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

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 ex...

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Veröffentlicht in:Shock and vibration Jg. 2019; H. 2019; S. 1 - 24
Hauptverfasser: Chen, Guangsong, Ma, Jia, Qian, Linfang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cairo, Egypt Hindawi Publishing Corporation 01.01.2019
Hindawi
John Wiley & Sons, Inc
Wiley
Schlagworte:
Accuracy
Analysis
Finite element analysis
Finite element method
Forced vibration
Mathematical analysis
Methods
Nodes
Nonlinear programming
Solid mechanics
Stability
Stiffness matrix
Taylor series
Vibration
Iran
Canada
ISSN:1070-9622, 1875-9203
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1070-9622
1875-9203
DOI:10.1155/2019/8610790