An algorithm for improved convergence in forming analysis

Abstract

Implicit finite element analysis of sheet-forming operations depends on the ability to find a converged solution, which is frequently difficult because of changing contact and friction conditions at arbitrarily shaped interfaces. This sensitivity is aggravated when draw-in is significant, when the well angle is large, and when the contact region or character changes rapidly (during re-draw, for example). A new algorithm has been developed based on the mesh normal and using a consistent full set (N-CFS) of equations, including equilibrium and contact conditions in the non-linear set. The “N-CFS” algorithm exhibits remarkable stability and strong convergence. In fact, we have not found a well-posed problem, i.e. one which is physically stable within the discrete numerical framework, which exhibits numerical instability. The N-CFS algorithm is presented and several challenging example problems are solved, illustrating the robustness of the new method relative to standard implicit formulations. A series of smaller improvements for implicit methods are also outlined.