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Dynamic Analysis of a Rotating FGM Beam with the point interpolation method

INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2022年第7期19卷

作者： Du, Chaofan Gao, Xiang Zhang, Dingguo Zhou, Xiaoting Yangzhou Univ Coll Civil Sci & Engn Yangzhou 225127 Jiangsu Peoples R China Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Peoples R China

The dynamic characteristics of a hub-functionally graded material beam undergoing large overall motions are studied. The deformation field of the flexible beam is described by using the assumed mode method (AMM), the finite element method (FEM) and the point interpolation method (PIM). Assuming that the physical parameters of functionally graded materials follow certain kind of power law gradient distribution and vary along the thickness direction. The longitudinal deformation and transversal deformation of the beam are both considered, and the nonlinear coupling term which is known as the longitudinal shortening caused by transversal deformation is also taken into account. The rigid-flexible coupling dynamics equations of the system described by three different discrete methods which have a uniform form are derived via employing Lagrange's equations of the second kind. The validity of the point interpolation method established in this paper is verified by comparing with the numerical simulation results of the assumed mode method and the finite element method. On this basis, the influence of the functional gradient distribution rules on the dynamic characteristics of flexible beams undergoing large overall motions is discussed. The results show that the assumed mode method cannot deal with large deformation problem. Remaining other physical parameters of functionally graded materials beam unchanged, the maximum displacement of the beam increases with the increase of functionally graded materials index. The natural frequency of transverse bending of beam increases with the increase of rotational speed, when rotational speed is constant, the natural frequency will decrease with the increase of functional gradient index.

关键词： point interpolation method functionally graded material beam rigid-flexible coupled natural frequencies

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A complex variable boundary point interpolation method for the nonlinear Signorini problem

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2020年第12期79卷 3297-3309页

作者： Li, Xiaolin Li, Shuling Chongqing Normal Univ Sch Math Sci Chongqing 400047 Peoples R China Chongqing Normal Univ Key Lab Optimizat & Control Minist Educ Chongqing 400047 Peoples R China

A complex variable boundary point interpolation method (CVBPIM) is presented for numerical analysis of the nonlinear Signorini problem. To reduce the computational cost and to improve the stability of the point interpolation method, a complex variable point interpolation method (CVPIM) is developed to construct meshless shape functions with interpolation properties. By using a projection technique to deal with the nonlinear inequality boundary conditions, and combining boundary integral equations with the CVPIM to establish discrete linear algebraic systems, the CVBPIM is an easy-to-implement and boundary-only meshless method for nonlinear Signorini problems. Numerical results are presented to show the accuracy and efficiency of the method. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Meshless method Boundary integral equation point interpolation method Complex variable Nonlinear inequality boundary condition Signorini problem

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A multi-physics node-based smoothed radial point interpolation method for transient responses of magneto-electro-elastic structures

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2019年 101卷 371-384页

作者： Zhou, Liming Ren, Shuhui Meng, Guangwei Li, Xiaolin Cheng, Fei Jilin Univ Sch Mech & Aerosp Engn Renmin St 5988 Changchun 130025 Jilin Peoples R China

A multi-physics node-based smoothed radial point interpolation method (MNS-RPIM) for the transient responses of two-dimensional magneto-electro-elastic (MEE) structures is presented, the displacement, electrical potential and magnetic potential are obtained by combining the coupling MEE Newmark method. Based on constitutive equation of MEE material and introducing the weakened weak (W-2) formulation and the G space theory, the discretized system equations are produced. The method developed here is suitable for arbitrary boundary conditions, which could be the complement to the analytical solution. For two-dimensional structures, triangular element is adopted to discrete models because it could be automatically generated for complex geometries. The generalized displacement is computed for a cantilever beam, a layered MEE sensor and a typical MEE energy harvester. Results shows the following important properties of MNS-RPIM: (1) insensitive to mesh distortion;(2) accurate and convergent;(3) volumetric locking free;(4) high efficiency over FEM at the same accuracy.

