A stable node-based smoothed finite element method for stability analysis of two circular tunnels at different depths in cohesive-frictional soils

2021 ◽  
Vol 129 ◽  
pp. 103865
Author(s):  
T. Vo-Minh ◽  
L. Nguyen-Son
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Stable Node ◽  
Smoothed Finite Element Method ◽  
Different Depths ◽  
Element Method ◽  
Frictional Soils

scholarly journals A Gradient Stable Node-Based Smoothed Finite Element Method for Solid Mechanics Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-24 ◽  
Author(s):  
Guangsong Chen ◽  
Linfang Qian ◽  
Jia Ma
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solid Mechanics ◽  
Stable Node ◽  
Fem Model ◽  
First Order ◽  
Dynamic Analyses ◽  
Comparative Accuracy ◽  
Smoothed Finite Element Method ◽  
Element Method

This paper presents a gradient stable node-based smoothed finite element method (GS-FEM) which resolves the temporal instability of the node-based smoothed finite element method (NS-FEM) while significantly improving its accuracy. In the GS-FEM, the strain is expanded at the first order by Taylor expansion in a node-supported domain, and the strain gradient is then smoothed within each smoothing domain. Therefore, the stiffness matrix includes stable terms derived by the gradient of the strain. The GS-FEM model is softer than the FEM but stiffer than the NS-FEM and yields far more accurate results than the FEM-T3 or NS-FEM. It even has comparative accuracy compared with those of the FEM-Q4. The GS-FEM owns no spurious nonzero-energy modes and is thus temporally stable and well-suited for dynamic analyses. Additionally, the GS-FEM is demonstrated on static, free, and forced vibration example analyses of solids.

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