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Simulation of bulk metal forming processes using the reproducing kernel particle method

COMPUTERS & STRUCTURES 2005年第8-9期83卷 574-587页

作者： Xiong, SW Liu, WK Cao, H Li, CS Rodrigues, JMC Martins, PAF Inst Super Tecn Dept Engn Mecan P-1049001 Lisbon Portugal Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Northeastern Univ State Key Lab Rolling & Automat Shenyang 110004 Peoples R China

A new approach based on the utilization of the reproducing kernel particle method 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 slightly compressible rigid-plastic materials. The effectiveness of the proposed methodology is discussed by comparing theoretical predictions with finite element calculations and experimental data. The later were obtained by means of simple metal forming experiments that were performed under laboratory-controlled conditions using aluminium, A16060 (natural aged). The overall comparisons comprise a wide range of topics such as material flow, geometry, forming load, strain and stress distributions. As results show, the proposed approach is capable of efficiently handling large plastic deformations without the need of remeshing procedures and providing results that are in close agreement with both finite element predictions and experimental measurements. (c) 2004 Elsevier Ltd. All rights reserved.

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

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Shape optimization using reproducing kernel particle method and an enriched genetic algorithm

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2005年第39-41期194卷 4048-4070页

作者： Zhang, ZQ Zhou, JX Zhou, N Wang, XM Zhang, L Xi An Jiao Tong Univ Sch Civil Engn & Mech Xian 710049 Peoples R China

Combining reproducing kernel particle method (RKPM) with the proposed Multi-Family Genetic Algorithm (MFGA), a novel approach to continuum-based shape optimization problems is brought forward in this paper. Taking full advantage of the features of meshfree method and the merits of MFGA, the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely. The effectiveness, versatility and performance of the proposed approach are demonstrated via three 2-D numerical examples. (c) 2004 Elsevier B.V. All rights reserved.

关键词： shape optimization meshfree methods reproducing kernel particle method genetic algorithms

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Steady and non-steady state analysis of bulk forming processes by the reproducing kernel particle method

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2005年第6期41卷 599-614页

作者： Xiong, SW Li, CS Rodrigues, JMC Martins, PAF Inst Super Tecn Dept Engn Mecan P-1049001 Lisbon Portugal Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Northeastern Univ State Key Lab Rolling & Automat Shenyang 110004 Peoples R China

A new approach is put forwards for the numerical simulation of steady and non-steady state bulk metal forming processes. The approach is based on the utilization of the reproducing kernel particle method in conjunction with the flow formulation for slightly compressible rigid-plastic materials. The effectiveness of the proposed approach is discussed by comparing theoretical predictions with finite-element calculations and experimental data for three different bulk metal forming operations: flat rolling (under steady-state conditions), compression of rods and heading of cylindrical billets. The overall comparisons comprise a wide range of topics such as material flow, geometry, strain distribution and forming load/torque. It is shown that, the proposed approach is capable of efficiently handling large plastic deformations without the need of remeshing procedures and providing results that are in close agreement with both finite-element predictions and experimental measurements. (C) 2004 Elsevier B.V. All rights reserved.

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

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h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE reproducing kernel particle method

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Applied Mathematics and Mechanics(English Edition) 2005年第8期26卷 1064-1071页

作者： ZHANG Zhi-qian（张智谦） ZHOU Jin-xiong（周进雄） WANG Xue-ming（王学明） ZHANG Yan-fen（张艳芬） ZHANG Ling（张陵） School of Civil Engineering and Mechanics Xi＇an Jiaotong University Xi＇ an 710049 P. R. China

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

关键词： meshfree method reproducing kernel particle method multiresolution analysis adaptive analysis

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Meshless Analysis of Radio Frequency Microelectromechanical Systems Shunt Switch

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DEFENCE SCIENCE JOURNAL 2009年第6期59卷 622-626页

作者： Kanthamani, S. Mohan, S. Vijay Raju, S. Abhaikumar, V. Mohan, V. Thiagarajar Coll Engn Madurai 15 Tamil Nadu India Bigtec Private Ltd Bangalore 560082 Karnataka India

Microelectromechanical systems (MEMS) have found applications in defence as well as in civilian sectors. Analysis of MEMS devices require complex 3-D meshes due to the presence of mechanical and electrostatic energy domains. On the other hand, meshless methods do not require the generation of mesh and perform the computational analysis by just sprinkling the points covering the domain. In this paper, meshless analysis of MEMS switches based on reproducing kernel particle method is reported. Numerical results for the static analysis of the switch are compared with the simulated results obtained using INTELLISUITE MEMS CAD tool.

关键词： MEMS devices meshless analysis methods RF MEMS switches shunt switches RF MEMS technology military communication coplaner waveguide platform reproducing kernel particle method RKPM

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NUMERICAL SIMULATION OF BULK METAL FORMING BY MESHLESS method

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INTERNATIONAL JOURNAL OF MODERN PHYSICS B 2009年第6-7期23卷 1615-1620页

作者： Liu, Hongsheng Xing, Zhongwen Harbin Inst Technol Sch Mech Engn Harbin 150001 Heilongjiang Peoples R China

Conventional finite element (FE) analysis of bulk metal forming processes often breaks down due to severe mesh distortion. In recent years, meshless methods have been considerably developed for structural applications. The main feature of these methods is that the problem domain is represented by a set of nodes, and a finite element mesh is unnecessary. This new generation of computational methods can avoid time-consuming meshing and remeshing. A meshless method based on reproducing kernel particle method (RKPM) is applied to bulk metal forming analysis. The displacement shape functions are developed from a reproducing kernel (RK) approximation that satisfies consistency conditions. The shape function is modified to impose essential boundary conditions accurately and expediently. A material kernel function that deforms with the material is introduced to assure the stability of the RKPM shape function during large deformations. A program based on RKPM is developed to simulate two examples of bulk metal forming process such as ring compression and cold upsetting, and numerical results demonstrate the performance of the meshless method in bulk metal forming analysis.

