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

Abstract EN

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.