Rigid-plastic finite element analysis of sheet metal forming processes using selective membrane/shell formulation and element refinement

Abstract

Recently, finite element simulation of real-world industrial processes in sheet metal working has become practicable due to the advancement of computer hardware and simulation software, but the efficiency of computation still remains to be improved. An improvement of conventional membrane element, selective-M/S scheme, and bi-section refinement technique are proposed for the effectiveness of computation in this work. In spite of various advantages of membrane elements, the conventional membrane is unstable for problems which involve the considerable effect of bending and shape change. As an improved version of conventional membrane element, a BEAM (Bending Energy Augmented Membrane) element based on edge spring is formulated. In order to maintain the numerical efficiency of conventional membrane elements, the bending effects are incorporated for the purpose of computational stabilization without increasing additional degrees of freedom by using the correlation of adjacent elements. A finite element formulation for layered degenerated shell is derived for the incremental analysis of the non-steady large deformation of normal anisotropic rigidplastic sheet metal obeying Hill``s new yield criterion by using natural convected coordinate system. Then, the rigid-plastic selective-M/S scheme is introduced which combines the layered degenerated shell elements with membrane elements according to the characteristics of deformation. The thickness modified curvature is proposed as a selection criterion for element. A three-dimensional bi-section refinement technique is proposed by introducing a unit zone concept. Criterion for refinement according to the nature of deformation is proposed for the three-dimensional refinement. In order to show the validity and effectiveness of the proposed schemes, several industrially useful sheet metal working processes are simulated and the computations are compared with the experiments. The comparison shows that the simulated results by ...