Coupled-field simulation of electromagnetic tube forming process using a stable nodal integration method

This paper proposes a stable nodal integration method for analyzing coupling problems of electromagnetic field and mechanical field using linear triangular mesh. For transient electromagnetic field analysis, the node-based smoothed solution is firstly formulated to compute system matrices, and then the equivalent smoothing domain and temporal integration points are constructed to achieve a stable nodal integration method (SNIM), whose coefficient matrix is finally computed using the smoothed shape function derivatives together with the variance terms over the equivalent smoothing domain associated with nodes of the mesh. For dynamic large-deformation analysis, the node-based smoothed finite element method (NS-FEM) is utilized after testifying its stability and effectiveness in thin-walled structures of electromagnetic forming (EMF) process. Furthermore, by treating the morphing region as a static mechanical problem, a weighted elastomer method is presented to accomplish the mesh updating in sequential coupling simulation. Finally, it turns out that the proposed methodologies can be applied successfully to simulate EMF process, and numerical examples for both tube bulging and tube compression are investigated to demonstrate the validity, accuracy and efficiency of the proposed methods.