Stable node-based smoothed finite element method for 3D contact problems

2022 ◽  
Author(s):  
Xiao Sun ◽  
Hong Yang ◽  
She Li ◽  
Xiangyang Cui
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problems ◽  
Stable Node ◽  
Smoothed Finite Element Method ◽  
Element Method

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.

Contact Analysis Based on a Linear Strain Node-Based Smoothed Finite Element Method with Linear Complementarity Formulations

2021 ◽  
pp. 2141008
Author(s):  
Yan Li ◽  
Junhong Yue
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Point ◽  
Linear Complementarity Problems ◽  
Contact Problems ◽  
Linear Complementarity ◽  
Linear Functions ◽  
Linear Strain ◽  
Smoothed Finite Element Method ◽  
Element Method

This paper presents the node-based smoothed finite element method with linear strain functions (NS-FEM-L) for solving contact problems using triangular elements. The smoothed strains are formulated by a complete order of polynomial functions and normalized with reference to the central points of smoothing domains. They are one order higher than those adopted in the finite element method (FEM) and the standard smoothed finite element method with the same triangular mesh. When using linear functions to describe strains in smoothing domains, the solutions are more accurate and stable. The contact interfaces are discretized by contact point pairs using a modified Coulomb frictional contact model. The contact problems are solved via converting into linear complementarity problems (LCPs) which can be tackled by using the Lemke method. Numerical implementations are conducted to simulate the contact behavior, including the bonding–debonding, contacting–departing and sticking–slipping. The effects of various parameters related to friction and adhesion are intensively investigated. The comparison of numerical results produced by different methods demonstrates the validity and efficiency of the NS-FEM-L for contact problems.

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