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

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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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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Analysis of functionally graded stiffened plates based on FSDT utilizing reproducing kernel particle method

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COMPOSITE STRUCTURES 2014年第1期112卷 231-240页

作者： Ardestani, M. Memar Soltani, B. Shams, Sh. Univ Kashan Fac Mech Engn Kashan *** Isfahan Iran

Using reproducing kernel particle method (RKPM), concentrically and eccentrically functionally graded stiffened plates (FGSPs) are analyzed based on first order shear deformation theory (FSDT). The plates are subjected to uniformly distributed loads with simply supported and clamped boundary conditions. The interactions between the plate and stiffeners are imposed by compatibility equations. Metal-ceramic composition is assumed as the functionally graded material (FGM). Material properties vary through the thickness direction according to the power law of volume fraction. Mori-Tanaka scheme is used to obtain effective material properties. Poisson's ratios of plates and stiffeners are taken to be constant. Full transformation approach is used to enforce essential boundary conditions. Effects of eccentricity of the stiffeners, dimensionless support domain parameter, dimensionless thickness, boundary conditions and the volume fractions of the constituents on the behavior of the stiffened plates are investigated. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Meshfree method reproducing kernel particle method Stiffened plate First order shear deformation theory Full transformation method Functionally graded materials

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Nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2016年第Feb.1期299卷 381-400页

作者： Hillman, Michael Chen, Jiun-Shyan Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA

Convective transport terms in Eulerian conservation laws lead to numerical instability in the solution of Bubnov-Galerkin methods for these non-self-adjoint PDEs. Stabilized Petrov-Galerkin methods overcome this difficulty, however gradient terms are required to construct the test functions, which are typically expensive for meshfree methods. In this work, the implicit gradient reproducing kernel particle method is introduced which avoids explicit differentiation of test functions. Stabilization is accomplished by including gradient terms in the reproducing condition of the reproducing kernel approximation. The proposed method is computationally efficient and simplifies stabilization procedures. It is also shown that the implicit gradient resembles the diffuse derivative originally introduced in the diffuse element method in Nayroles et al. (1992), and maintains the desirable properties of the full derivative. Since careful attention must be paid to efficiency of domain integration in meshfree methods, nodal integration is examined for this class of problems, and a nodal integration method with enhanced accuracy and stability is introduced. Numerical examples are provided to show the effectiveness of the proposed method for both steady and transient problems. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Convection dominated problems reproducing kernel particle method Implicit gradient Stabilization Nodal integration

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A quasi-linear reproducing kernel particle method

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2017年第7期109卷 1045-1064页

作者： Yreux, Edouard Chen, Jiun-Shyan Univ Calif San Diego Dept Struct Engn San Diego CA 92093 USA

reproducing kernel particle method (RKPM) has been applied to many large deformation problems. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties but requires appropriate kernel support coverage of neighboring nodes to ensure kernel stability. This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment-impact processes that commonly exist in extreme events. A new reproducing kernel formulation with ` quasi-linear' reproducing conditions is introduced. In this approach, the first-order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first-order completeness, nearly second-order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this quasi-linear RKPM formulation is demonstrated by modeling several extremely large deformation and fragment-impact problems. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： meshfree methods reproducing kernel particle method semi-Lagrangian quasi-linear approximation kernel stability

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Numerical simulation of slab edging process by the reproducing kernel particle method considering friction effect

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INTERNATIONAL JOURNAL OF SURFACE SCIENCE AND ENGINEERING 2009年第5-6期3卷 482-489页

作者： Xiong, Shangwu Jiang, Zhengyi Xie, Haibo Liu, Xianghua Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Univ Wollongong Sch Mech Mat & Mechatron Engn Wollongong NSW 2522 Australia Northeastern Univ State Key Lab Rolling & Automat Shenyang 110004 Liaoning Peoples R China

A mesh-free approach is used for analysing the effect of the friction factor on three-dimensional steady state slab edging, which is based on the reproducing kernel particle method (RKPM, Liu et al., 1995) and the material flow formulation for slightly compressible materials (Osakada et al., 1982). In order to cope with the singularity at the corner of the roll entry, a simple technique with a very thin array of cells at the inlet region adjacent to the plastic deformation zone (Xiong et al., 2003) is used. The results show that the dog-bone shape becomes smaller with the increment of friction factor. The roll separating force and total rolling torque increase with the friction factor.

关键词： RKPM reproducing kernel particle method steady-state slab edging process friction

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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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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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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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Application of reproducing kernel particle method and element-free Galerkin method on the simulation of the membrane of capacitive micromachined microphone in viscothermal air

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COMPUTATIONAL MECHANICS 2013年第3期51卷 295-308页

作者： Yang, Cheng-Ta Natl Kaohsiung Marine Univ Dept Marine Engn Kaohsiung 805 Taiwan

Simulation of the microphone membrane determines whether highest yield and sensitivity is attainable when it comes to the field of microelectromechanical system (MEMS) capacitive microphone design. Consequently, it is significantly critical to predict and understand the behavior of the membrane in the air. The reproducing kernel particle method and element-free Galerkin, RKPM and EFG respectively, are introduced to differentiate from the traditional finite element method (FEM) since RKPM and EFG models are meshless to greatly improve the problems of FEM with large size aspect ratio. The result from a numerical axisymmetry model of 1 mm radius and 10 mu m thickness membrane with fixed boundary condition upon 1 mm thickness viscothermal air is identical to that from the theoretical model. Finally, a MEMS axisymmetry model of a 180 mu m radius and 10 mu m thickness membrane upon 10 mu m thickness viscothermal air is simulated in this paper.

关键词： reproducing kernel particle method Element-free Galerkin Capacitive microphone

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