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International Conference on Future Materials Engineering and Industry Application (ICFMEIA 2011)

作者： Sun, Haina Cheng, Rongjun Zhejiang Univ Ningbo Inst Technol Ningbo 315100 Zhejiang Peoples R China

ISBN: (纸本)9783037852712

The meshless reproducing kernel particle method (RKPM) is used to find the numerical solution of a kind of hyperbolic equations. A variational method is used to obtain the discrete equations and the essential boundary conditions are enforced by the penalty method. The effectiveness RKPM for two-dimensional hyperbolic problems is investigated by numerical example in this paper.

关键词： reproducing kernel particle method Meshless method Hyperbolic problem

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The Hermit-Type reproducing kernel particle method for Elasticity Problems

The Hermit-Type Reproducing Kernel Particle Method for Elast...

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SPHERIC Beijing International Workshop (SPHERIC Beijing)

作者： Ma, Jichao Wei, Gaofeng Gao, Hongfen Qilu Univ Technol Shandong Acad Sci Sch Mech & Automot Engn Jinan 250353 Shandong Peoples R China Shandong Management Univ Coll Mech & Elect Engn Jinan 250357 Shandong Peoples R China

To reduce the error on the boundary and improve computational accuracy, the normal derivative of radial basis function (RBF) is introduced into the reproducing kernel particle method (RKPM), and the Hermit-type reproducing kernel particle method (Hermit-type RKPM) is proposed. The Hermit-type RKPM approximation function is constructed and the governing equation of the elasticity problems is deduced. Then the Hermit-type RKPM is applied to the numerical simulation of the elasticity problems, and the results illustrate that the proposed method is more accurate than the RKPM.

关键词： Meshless methods elasticity problems Hermit-type radial basis functions reproducing kernel particle method numerical simulation

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LEVEL SET TOPOLOGY OPTIMIZATION FOR DESIGN DEPENDENT HYDROSTATIC LOADING USING THE reproducing kernel particle method

LEVEL SET TOPOLOGY OPTIMIZATION FOR DESIGN DEPENDENT HYDROST...

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ASME International Design Engineering Technical Conferences / Computers and Information in Engineering Conference

作者： Neofytou, Andreas Picelli, Renato Chen, Jiun-Shyan Kim, Hyunsun Alicia Cardiff Univ Cardiff Sch Engn Queens Bldg 14-17 Parade Cardiff CF24 3AA S Glam Wales Univ Sao Paulo Dept Min & Petr Engn Santos SP Brazil Univ Calif San Diego Struct Engn Dept 9500 Gilman Dr San Diego CA 92093 USA

ISBN: (纸本)9780791859193

Level set topology optimization for the design of structures subjected to design dependent hydrostatic loads is considered in this paper. Problems involving design-dependent loads remain a challenge in the field of topology optimization. In this class of problems, the applied loads depend on the structure itself. The direction, location and magnitude of the loads may change as the shape of the structure changes throughout optimization. The main challenge lies in determining the surface on which the load will act. In this work, the reproducing kernel particle method (RKPM) is used in combination with the level set method to handle the dependence of loading by moving the particles on the structural boundary throughout the optimization process. This allows for the hydrostatic pressure loads to be applied directly on the evolving boundary. One-way fluid-structure coupling is considered here. A hydrostatic pressure field governed by Laplace's equation is employed to compute the pressure acting on linear elastic structures. The objective in this optimization problem is to minimize compliance of these structures. Numerical results show good agreement with those in the literature.