关键词： Meshless method reproducing kernel particle method finite element method bulk metal forming large deformation

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On coupling of reproducing kernel particle method and boundary element method

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COMPUTATIONAL MECHANICS 2004年第4期34卷 282-297页

作者： Lee, CK Lie, ST Shuai, YY Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore

In this paper a new coupling method to merge the reproducing kernel particle method (RKPM) and the boundary element method (BEM) is proposed. In this formulation, the whole problem domain will first be divided into two subdomains in which the RKPM and the BEM are applied respectively. A simple and direct coupling procedure is then applied to preserve the compatibility of the solution along the interface of the two subdomains. Unlike other coupling procedures suggested previously, the present coupling procedure neither requires modification of the RKPM and the BEM formulations nor the use of finite elements along the interface boundary between the two subdomains. The validity and efficiency of the coupling procedure are demonstrated by using it to solve five benchmark elastostatic stress analysis problems. In addition, a simple analysis of the a priori convergence rate of the coupling procedure is given. Preliminary assessment of the convergence characteristics of the coupling procedure is done by carrying out uniform refinements on the benchmark problems.

关键词： meshless method reproducing kernel particle method boundary element method a priori error estimation

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Investigations on reproducing kernel particle method enriched by partition of unity and visibility criterion

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COMPUTATIONAL MECHANICS 2004年第4期34卷 310-329页

作者： Zhang, ZQ Zhou, JX Wang, XM Zhang, YF Zhang, L Xi An Jiao Tong Univ Sch Civil Engn & Mech Xian 710049 Peoples R China

This work introduces a numerical integration technique based on partition of unity (PU) to reproducing kernel particle method (RKPM) and presents an implementation of the visibility criterion for meshfree methods. According to the theory of PU and the inherent features of Gaussian quadrature, the convergence property of the PU integration is studied in the paper. Moreover, the practical approaches to implement the PU integration are presented in different strategies. And a method to carry out visibility criterion is presented to handle the problems with a complex domain. Furthermore, numerical examples have been performed on the h-version and p-like version convergence studies of the PU integration and the validity of visibility criterion. The results demonstrate that PU integration is a feasible and effective numerical integration technique, and RKPM enriched by PU integration and visibility criterion is of more efficiency, versatility and high performance.

关键词： meshfree method reproducing kernel particle method partition of unity visibility criterion

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Simulation and prediction of endothelial cell adhesion modulated by molecular engineering

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2008年第25-28期197卷 2340-2352页

作者： Kopacz, Adrian Marcin Liu, Wing Kam Liu, Shu Q. Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Northwestern Univ Dept Biomed Engn Evanston IL 60208 USA

Computational modeling is an effective approach for simulating and predicting the development and remodeling of biological systems. Here, we propose to integrate a probabilistic mathematical modeling approach into an emerging bioengineering area known as molecular regenerative engineering. This experimental-computational framework can be used to simulate and predict the efficacy of molecular engineering in controlling and enhancing the regenerative processes of pathologically disordered cells, tissues and organs. We demonstrate the significance and principles of this approach by using a special case as an example: enhancement of endothelial cell adhesion to arterial constructs by siRNA-mediated modulation of an adhesion-inhibiting factor known as Src homology 2 domain-containing protein tyrosine phosphatase (SHP)-1. A continuum approach is used to model endothelial cell adhesion at the cellular level, while the Kramers reaction-rate theory is used to model cell adhesion at the subcellular and molecular levels. We show that the proposed computational model can potentially be used to simulate the processes and alterations of endothelial cell adhesion at the molecular and cellular levels under shear flow and to predict the effectiveness of siRNA-mediated SHP-1 knockdown in enhancing endothelial cell adhesion in arterial constructs. These preliminary investigations suggest that this integrated experimental-computational approach may be used for the simulation and prediction of regenerative processes in response to molecular engineering. (C) 2008 Elsevier B.V. All rights reserved.

关键词： immersed finite element method reproducing kernel particle method mesh-free method fluid-structure interaction endothelial cell adhesion arterial reconstruction atherosclerosis

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Structural dynamic shape optimization and sensitivity analysis based on RKPM

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2008年第3期36卷 307-317页

作者： Zhang, Jianping Gong, Shuguang Huang, Yunqing Qiu, Aihong Chen, Renke Xiangtan Univ Sch Mech Engn Xiangtan 411105 Peoples R China Xiangtan Univ Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan 411105 Peoples R China

A numerical method of structural dynamic shape optimization is presented by using reproducing kernel particle method (RKPM), by which the mesh distortion that exists in shape optimal method based on finite element can be eliminated completely and the optimal model for structural dynamic optimization design is built. The discreteness-based design sensitivity analysis in both natural frequency and dynamic response is proposed by using direct differentiation method and discrete derivatives on the basis of structural dynamic analysis, in which the penalty method is employed into imposing the essential boundary conditions, and the derivatives of shape functions with respect to design variables are derived. The algorithm of dynamic sensitivity analysis is testified by numerical example, and the numerical results obtained are in good agreement with those obtained using semi-analytical method and global finite differences method. Finally, by integrating the algorithm mentioned based on RKPM with parameterized descriptive method of boundary shape, two examples for structural dynamic shape optimization are performed.

关键词： meshless method reproducing kernel particle method dynamic sensitivity analysis dynamic optimization design shape optimization

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