关键词： Magneto-electro-elastic materials Multi-physics node-based smoothed radial point interpolation method GS-Galerkin weak form Transient responses Coupling magneto-electro-elastic Newmark method

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Elastic-plastic analysis of multi-material structures using edge-based smoothed point interpolation method

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2019年第4期233卷 1289-1298页

作者： Feng, S. Z. Cheng, Y. H. Li, A. M. Hebei Univ Technol Sch Mech Engn Tianjin 300130 Peoples R China China Univ Min & Technol Sch Mech & Elect Engn Xuzhou Jiangsu Peoples R China

An edge-based smoothed point interpolation method is formulated to deal with elastic-plastic analysis of multi-material structures. The problem domain is discretized using triangular elements and field functions are approximated using point interpolation method shape functions. Edge-based smoothing domains are constructed based on the edge of triangular cells and smoothing operations are then performed in these integral domains. Numerical examples with different kinds of material models are investigated to fully verify the validity of the present method. It is observed that all edge-based smoothed point interpolation method models can achieve much better accuracy and higher convergence rate than the standard finite element method, when dealing with elastic-plastic analysis of multi-material structures.

关键词： point interpolation method multi-material elastic-plastic meshfree structural mechanics

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A Fully Automatic h-Adaptive Analysis Procedure Using the Edge-Based Smoothed point interpolation method

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2020年第2期17卷

作者： Tang, Qian Wei, Kexiang Zhang, Guiyong Sun, Xiaogang Hunan Inst Engn Dept Mech Engn Xiangtan 411101 Peoples R China Hunan Prov Cooperat Innovat Ctr Wind Power Equipm Xiangtan 411101 Peoples R China Dalian Univ Technol Sch Naval Architecture Liaoning Engn Lab Deep Sea Floating Struct Dalian 116024 Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Collaborat Innovat Ctr Adv Ship & Deep Sea Explor Shanghai 200240 Peoples R China

Within the framework of edge-based smoothed point interpolation method (ES-PIM), a fully automatic adaptive procedure has been proposed by introducing a novel local critical value definition. Owing to the softened stiffness, ES-PIM can generally provide much better results than the traditional finite element method using the simplest linear triangle elements. By comparing with most adaptive models which need to set a refinement rate manually, a novel local critical value considering the area-dependent average magnitude of error indicator for all the cells has been introduced in this work, which leads to an adaptive ES-PIM model without manual operation during the adaptive process. Numerical results have shown that the present adaptive model conducts the adaptive process dynamically, adds the new nodes properly and provides more accurate results with less field nodes than both the model with uniform refinement and the adaptive model using predefined refinement rate. Also considering linear triangular background elements used, the present method is supposed to have much potential for solving complicated engineering problems.

关键词： Adaptive analysis error indicator refinement strategy local critical values point interpolation method

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A novel framework using point interpolation method with voxels for variational asymptotic method unit cell homogenization of woven composites

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COMPOSITE STRUCTURES 2018年 202卷 261-274页

作者： Nair, Rajeev G. Sundararajan, T. Guruprasad, P. J. Indian Inst Technol Dept Aerosp Engn Bombay 400076 Maharashtra India Indian Space Res Org Vikram Sarabhai Space Ctr Thiruvananthapuram Kerala India

Micromechanical analysis of woven composites can be effectively carried out using variational asymptotic method (VAM) unit cell homogenization technique. The governing equations obtained by adopting this technique can be solved using numerical methods by conformal discretization of the domain. In the case of woven composites conformal discretization of the domain becomes difficult and time consuming. It is preferable to have a non-conformal discretization procedure for problems involving complex geometries like woven composites. A novel numerical framework for micromechanical analysis of woven composites based on VAM is proposed, where level-set method is used to define the interface as well as to decompose the domain into voxel regions of inclusions and matrix. point interpolation method (PIM) is used to connect these voxel regions. The PIM-VOXEL framework thus developed is validated using examples having complex geometries taken from open literature for predicting elastic, thermal, thermo-elastic and visco-elastic properties. The proposed methodology alleviates the requirement for conformal meshing without compromising the accuracy and is capable of automation for homogenization and localization applications.