关键词： Level set topology optimization Design dependent pressure loads reproducing kernel particle method

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A Moving Least Square reproducing kernel particle method for Unified Multiphase Continuum Simulation

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ACM TRANSACTIONS ON GRAPHICS 2020年第6期39卷 176-176页

作者： Chen, Xiao-Song Li, Chen-Feng Cao, Geng-Chen Jiang, Yun-Tao Hu, Shi-Min Tsinghua Univ Dept Comp Sci & Technol BNRist Beijing Peoples R China Swansea Univ Coll Engn Swansea W Glam Wales

In physically based-based animation, pure particle methods are popular due to their simple data structure, easy implementation, and convenient parallelization. As a pure particle-based method and using Galerkin discretization, the Moving Least Square reproducing kernel method (MLSRK) was developed in engineering computation as a general numerical tool for solving PDEs. The basic idea of Moving Least Square (MIS) has also been used in computer graphics to estimate deformation gradient for deformable solids. Based on these previous studies, we propose a multiphase MLSRK framework that animates complex and coupled fluids and solids in a unified manner. Specifically, we use the Cauchy momentum equation and phase field model to uniformly capture the momentum balance and phase evolution/interaction in a multiphase system, and systematically formulate the MLSRK discretization to support general multiphase constitutive models. A series of animation examples are presented to demonstrate the performance of our new multiphase MLSRK framework, including hyperelastic, elastoplastic, viscous, fracturing and multiphase coupling behaviours etc.

关键词： reproducing kernel particle method physically-based animation modelling and simulation fluids and solids

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Numerical Analysis of Functionally Graded Materials Using reproducing kernel particle method

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2019年第6期11卷

作者： Liu, Zheng Wei, Gaofeng Wang, Zhiming Qilu Univ Technol Shandong Acad Sci Sch Mech & Automot Engn Jinan 250353 Shandong Peoples R China

The reproducing kernel particle method (RKPM) for the elastic mechanical problems of the functionally graded materials (FGM) is proposed in this paper. The corresponding formulae of the RKPM for the FGM are derived. Furthermore, the control parameter of influence domain radius, penalty factor and different node distribution on the calculation accuracy are discussed. The different functional gradient exponents of the FGM are analyzed. The numerical results illustrate that the RKPM is correct and effective to solve the elastic mechanical problems of the FGM.

关键词： Functionally graded materials meshless method reproducing kernel particle method penalty function method elastic mechanical problem

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Research on Superelasticity of Shape Memory Alloys Based on reproducing kernel particle method

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2024年第4期16卷

作者： Zhang, Yijie Wei, Gaofeng Liu, Tengda Li, Anqing Ren, Fei Qilu Univ Technol Shandong Acad Sci Sch Mech Engn Jinan 250353 Shandong Peoples R China Shandong Inst Mech Design & Res Jinan 250353 Shandong Peoples R China

Shape memory alloys (SMAs), known for their unique superelastic effect, exhibit superior mechanical properties compared to traditional materials. In this study, the reproducing kernel particle method (RKPM) is applied to investigate the superelastic effect of the SMAs. A segmented linearization RKPM model is developed to establish the stress-strain relationship for the superelastic effect, and relevant formulas of superelasticity for the SMAs are derived. Finally, the applicability and accuracy of the RKPM in analyzing the superelastic effect of the SMAs are demonstrated through numerical examples.

关键词： Shape memory alloys superelastic effect meshless method reproducing kernel particle method smart materials

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Level set topology optimization with nodally integrated reproducing kernel particle method

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2021年 385卷 114016-114016页

作者： Neofytou, Andreas Huang, Tsung-Hui Kambampati, Sandilya Picelli, Renato Chen, Jiun-Shyan Kim, H. Alicia Cardiff Univ Cardiff Sch Engn Queens Bldg14-17 Parade Cardiff CF24 3AA Wales Univ Calif San Diego Struct Engn Dept 9500 Gilman Dr San Diego CA 92093 USA Univ Sao Paulo Dept Min & Petr Engn BR-11013560 Santos SP Brazil Natl Tsing Hua Univ Dept Power Mech Engn Hsinchu Taiwan

A level set topology optimization (LSTO) using the stabilized nodally integrated reproducing kernel particle method (RKPM) to solve the governing equations is introduced in this paper. This methodology allows for an exact geometry description of a structure at each iteration without remeshing and without any interpolation scheme. Moreover, useful characteristics of the RKPM such as the easily controlled order of continuity and the ability to freely place particles in a design domain wherever needed are illustrated through stress based and design-dependent surface loading examples. The numerical results illustrate the effectiveness and robustness of the methodology with good optimization convergence behavior and ability to handle large topological changes. Furthermore, it is shown that different particle distributions can be used to increase efficiency without additional complexity. (C) 2021 The Author(s). Published by Elsevier B.V.

