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On background cells during the analysis of bulk forming processes by the reproducing kernel particle method

COMPUTATIONAL MECHANICS 2007年第2期40卷 233-247页

作者： Xiong, Shangwu Rodrigues, J. M. C. Martins, P. A. F. Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Inst Super Tecn Dept Engn Mecan P-1049001 Lisbon Portugal

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.

关键词： bulk metal forming background cells reproducing kernel particle method finite element method

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An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement

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COMPUTATIONAL MECHANICS 2007年第3期40卷 415-427页

作者： Lee, C. K. Shuai, Y. Y. Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore HoHai Univ Coll Civil Engn Nanjing 210098 Peoples R China

In Part II of this study, an automatic adaptive refinement procedure using the reproducing kernel particle method (RKPM) for the solution of 2D linear boundary value problems is suggested. Based in the theoretical development and the numerical experiments done in Part I of this study, the Zienkiewicz and Zhu (Z-Z) error estimation scheme is combined with a new stress recovery procedure for the a posteriori error estimation of the adaptive refinement procedure. By considering the a priori convergence rate of the RKPM and the estimated error norm, an adaptive refinement strategy for the determination of optimal point distribution is proposed. In the suggested adaptive refinement scheme, the local refinement indicators used are computed by considering the partition of unity property of the RKPM shape functions. In addition, a simple but effective variable support size definition scheme is suggested to ensure the robustness of the adaptive RKPM procedure. The performance of the suggested adaptive procedure is tested by using it to solve several benchmark problems. Numerical results indicated that the suggested refinement scheme can lead to the generation of nearly optimal meshes for both smooth and singular problems. The optimal convergence rate of the RKPM is restored and thus the effectivity indices of the Z-Z error estimator are converging to the ideal value of unity as the meshes are refined.

关键词： reproducing kernel particle method stress recovery procedure a posteriori error estimation adaptive refinement

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Splitting Rolling Simulated by reproducing kernel particle method

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Journal of Iron and Steel Research International 2007年第3期14卷 42-46页

作者： CUI Qing-ling LIU Xiang-hua WANG Guo-dong State Key Laboratory of Rolling and Automation Northeastern University Shenyang 110004 Liaoning China

During splitting rolling simulation, re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used. However, extreme deformation cannot be solved by the finite element method in splitting rolling. The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes, and a finite element mesh is unnecessary, and there is no explicit limitation of mesh when the metal is split. To ensure stability in the large deformation elastoplastic analysis, the Lagrange material shape function was introduced. The transformation method was utilized to impose the essential boundary conditions. The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature.

关键词： elasto-plasticity large deformation reproducing kernel particle method splitting rolling

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

The Meshless Method for Numerical Solution of Modified Equal...

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2nd International Conference on Engineering Design and Optimization (ICEDO 2011)

作者： Cheng, Rongjun Ge, Hongxia Zhejiang Univ Ningbo Inst Technol Ningbo 315100 Zhejiang Peoples R China Ningbo Univ Fac Sci Ningbo 315211 Zhejiang Peoples R China

ISBN: (纸本)9783037852590

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.

关键词： reproducing kernel particle method Meshless method Modified equal width wave (MEW) equation Solitary wave

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

Meshless Method for the Numerical Solution of a Kind of Line...

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2nd International Conference on Engineering Design and Optimization (ICEDO 2011)

作者： Sun, Haina Cheng, Rongjun Ge, Hongxia Zhejiang Univ Ningbo Inst Technol Ningbo 315211 Zhejiang Peoples R China Ningbo Univ Fac Sci Ningbo Zhejiang Peoples R China

ISBN: (纸本)9783037852590

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.

关键词： reproducing kernel particle method Meshless method Hyperbolic problem

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reproducing kernel particle method for Non-Linear Fracture Analysis

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Journal of Southwest Jiaotong University(English Edition) 2006年第4期14卷 372-378页

作者：曹中清周本宽陈大鹏 Institute of Engineering and Science Southwest Jiaotong University Chengdu 610031 China

To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method （RKPM）. Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.

关键词： Meshless methods reproducing kernel particle method Facture Piezoelectric ceramics

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Numerical solution of bulk metal forming processes by the reproducing kernel particle method

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JOURNAL OF MATERIALS PROCESSING TECHNOLOGY 2006年第1-3期177卷 49-52页

作者： Xiong, Shangwu Martins, P. A. F. Inst Super Tecn Dept Engn Mech P-1049001 Lisbon Portugal Northwestern Univ Dept Mech Engn Evanston IL 60208 USA

A new mesh free approach is put forwards for the numerical simulation of bulk metal forming processes. The approach is based on the utilization of the reproducing kernel particle method in conjunction with the flow formulation for incompressible and slightly compressible rigid-plastic materials. Special emphasis is placed on the utilization of adaptive cell procedures that are capable of generating a new set of background cells at the end of each increment of deformation. Results show that the proposed methodology is capable of efficiently handling large plastic deformations without remeshing and providing results that are in close agreement with both finite element predictions and experimental measurements. (c) 2006 Elsevier B.V All rights reserved.

关键词： metal forming reproducing kernel particle method

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Application of reproducing kernel particle method in an Analysis of Elasto-plastic Deformation Under Taylor Impact

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Journal of China University of Mining and Technology 2006年第4期16卷 485-489页

作者： ZHAO Guang-ming SONG Shun-cheng MENG Xiang-rui Department of Resource Exploration and Management Engineering Anhui University of Science and Technology Huainan Anhui 232001 China Department of Applied Mechanics and Engineering Southwest Jiaotong University Chengdu Sichuan 610031 China

The reproducing kernel particle method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials.

关键词： reproducing kernel particle method Taylor impact large deformation meshless method

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Theory Research on Analysis of Taylor Impact Experiment for Material Dynamic Mechanical Properties

Theory Research on Analysis of Taylor Impact Experiment for ...

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2011爆轰与冲击动力学国际会议

作者： ZHAO Guang-ming (Key lab on safe and effective coal mining sponsored by Anhui province and ministry of education,Anhui University of Science and Technology,Huainan,Anhui 232001,China)

By suitable hypothesization and approximation of the Taylor impact process,the present paper has proposed a method to calculate the dynamic yielding strength of the material by turning to the length of the projectile ... 详细信息

关键词： Dynamic mechanical properties Taylor impact reproducing kernel particle method Impact

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Meshless analysis of three-dimensional steady-state heat conduction problems

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Chinese Physics B 2010年第9期19卷 36-41页

作者：程荣军葛红霞 Ningbo Institute of Technology Zhejiang University Faculty of Science Ningbo University

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.

关键词： reproducing kernel particle method meshless method steady-state heat conduction problem

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