A novel node-based smoothed radial point interpolation method for 2D and 3D solid mechanics problems

Li, Ying Zhen; Liu, G.R.; Yue, Junhong

doi:10.1016/j.compstruc.2017.11.010

Cited by 48 publications

(11 citation statements)

References 31 publications

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“…The RPIM has been successfully used to solve many problems [37][38][39][40][41]. In addition, some improved RPIMs and coupling technologies based on RPIM have emerged [42][43][44][45]. Unfortunately, the stress solutions at weld toe obtained by RPIM are strongly influenced by the parameters used in RPIM as a result of singularity at notch, which makes the conventional RPIM unable to effectively and consistently determine the stress concentration factor and stress intensity factors at the weld toe.…”

Section: Introductionmentioning

confidence: 99%

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An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

et al. 2020

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The study of characterizing the stress concentration effects at welds is one of the most important research directions for predicting the fatigue life of welded components. Stress solutions at the weld toe obtained from conventional meshfree methods are strongly influenced by parameters used in the methods as a result of stress singularity. In this study, an improved 2D meshfree radial point interpolation method (RPIM) is proposed for stress concentration evaluation of a welded component. The stress solutions are insensitive to parameters used in the improved RPIM. The improved RPIM-based scheme for consistently calculating stress concentration factor (SCF) and stress intensity factor at weld toe are presented. Our studies provide a novel approach to apply global weak-form meshfree methods in consistently computing SCFs and stress intensity factors at welds.

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Section: Introductionmentioning

confidence: 99%

“…, σ b(2) defined in Equation (47) and σ m , σ b defined in Equations(44) and(45), the distributions of notch stresses can then be obtained in terms of p m and p b expressed as Equation (48) as shown inFigure 5b. The detailed discussion on deriving the relationship between p m , p m and σ m(2) , σ b(2) , σ m , σ b were given in[2].…”

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confidence: 99%

An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

et al. 2020

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“…Besides, the node-based S-RPIM (NS-RPIM) is a novel numerical method (Bie et al, 2018; Cui et al, 2016; Hu et al, 2017) with the gradient smoothing technique (Liu, 2008; Zhou et al, 2020). NS-RPIM can produce more stable, efficient, and accurate solutions and perform well in the MEE coupling problems (Li et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Zhou

Nie

Ren

et al. 2020

Journal of Intelligent Material Systems and Structures

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The node-based smoothed radial point interpolation method combined with the asymptotic homogenization method was proposed, as an addition to the finite element method, to address the static and dynamic reactions of magneto-electro-elastic coupling micromechanical problems. First, several basic equations for relevant problems were derived. Second, asymptotic homogenization method was utilized to determine the material properties of magneto-electro-elastic nanomaterials. Third, node-based smoothed radial point interpolation method was applied to obtain the discrete equations of magneto-electro-elastic nanostructures. Then, the Newmark method was introduced to solve the response of microcosmic problems. Finally, several numerical examples were calculated to prove the accuracy, convergence, and reliability of node-based smoothed radial point interpolation method by comparing the results of node-based smoothed radial point interpolation method with those of finite element method.

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“…developed the radial point interpolation method based on a predefined background mesh to deal with various mechanical problems [15][16]. Recently, the combination of the finite integration method with RBFs [17][18] was developed to deal with stiff…”

Section: Introductionmentioning

confidence: 99%

“…For large scale problems, the localized radial basis function method was developed and had been successfully applied to solve diffusion and convection-diffusion problems by Sarler et al [13][14]. Liu et aldeveloped the radial point interpolation method based on a predefined background mesh to deal with various mechanical problems [15][16]. Recently, the combination of the finite integration method with RBFs [17][18] was developed to deal with stiff…”

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confidence: 99%

Finite and infinite block Petrov–Galerkin method for cracks in functionally graded materials

Wen

2019

Applied Mathematical Modelling

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This paper presents a novel weak-form block Petrov-Galerkin method (BPGM) for linear elastic and crack problems in functionally graded materials with bounded and unbounded problem domains. The main idea of this approach is to combine the meshless local Petrov-Galerkin method with block method. Once the problem domain is discretized into several sub-regions, named blocks, which can be mapped into normalized square domains. The weak-form Petrov-Galerkin method and polynomial series of interpolations are employed in each block. The computational efficiency is rigorously examined against the strong-form finite block method, the finite element technique and meshless approaches. Numerical results demonstrate that the BPGM possess the following important properties: (1) only a few blocks are required for calculating problems in unbounded regions which saves tedious work of meshing; (2) the displacements and stresses are continuous at the interfaces of neighboring blocks;(3) due to the use of weak formulation, the continuity requirements of the approximation functions are reduced and numerical solutions are stable; (4) because of using Lagrange polynomial interpolation, highly accurate results can be obtained with a small amount of nodes in each block.Emails: liyan001de@gmail.com 2 IntroductionMany engineering problems can be modeled as an extension of either finite or semi-infinite regions. The analytical solutions of these models are often difficult to obtain due to the complexity of material properties and irregular geometries.Numerical techniques are developed to deal with these problems which are modeled by partial differential equations (PDEs), among which the widely used approaches are finite difference method (FDM) [1], finite element method (FEM) [2] and boundary element method (BEM) [3]. The FDM and FEM are mesh dependent and become computationally time demanding on generation of high quality meshes for efficient solutions. The use of fundamental solutions or Green's functions in BEM provides more accurate and efficient approximation. However, it is usually difficult to obtain the fundamental solutions in closed forms, especially for nonhomogeneous and anisotropic materials. In recent decades, meshless techniques were developed to solve practical problems and had drawn the attention of many investigators, including the smooth particle hydrodynamics method [4] , the diffuse element method [5], the element-free Galerkin method (EFG) [6] and the reproducing kernel particle method [7]. Based on the weak Petrov-Galerkin formulation, Atluri and his co-workers developed the meshless local Petrov-Galerkin method (MLPG) with moving least square approximation for problems in arbitrary geometries [8]. Sladek et al. [9] introduced the local boundary integral equation method for boundary value problems in anisotropic non-homogeneous media. Among these meshless approaches, the radial basis functions (RBFs) method [10] was a truly meshless collocation method using in particular the multiquadric shape function [11][12] for...

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A novel node-based smoothed radial point interpolation method for 2D and 3D solid mechanics problems

Cited by 48 publications

References 31 publications

An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

Finite and infinite block Petrov–Galerkin method for cracks in functionally graded materials

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