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Showing papers by "YuanTong Gu published in 2001"


Journal ArticleDOI
TL;DR: In this article, a point interpolation method (PIM) is presented for stress analysis for two-dimensional solids, where the problem domain is represented by properly scattered points.
Abstract: A point interpolation method (PIM) is presented for stress analysis for two-dimensional solids. In the PIM, the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points. The PIM equations are then derived using variational principles. In the PIM, the essential boundary conditions can be implemented with ease as in the conventional finite element methods. The present PIM has been coded in FORTRAN. The validity and efficiency of the present PIM formulation are demonstrated through example problems. It is found that the present PIM is very easy to implement, and very flexible for obtained displacements and stresses of desired accuracy in solids. As the elements are not used for meshing the problem domain, the present PIM opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures. Copyright © 2001 John Wiley & Sons, Ltd.

669 citations


01 Feb 2001
TL;DR: In this article, a Point Interpolation Method (PIM) is presented for stress analysis for two-dimensional solids, where the problem domain is represented by properly scattered points.
Abstract: A Point Interpolation Method (PIM) is presented for stress analysis for two-dimensional solids. In the PIM, the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points. The PIM equations are then derived using variational principles. In the PIM, the essential boundary conditions can be implemented with ease as in the conventional Finite Element Methods. The present PIM has been coded in FORTRAN. The validity and efficiency of the present PIM formulation are demonstrated through example problems. It is found that the present PIM is very easy to implement, and very flexible for obtained displacements and stresses of desired accuracy in solids. As the elements are not used for meshing the problem domain, the present PIM opens new avenue to develop adaptive analysis codes for stress analysis in solids and structures.

639 citations


Journal ArticleDOI
TL;DR: In this article, a local radial point interpolation method (LRPIM) is presented to deal with boundary value problems for free vibration analyses of two-dimensional solids, where local weak forms are developed using weighted residual method locally from the partial differential equation of free vibration.

496 citations


Journal ArticleDOI
TL;DR: The meshless local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants and local weak forms.
Abstract: The meshless local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the free vibration analysis, the essential boundary conditions are implemented through the direct interpolation form and imposed using orthogonal transformation techniques. In the forced vibration analysis, the penalty method is used in implementation essential boundary conditions. Two different time integration methods are used and compared in the forced vibration analyses using the present MLPG method. The validity and efficiency of the present MLPG method are demonstrated through a number of examples of two-dimensional solids.

185 citations


Journal ArticleDOI
TL;DR: In this article, 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.

152 citations


01 Aug 2001
TL;DR: In this article, 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.
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 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.

132 citations


Journal ArticleDOI
TL;DR: In this article, a local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids, which is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration.
Abstract: A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids.

118 citations


Journal ArticleDOI
TL;DR: In this article, a meshless method for the analysis of Kirchhoff plates based on the meshless Local PetrovGalerkin (MLPG) concept is presented for static and free vibration analyses of thin plates.
Abstract: A meshless method for the analysis of Kirchhoff plates based on the Meshless Local PetrovGalerkin (MLPG) concept is presented. A MLPG formulation is developed for static and free vibration analyses of thin plates. Local weak form is derived using the weighted residual method in local supported domains from the 4th order partial differential equation of Kirchhoff plates. The integration of the local weak form is performed in a regular-shaped local domain. The Moving Least Squares (MLS) approximation is used to constructed shape functions. The satisfaction of the high continuity requirements is easily met by MLS interpolant, which is based on a weight function with high continuity and a quadratic polynomial basis. The validity and efficiency of the present MLPG method are demonstrated through a number of examples of thin plates under various loads and boundary conditions. Some important parameters on the performance of the present method are investigated thoroughly in this paper. The present method is also compared with EFG method and Finite Element Method in terms of robustness and performance. keyword: Meshless Method; Meshless Local PetrovGalerkin (MLPG) method; Kirchhoff plates; Free Vibration; Numerical Analysis

86 citations


Journal ArticleDOI
TL;DR: In this paper, a coupled EFG/boundary element (BE) method is proposed to improve the solution efficiency, where the continuity and compatibility are preserved on the interface of the two domains, where EFG and BE methods are applied.

79 citations


Book ChapterDOI
TL;DR: In this paper, two local point interpolation methods, Local Point Interpolation Method (LPIM) using the polynomial basis and Local Radial Point Interprocedure Method (LR-PIM), were compared and compared with each other on several technical issues.
Abstract: Two local point interpolation methods, Local Point Interpolation Method (LPIM) using the polynomial basis and the Local Radial Point Interpolation Method (LR-PIM) using the radial basis, are examined and compared with each other on several technical issues As truly meshless methods, LPIM and LR-PIM were developed based on a local weak form integrated in a local domain of very simple shape The numerical implementations of these two methods are discussed in detail, including the formulation of test functions, sizes of domains for the integration and interpolation These local point interpolation methods are first used to analyze 2-D elasto-dynamic problems and Timoshenko beams It is found that the local point interpolation methods are very easy to implement, and very robust for obtaining numerical solutions to problems of computational mechanics In addition, the effects of some parameters on the performances of these local point interpolation methods are also investigated in great detail

6 citations


01 May 2001
TL;DR: In this article, a coupled EFG/Boundary Element Free Galerkin (EFG) and Boundary Element Element (BE) method is proposed to improve the solution efficiency.
Abstract: Element Free Galerkin (EFG) method is a newly developed meshless method for solving partial differential equations using Moving Least Squares interpolants. It is, however, computationally expensive for many problems. A coupled EFG/Boundary Element (BE) method is proposed in this paper to improve the solution efficiency. A procedure is developed for the coupled EFG/BE method so that the continuity and compatibility are preserved on the interface of the two domains where the EFG and BE methods are applied. The present coupled EFG/BE method has been coded in FORTRAN. The validity and efficiency of the EFG/BE method are demonstrated through a number of examples. It is found that the present method can take the full advantages of both EFG and BE methods. It is very easy to implement, and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains.