Intervention-point principle of meshless method

Yang, Jianjun; Zheng, Jianlong

doi:10.1007/s11434-012-5471-x

Cited by 9 publications

(3 citation statements)

References 15 publications

(20 reference statements)

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“…where   x [40], x which is sheared off by the boundary  , as shown in Fig.1 (a). Note that we use a superscript "J" in the function  to denote a correspondence with the source node Note that the diffuse domain J  could be arbitrary selected outside the domain.…”

Section: Generalized Fundamental Solution Approximationmentioning

confidence: 99%

Generalized method of fundamental solutions (GMFS) for boundary value problems

Yang

Zheng

Wen

2018

Engineering Analysis with Boundary Elements

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In order to cope with the instability of the method of fundamental solutions (MFS), which caused by source offset, or source location, or fictitious boundary, a generalized method of fundamental solutions (GMFS) is proposed. The crucial part of the GMFS is used a generalized fundamental solution approximation (GFSA), which adopts a bilinear combination of fundamental solutions to approximate, rather than the linear combination of the MFS. Then the numerical solution of the GMFS is decided by a group of offsets corresponding to an intervention-point diffuse (IPD), instead of the MFS' only offset of a single source. To demonstrate the effectiveness of the proposed approach, four numerical tests are given. The results have shown that the GMFS is more accurate, stable, and better convergence than the traditional MFS.

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Section: Generalized Fundamental Solution Approximationmentioning

confidence: 99%

Generalized method of fundamental solutions (GMFS) for boundary value problems

Yang

Zheng

Wen

2018

Engineering Analysis with Boundary Elements

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“…In 1995, Liu et al proposed a Reproducing Kernel Particle Method (RKPM) approximation [33][34][35]. Thereafter, several meshless methods were developed such as the Method of Fundamental Solution (MFS) [36][37][38], the local Radial Point Interpolation Method (RPIM) [39][40][41], the local Radial Basis Function (RBF) collocation method [42][43][44] and the Meshless Intervention-Point (MIP) method [45], etc. In 2014, Wen et al proposed the meshless FBM [46].…”

Section: Introductionmentioning

confidence: 99%

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

et al. 2022

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The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

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“…Hardy [30] and Hon et al [31] developed the multiquadric interpolation method for solving linear partial differential equation. Recently, strong-form meshless methods also have been made progress, such as the Meshless Intervention Point (MIP) method, see Yang et al [32,33,34], and estimation of the qualitative convergence by Deng et al [35,36]). Based on the point collocation concept, the Finite Block Method (FBM) with mapping technique was proposed by Wen et al [37] and Li et al [38,39,40] to solve the heat transfer and elastodynamic 2D and 3D problems in the functionally graded media with excellent accuracy and convergence both in the Cartesian coordinate and polar coordinate systems.…”

Section: Introductionmentioning

confidence: 99%

Infinite element in meshless approaches

Wen

Yang

Huang

et al. 2018

European Journal of Mechanics - A/Solids

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The meshless methods combined with infinite element to deal with unbounded problems are developed in this paper. The meshless methods with moving least square algorithm, radial basis function interpolation and finite block method (Lagrange polynomial) are observed. With mapping of physical domain into a normalised square domain, the first order partial differential matrices both for regular and infinite elements (blocks) are determined. The governing equations and boundary conditions are formulated with the partial differential matrices. Numerical examples in the elasticity solid mechanics with non-homogenous and unbounded media are given to demonstrate the efficiency and accuracy of the meshless method combined with infinite elements. It is observed that the accurate numerical solutions of unbounded media can be obtained using the infinite elements at a much lesser computational effort than the conventional meshless methods in which unbounded media are represented by large number of collocation points.

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Intervention-point principle of meshless method

Cited by 9 publications

References 15 publications

Generalized method of fundamental solutions (GMFS) for boundary value problems

Generalized method of fundamental solutions (GMFS) for boundary value problems

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

Infinite element in meshless approaches

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