D. Zhou et Rh. Wagoner, AN ALGORITHM FOR IMPROVED CONVERGENCE IN FORMING ANALYSIS, International journal of mechanical sciences, 39(12), 1997, pp. 1363-1384
Implicit finite element analysis of sheet-forming operations depends o
n the ability to find a converged solution, which is frequently diffic
ult because of changing contact and friction conditions al arbitrarily
shaped interfaces. This sensitivity is aggravated when draw-in is sig
nificant, when the well angle is large, and when the contact region or
character changes rapidly (during re-draw, for example). A new algori
thm has been developed based on the mesh normal and using a consistent
full set (N-CFS) of equations, including equilibrium and contact cond
itions in the non-linear set. The ''N-CFS'' algorithm exhibits remarka
ble stability and strong convergence. In fact, we have not found a wel
l-posed problem, i.e. one which is physically stable within the discre
te numerical framework, which exhibits numerical instability. The N-CF
S algorithm is presented and several challenging example problems are
solved, illustrating the robustness of the new method relative to stan
dard implicit formulations. A series of smaller improvements for impli
cit methods are also outlined. (C) 1997 Published by Elsevier Science
Ltd.