A LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD FOR SOLID MECHANICS PROBLEMS

By Guirong Liu, Y. Li, K. Y. Dai, Maotian Luan, W. Xue. 2006

134 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f0475adab44d7d24cdb6f3165ed51ab8784e7c6d

How researchers see this paper

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

In Civil and Structural Engineering

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

In Computational Mechanics

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

In Mechanics of Materials

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

Citations in the corpus

• On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM) (2009, methodology): “The generalized smoothing technique forms the theoretical foundation for NS-PIM [19], NS-RPIM [18–21], ES-PIM and ES-RPIM [22] where incompatible PIM shape functions were used to establish conforming models.”
• A novel alpha finite element method (αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements (2008, unknown): “interpolation method (LC-RPIM) [11].”
• Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) (2011, methodology): “have applied this technique to formulate the linear conforming point interpolation method (LC-PIM) [20] and the linearly conforming radial point interpolation method [21].”
• EDGE-BASED SMOOTHED POINT INTERPOLATION METHODS (2008, methodology): “Using the radial PIM shape functions and node-based strain smoothing operation, the node-based smoothed radial point interpolation method (NS-RPIM, or LC-RPIM originally) has also been formulated and applied for contact problems [Liu et al. (2006); Li et al. (2007)].”
• A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, methodology): “[2] or the LC-PIM [12] using linear interpolation.”
• An n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM) for solid mechanics (2010, methodology): “Liu [5] has generalized the gradient (strain) smoothing technique and applied it in the meshfree context to formulate the node-based smoothed point interpolation method (NS-PIM or LC-PIM) [6, 7] and the node-based smoothed radial point interpolation method (NS-RPIM or LC-RPIM) [8].”
• ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS (2009, methodology): “…used in the nodal integrated meshfree methods [Chen et al. (2001); Yoo et al. (2004)] to formulate the linear conforming point interpolation method (LC-PIM or NS-PIM) [Liu et al. (2005)] and the linearly conforming radial point interpolation method (LC-RPIM or NS-RPIM) [Liu et al. (2006)].”
• An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids (2009, methodology): “The linearly conforming radial point interpolation method (LC-RPIM or NS-RPIM) using RPIM shape functions has also been formulated that works for extremely irregularly distributed nodes [4].”
• An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh (2009, methodology): “has generalized the gradient (strain) smoothing technique [9] and applied it in the meshfree context to formulate the node-based smoothed point interpolation method (NS-PIM or LC-PIM) [17,18] and the linearly conforming radial point interpolation method (NS-RPIM or LC-RPIM) [11].”