The Experts below are selected from a list of 2901 Experts worldwide ranked by ideXlab platform
G R Liu - One of the best experts on this subject based on the ideXlab platform.
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a cell based smoothed radial point interpolation method cs rpim for static and free vibration of solids
Engineering Analysis With Boundary Elements, 2010Co-Authors: Xiangyang Cui, G R LiuAbstract:A cell-based smoothed radial point interpolation method (CS-RPIM) based on the generalized gradient smoothing operation is proposed for static and free vibration analysis of solids. In present method, the problem domain is first discretized using triangular background cells, and each cell is further divided into several smoothing cells. The displacement field Function is approximated using RPIM shape Functions which have Kronecker Delta Function property. Supporting node selection for shape Function construction uses the efficient T2L-scheme associated with edges of the background cells. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM). The effects of the number of divisions smoothing cells on the solution properties of the CS-RPIM are investigated in detail, and preferable numbers of smoothing cells is recommended. To verify the accuracy and stability of the present formulation, a number of numerical examples are studied to demonstrate numerically the efficiency of the present CS-RPIM.
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a linearly conforming radial point interpolation method for solid mechanics problems
International Journal of Computational Methods, 2006Co-Authors: G R Liu, K Y Dai, Maotian Luan, W XueAbstract:A linearly conforming radial point interpolation method (LC-RPIM) is presented for stress analysis of two-dimensional solids. In the LC-RPIM method, each field node is enclosed by a Voronoi polygon, and the displacement field Function is approximated using RPIM shape Functions of Kronecker Delta Function property created by simple interpolation using local nodes and radial basis Functions augmented with linear polynomials to guarantee linear consistency. The system equations are then derived using the Galerkin weak form and nodal integration techniques, and the essential boundary conditions are imposed directly as in the finite element method. The LC-RPIM method is verified via various numerical examples and an extensive comparison study is conducted with the conventional RPIM, analytical approach and FEM. It is found that the presented LC-RPIM is more stable, more accurate in stress and more efficient than the conventional RPIM.
Xiangyang Cui - One of the best experts on this subject based on the ideXlab platform.
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An edge/face-based smoothed radial point interpolation method for static analysis of structures
Engineering Analysis with Boundary Elements, 2016Co-Authors: S.z. Feng, Xiangyang Cui, F. Chen, Songyong Liu, D.y. MengAbstract:Abstract This paper formulates an edge/face-based smoothed radial point interpolation method (ES/FS-RPIM) for the 2D and 3D static analysis of structures. In present method, the problem domain is discretized using triangular or tetrahedron cells and the edge-based or face-based smoothing domains are then constructed based on these background meshes. Field Functions are approximated using RPIM shape Functions which have Kronecker Delta Function property. An efficient T2L-scheme is employed for the RPIM shape Function construction. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form and essential boundary conditions can be imposed directly as in the finite element method (FEM). Several numerical examples with different material models are investigated to verify the proposed method in terms of accuracy, stability, efficiency and convergence.
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a cell based smoothed radial point interpolation method cs rpim for static and free vibration of solids
Engineering Analysis With Boundary Elements, 2010Co-Authors: Xiangyang Cui, G R LiuAbstract:A cell-based smoothed radial point interpolation method (CS-RPIM) based on the generalized gradient smoothing operation is proposed for static and free vibration analysis of solids. In present method, the problem domain is first discretized using triangular background cells, and each cell is further divided into several smoothing cells. The displacement field Function is approximated using RPIM shape Functions which have Kronecker Delta Function property. Supporting node selection for shape Function construction uses the efficient T2L-scheme associated with edges of the background cells. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM). The effects of the number of divisions smoothing cells on the solution properties of the CS-RPIM are investigated in detail, and preferable numbers of smoothing cells is recommended. To verify the accuracy and stability of the present formulation, a number of numerical examples are studied to demonstrate numerically the efficiency of the present CS-RPIM.
S.z. Feng - One of the best experts on this subject based on the ideXlab platform.
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An edge/face-based smoothed radial point interpolation method for static analysis of structures
Engineering Analysis with Boundary Elements, 2016Co-Authors: S.z. Feng, Xiangyang Cui, F. Chen, Songyong Liu, D.y. MengAbstract:Abstract This paper formulates an edge/face-based smoothed radial point interpolation method (ES/FS-RPIM) for the 2D and 3D static analysis of structures. In present method, the problem domain is discretized using triangular or tetrahedron cells and the edge-based or face-based smoothing domains are then constructed based on these background meshes. Field Functions are approximated using RPIM shape Functions which have Kronecker Delta Function property. An efficient T2L-scheme is employed for the RPIM shape Function construction. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form and essential boundary conditions can be imposed directly as in the finite element method (FEM). Several numerical examples with different material models are investigated to verify the proposed method in terms of accuracy, stability, efficiency and convergence.
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A cell-based smoothed radial point interpolation method (CS-RPIM) for three-dimensional solids
Engineering Analysis with Boundary Elements, 2015Co-Authors: X.y. Cui, H. Feng, S.z. FengAbstract:Abstract A cell-based smoothed radial point interpolation method (CS-RPIM) is formulated for three-dimensional elasticity problems. In present method, the problem domain is firstly discretized by tetrahedron background cells, and each tetrahedron cell is then further divided into several smoothing cells. The displacement field Function is approximated using RPIM shape Functions which have Kronecker Delta Function property. Supporting node selection for shape Function construction uses the efficient T2L-scheme associated with the background cells. The smoothed Galerkin weak form is employed to create discretized system equations, and then the gradient smoothing operation is adopted to construct smoothed strain fields in every smoothing cell. Numerical examples are used to examine the present method in terms of accuracy, convergence, and efficiency. Compared with the finite element method using linear interpolation and node-based smoothed finite element method, the CS-RPIM solutions can achieve better efficiency, higher accuracy, and greater stability in static and free vibration analysis in presented examples.
