heat conduction problems [28][29][30], and fragment-impact problem [31,32]. But up to now, to the best of our knowledge, there is still lack of literature on the application of RKPM for radiative heat transfer.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Dong

2015

Mathematical Problems in Engineering

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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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Research on rigid/visco-plastic element-free Galerkin method and key simulation techniques for three-dimensional bulk metal forming processes

Lü

Zhao

Guan

et al. 2010

Int J Adv Manuf Technol

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On the utilization of the reproducing kernel particle method for the numerical simulation of plane strain rolling

Cited by 20 publications

References 34 publications

On background Cells during the Analysis of Bulk Forming Processes by the Reproducing Kernel Particle Method

On background Cells during the Analysis of Bulk Forming Processes by the Reproducing Kernel Particle Method

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

Research on rigid/visco-plastic element-free Galerkin method and key simulation techniques for three-dimensional bulk metal forming processes

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