A Gradient Stable Node-Based Smoothed Finite Element Method for Solid Mechanics Problems. (4th June 2019)

• Record Type: Journal Article
• Authors: Chen, Guangsong; Qian, Linfang; Ma, Jia
• Other Names: Ruta Giuseppe Academic Editor.
• Is Part Of: Shock and vibration. Volume 2019(2019)
• Publication Date: 2019-06-04
• Subjects: Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.1155/2019/8610790
• Languages: English
• ISSNs: 1070-9622

Abstract

Abstract : 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.