Gui-rong Liu - One of the best experts on this subject based on the ideXlab platform.
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Meshless methods coupled with other numerical methods
Tsinghua Science and Technology, 2005Co-Authors: Gui-rong LiuAbstract:Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape Functions used in some MFree methods do not have the Kronecker Delta Function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape Function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape Functions are modified to the hybrid forms that possess the Kronecker Delta Function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical examples are presented to demonstrate the effectiveness of the present coupling methods.
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A matrix triangularization algorithm for the polynomial point interpolation method
Computer Methods in Applied Mechanics and Engineering, 2003Co-Authors: Gui-rong LiuAbstract:A novel matrix triangularization algorithm (MTA) is proposed to overcome the singularity problem in the point interpolation method (PIM) using the polynomial basis, and to ensure stable and reliable construction of PIM shape Functions. The present algorithm is validated using several examples, and implemented in the local point interpolation method (LPIM) that is a truly meshfree method based on a local weak form. Numerical examples demonstrate that LPIM using the present MTA are very easy to implement, and very robust for solving problems of computational mechanics. It is shown that PIM with the present MTA is very effective in constructing shape Functions. Most importantly, PIM shape Functions possess Kronecker Delta Function properties. Parameters that influence the performance of them are studied in detail. The convergence and efficiency of them are thoroughly investigated.
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A local point interpolation method (LPIM) for static and dynamic analysis of thin beams
2001Co-Authors: Gui-rong LiuAbstract:The Local Point Interpolation Method (LPIM) is a newly developed truly meshless method, based on the idea of Meshless Local Petrov-Galerkin (MLPG) approach. In this paper, a new LPIM formulation is proposed to deal with 4th order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams. Local weak forms are developed using weighted residual method locally. In order to introduce the derivatives of the field variable into the interpolation scheme, a technique is proposed to construct polynomial interpolation with Kronecker Delta Function property, based only on a group of arbitrarily distributed points. Because the shape Functions so-obtained possess Delta Function property, the essential boundary conditions can be implemented with ease as in the conventional Finite Element Method (FEM). The validity and efficiency of the present LPIM formulation are demonstrated through numerical examples of beams under various loads and boundary conditions.
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A local point interpolation method for static and dynamic analysis of thin beams
Computer Methods in Applied Mechanics and Engineering, 2001Co-Authors: Gui-rong LiuAbstract:Abstract The local point interpolation method (LPIM) is a newly developed truly meshless method, based on the idea of meshless local Petrov–Galerkin (MLPG) approach. In this paper, a new LPIM formulation is proposed to deal with fourth-order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams. Local weak forms are developed using weighted residual method locally. In order to introduce the derivatives of the field variable into the interpolation scheme, a technique is proposed to construct polynomial interpolation with Kronecker Delta Function property, based only on a group of arbitrarily distributed points. Because the shape Functions so-obtained possess Delta Function property, the essential boundary conditions can be implemented with ease as in the conventional finite element method (FEM). The validity and efficiency of the present LPIM formulation are demonstrated through numerical examples of beams under various loads and boundary conditions.
J.d. Lavers - One of the best experts on this subject based on the ideXlab platform.
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A Comparison of Point Interpolative Boundary Meshless Method Based on PBF and RBF for Transient Eddy-Current Analysis
IEEE Transactions on Magnetics, 2007Co-Authors: K.r. Shao, J.d. LaversAbstract:This paper presents the boundary polynomial point interpolation meshless method (BPPIM) and the boundary radial point interpolation meshless method (BRPIM) based on the polynomial basis Function (PBF) and radial basis Function (RBF), respectively, for transient eddy-current analysis, and their interpolation shape Functions satisfy the Kronecker Delta Function, thus, the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column is set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM is analyzed as well
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A boundary meshless method for transient Eddy current analysis
2005 IEEE International Magnetics Conference (INTERMAG), 2005Co-Authors: K.r. Shao, J.d. LaversAbstract:A boundary meshless method (BMLM) for transient analysis was presented. This method combined a point interpolation method for construction of spatial shape Functions for the governing equations. The spatial shape Functions satisfied the Kronecker Delta Function and the essential boundary condition can be directly imposed on the boundary. Eddy current distribution and eddy current density on symmetry axis were also given using the proposed method. The results all proved that BMLM is an effective technique to analyze the transient eddy current problems.
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A boundary meshless method for transient eddy current problems
IEEE Transactions on Magnetics, 2005Co-Authors: K.r. Shao, J.d. LaversAbstract:This paper presents a boundary meshless method (BMLM) for transient eddy current problems. With difference to the traditional boundary element method (BEM), the BMLM combines a point interpolation method (PIM) for construction of spatial interpolation Functions with a boundary integral formulation for the governing equations, thus the spatial interpolation Functions satisfy the Kronecker Delta Function and the essential boundary condition can be directly imposed without any other procedure. Theoretical analysis in details is given and a transient eddy current example is also presented to prove the proposed theory.
