A point interpolation method for two-dimensional solids

By Guirong Liu, Yuantong T. Gu. 2001

797 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f0ef2c08308101f9e1cb60e9cb1b100da8a1e26e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Guirong Liu
2. Trung Nguyen-Thoi
3. Hung Nguyen-Xuan
4. Guiyong Zhang
5. Guangyao Li
6. Khin Yong Lam
7. Lei Chen
8. K. Zeng

In Electrical and Electronic Engineering

1. Guirong Liu
2. Trung Nguyen-Thoi
3. Hung Nguyen-Xuan
4. Guiyong Zhang
5. Lei Chen
6. Guangyao Li
7. K. Zeng
8. Xiangyang Cui

In Mechanics of Materials

1. Guirong Liu
2. Trung Nguyen-Thoi
3. Hung Nguyen-Xuan
4. Guiyong Zhang
5. Guangyao Li
6. R. N. Jorge
7. Khin Yong Lam
8. Timon Rabczuk

Citations in the corpus

• Assessment and applications of point interpolation methods for computational mechanics (2004, methodology): “However, like other methods that use polynomial as basis functions, it is tricky in choosing basis for interpolation in polynomial basis point interpolation [7].”
• Consistent element‐free Galerkin method (2014, neutral): “[5] and so on.”
• A novel virtual node method for polygonal elements (2009, background): “It should be mentioned that, the inverse of this matrix A does not exist in some situation [ 7 ] .”
• Assessment of smoothed point interpolation methods for elastic mechanics (2010, methodology): “In the other front of development related to meshfree methods, the polynomial basis function [36] and the radial basis function (RBF) [37], respectively, have been proposed to construct shape functions for the meshfree point interpolation methods (PIMs) [36–39].”
• Time‐dependent fractional advection–diffusion equations by an implicit MLS meshless method (2011, methodology): “This category of meshless methods includes the diffuse element method (DEM) [25], the elementfree Galerkin (EFG) method [21], the reproducing kernel particle method [26], and the point interpolation method (PIM) [27, 28], the meshless local Petrov–Galerkin (MLPG) method [29], the local radial point ”
• Composite laminated plate analysis using the natural radial element method (2013, methodology): “Based only on a group of arbitrarily distributed points, the Point Interpola tion Method (PIM) [15] constructs a polynomial interpolation with Kronecker delta function property .”
• A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials (2003, methodology): “Meshless methods include the Discrete Element Method (DEM, see for example Sakaguchi and � Mühlhaus 1997 [16]), Smoothed Particles Hydro dynamics (SPH, Monaghan 1992 [12]), Element Free Galerkin (EFG, Belytschko et al 1994 [2]), and the Point Integration Method (PIM, Liu & Gu, 2001 [11]).”
• Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method (2008, methodology): “Such as element-free Galerkin (EFG) method [4], smooth particle hydrodynamic (SPH) method [5,6], reproducing kernel particle method (RKPM) [7], Petrov–Galerkin mesh-free [8], corrective smoothed particle method (CSPM) [9], modified smoothed-particle hydrodynamics (MSPH) [10] and point interpolation ”