关键词： Level set topology optimization reproducing kernel particle method Naturally stabilized nodal integration Stress-based Design-depended

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The meshless analysis of elastic dynamic problem based on radial basis reproducing kernel particle method

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SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 2020年 139卷 106340-106340页

作者： Qin, Shaopeng Wei, Gaofeng Tang, Bingtao Qilu Univ Technol Sch Mech & Automot Engn Shandong Acad Sci Jinan 250353 Shandong Peoples R China

In this article, introducing the method of radial basis function (RBF) into reproducing kernel particle method (RKPM), and the radial basis reproducing kernel particle method (RRKPM) is presented. The RRKPM has higher computational accuracy and better convergence than the RKPM. Then the RRKPM is used in elastic dynamic problem, and the weak form of integral is used to find the discretized governing equations. The penalty method is used to determine the essential boundary condition, and the two-point difference method is applied to discretizing the time. The RRKPM for elastic dynamic problem is constructed, and the accuracy and effectiveness of the RRKPM for elastic dynamic problem are verified by the numerical examples.

关键词： Meshless method reproducing kernel particle method Radial basis function Elastic dynamic problem Numerical analysis

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A Hybrid reproducing kernel particle method for Three-Dimensional Advection-Diffusion Problems

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2021年第7期13卷

作者： Peng, Piaopiao Fu, Yida Cheng, Yumin Shanghai Univ Sch Mech & Engn Sci Shanghai Inst Appl Math & Mech Shanghai Key Lab Mech Energy Engn Shanghai 200072 Peoples R China Shanghai Univ Coll Sci Dept Math Shanghai 20044 Peoples R China

In this paper, a hybrid reproducing kernel particle method (HRKPM) for three-dimensional (3D) advection-diffusion problems is presented. The governing equation of the advection-diffusion problem includes the second derivative of the field function to space coordinates, the first derivative of the field function to space coordinates and time, so it is necessary to discretize the time domain after discretizing the space domain. By introducing the idea of dimension splitting, a 3D advection-diffusion problem can be transformed into a series of related two-dimensional (2D) ones in the dimension splitting direction. Then, the discrete equations of these 2D problems are established by using the RKPM, and these discrete equations are coupled by using the difference method. Finally, by using the difference method to discretize the time domain, the formula of the HRKPM for solving 3D advection-diffusion problem is obtained. Numerical results show that the HRKPM has higher computational efficiency than the RKPM when solving 3D advection-diffusion problems.

关键词： Meshless method reproducing kernel particle method dimension splitting method hybrid reproducing kernel particle method advection-diffusion problem

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The Meshfree Analysis of Geometrically Nonlinear Problem Based on Radial Basis reproducing kernel particle method

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2020年第4期12卷

作者： Liu, Zheng Wei, Gaofeng Wang, Zhiming Qiao, Jinwei Qilu Univ Technol Shandong Acad Sci Sch Mech & Automot Engn Jinan 250353 Shandong Peoples R China

Based on the reproducing kernel particle method (RKPM) and the radial basis function (RBF), the radial basis reproducing kernel particle method (RRKPM) is presented for solving geometrically nonlinear problems. The advantages of the presented method are that it can eliminate the negative effect of diverse kernel functions on the computational accuracy and has greater computational accuracy and better convergence than the RKPM. Using the weak form of Galerkin integration and the Total Lagrangian (T.L.) formulation, the correlation formulae of the RRKPM for geometrically nonlinear problem are obtained. Newton-Raphson (N-R) iterative method is utilized in the process of numerical solution. Moreover, penalty factor, the scaling parameter, the shaped parameter of the RBF and loading step number are discussed. To prove validity of the proposed method, several numerical examples are simulated and compared to finite element method (FEM) solutions.

关键词： Meshfree method reproducing kernel particle method radial basis function geometrically nonlinear problem numerical analysis

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