A boundary point interpolation method for stress analysis of solids

Gu, YuanTong; Liu, Guirong

doi:10.1007/s00466-001-0268-9

Cited by 136 publications

(60 citation statements)

References 12 publications

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“…Meshless (mesh-free) methods have been developed in the past decades to reduce the required effort for mesh generation. Many meshless methods have been proposed thus far, including the smoothed particle hydrodynamics (SPH) method [6,7], the reproducing kernel particle methods (RKPM) [8], the hpclouds method [9], the element-free Galerkin method (EFG) [10], the meshless local Petrov-Galerkin (MLPG) approach [11], the boundary node method (BNM) [12][13][14], the boundary element-free method (BEFM) [15], the hybrid boundary node method (hybrid BNM) [16][17][18][19][20], the Galerkin boundary node method (GBNM) [21], the boundary face method (BFM) [22,23], and the boundary point interpolation method [24].…”

Section: Introductionmentioning

confidence: 99%

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Yang

Chen

2017

Mathematical Problems in Engineering

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The presented study proposed an improved interpolating boundary node method (IIBNM) for 2D potential problems. The improved interpolating moving least-square (IIMLS) method was applied to construct the shape functions, of which the delta function properties and boundary conditions were directly implemented. In addition, any weight function used in the moving least-square (MLS) method was also applicable in the IIMLS method. Boundary cells were required in the computation of the boundary integrals, and additional discretization error was not avoided if traditional cells were used to approximate the geometry. The present study applied the parametric cells created in the parameter space to preserve the exact geometry, and the geometry was maintained due to the number of cells. Only the number of nodes on the boundary was required as additional information for boundary node construction. Most importantly, the IIMLS method can be applied in the parameter space to construct shape functions without the requirement of additional computations for the curve length.

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Section: Introductionmentioning

confidence: 99%

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Yang

Chen

2017

Mathematical Problems in Engineering

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“…An attractive alternative is to combine meshless techniques (see References [7][8][9][10][11][12][13][14][15][16] and other references in these papers) with boundary integral formulations to alleviate meshing requirements. Boundary-type methods [17,18] that combine boundary integral formulations with meshless techniques have been developed. We have recently introduced a boundary cloud method (BCM) [19] that also combines boundary integral formulations with meshless techniques.…”

Section: Introductionmentioning

confidence: 99%

A fast boundary cloud method for exterior 2D electrostatic analysis

Shrivastava

Aluru

2002

Numerical Meth Engineering

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SUMMARYAn accelerated boundary cloud method (BCM) for boundary-only analysis of exterior electrostatic problems is presented in this paper. The BCM uses scattered points instead of the classical boundary elements to discretize the surface of the conductors. The dense linear system of equations generated by the BCM are solved by a GMRES iterative solver combined with a singular value decomposition based rapid matrix-vector multiplication technique. The accelerated technique takes advantage of the fact that the integral equation kernel (2D Green's function in our case) is locally smooth and, therefore, can be dramatically compressed by using a singular value decomposition technique. The acceleration technique greatly speeds up the solution phase of the linear system by accelerating the computation of the dense matrix-vector product and reducing the storage required by the BCM.

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“…Weight function derivatives with respect to the spatial coordinates are also required for the shape function derivatives as given in Equation (14) and are given as follows [2]:…”

Section: Weight Functionmentioning

confidence: 99%

“…In the past few decades, a variety of new meshless methods have been developed, including the smoothed particle hydrodynamics (SPH) method [4], the finite point method (FPM) [5], the diffuse element method (DEM) [6], the element free Galerkin (EFG) method [7], the point interpolation method (PIM) [8], the hp clouds method [9], the partition of unity method (PUM) [10], the meshless local Petrov-Galerkin (MLPG) method [11], the local point interpolation method (LPIM) [12], the discrete least squares meshless (DLSM) method [13], the boundary point interpolation method (BPIM) [14], and the meshless method with boundary integral equations [15]- [18].…”

Section: Introductionmentioning

confidence: 99%

Element Free Gelerkin Method for 2-D Potential Problems

Firoozjaee¹,

Hendi²,

Farvizi³

2015

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A meshfree method namely, element free Gelerkin (EFG) method, is presented in this paper for the solution of governing equations of 2-D potential problems. The EFG method is a numerical method which uses nodal points in order to discretize the computational domain, but where the use of connectivity is absent. The unknowns in the problems are approximated by means of connectivityfree technique known as moving least squares (MLS) approximation. The effect of irregular distribution of nodal points on the accuracy of the EFG method is the main goal of this paper as a complement to the precedent researches investigated by proposing an irregularity index (II) in order to analyze some 2-D benchmark examples and the results of sensitivity analysis on the parameters of the method are presented.

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A boundary point interpolation method for stress analysis of solids

Cited by 136 publications

References 12 publications

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

A fast boundary cloud method for exterior 2D electrostatic analysis

Element Free Gelerkin Method for 2-D Potential Problems

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