关键词： point interpolation method Variational asymptotic method Homogenization Woven composites

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Numerical analysis for multi-group neutron-diffusion equation using Radial point interpolation method (RPIM)

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ANNALS OF NUCLEAR ENERGY 2017年 99卷 193-198页

作者： Kim, Kyung-O Jeong, Hae Sun Jo, Daeseong Korea Atom Energy Res Inst 1045 Daedeok Daero Daejeon 305353 South Korea Kyungpook Natl Univ Sch Mech Engn 80 Daehak Ro Daegu South Korea

A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the point interpolation method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and Hermite-type collocation method) in order to solve this problem. On the basis of these results, it is expected that the mesh-free method including the RPIM can be sufficiently employed in numerical analysis for the multi-group neutron-diffusion equation and can be considered as an alternative numerical approach

关键词： Mesh-free method point interpolation method Radial point interpolation method Neutron-diffusion equation Multiplication eigenvalue

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A Quasi-Conforming point interpolation method (QC-PIM) for Elasticity Problems

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2016年第5期13卷

作者： Xu, X. Zheng, Z. Q. Gu, Y. T. Liu, G. R. Jilin Univ Coll Math 2699 Qianjin St Changchun 130012 Peoples R China Queensland Univ Technol Sch Chem Phys & Mech Engn Brisbane Qld 4001 Australia Univ Cincinnati Sch Aerosp Syst Cincinnati OH 45221 USA

It is well known that a high-order point interpolation method (PIM) based on the standard Galerkin formations is not conforming, and thus the solution may not always be convergent. This paper proposes a new interesting technique called quasi-conforming point interpolation method (QC-PIM) for solving elasticity problems, by devising a novel scheme that smears the discontinuity. In the QC-PIM, the problem domain is first discretized by a set of background cells (typically triangles that can be automatically generated), and the average displacements on the interfaces of the two neighboring cells are assumed to be equal. We prove that when the size of background cells approaches to zero, all the additional potential energy coming from the discontinuous displacement field becomes zero, which ensures the pass of the standard patch test and hence the convergence. Numerical experiments verify that QC-PIM can produce the convergent solutions with higher accuracy and convergent rate that is in between fully conforming linear and quadratic models.

关键词： point interpolation method quasi-conforming Galerkin formations patch test convergence

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A meshless method based on point interpolation method (PIM) for the space fractional diffusion equation

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APPLIED MATHEMATICS AND COMPUTATION 2015年 256卷 930-938页

作者： Liu, Q. Liu, F. Gu, Y. T. Zhuang, P. Chen, J. Turner, I. Xiamen Univ Sch Math Sci Xiamen Fujian Peoples R China Queensland Univ Technol Sch Math Sci Brisbane Qld 4001 Australia Queensland Univ Technol Sch Chem Phys & Mech Engn Brisbane Qld 4001 Australia Jimei Univ Sch Sci Xiamen Fujian Peoples R China Xiamen Univ Fujian Prov Key Lab Math Modeling & High Performa Xiamen 361005 Peoples R China

This paper aims to develop a meshless approach based on the point interpolation method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Fractional diffusion equation Meshless approach point interpolation method Numerical simulation

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A Meshless point interpolation method for Time Domain Analysis of Lossy Nonuniform Transmission Lines

A Meshless Point Interpolation Method for Time Domain Analys...

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International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO)

作者： Benkhaoua, L. Benhabiles, M. T. Riabi, M. L. Univ Constantine 1 Lab Electromagnetisme & Telecommun Constantine Algeria

ISBN: (纸本)9781479928200

A Meshless Time Domain method is proposed to solve the telegrapher's equation for the Nonuniform Transmission Line. The approach is based on a combination of the point interpolation method PIM and the Leapfrog algorithm. The accuracy of the proposed method is confronted with both the conventional FDTD and a wavelet expansion method. The strong stability of the computing scheme is set in evidence from the computational results for a linear tapered planar line.

关键词： Nonuniform Transmission Line Meshless methods point interpolation method FDTD Time-domain analysis Tapered line Telegrapher's Equations

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