A stable node-based smoothed finite element method for metal forming analysis

In this paper, a stable node-based smoothed finite element method (SNS-FEM) is presented for analyzing metal forming problems using linear triangular or tetrahedral elements. In present method, the numerical integration domains are approximately circular or spherical regions of the node-based smoothing domains generated by the node-based smoothed finite element method (NS-FEM). Four or six supplementary integration points, which are symmetrically located at the crossover points of the region and the coordinate axis, are employed for each node to form the stabilization items associated with the variance of smoothed shape function gradient. Through this operation without the introducing of any uncertain parameter, the SNS-FEM not only significantly cures the temporal instability of NS-FEM but also performs better in effectiveness and efficiency than FEM, which is well validated by several numerical examples containing benchmark cases. Additionally, a simple but effective contact algorithm including contact searching and contact force computation is presented.