Since the modified membrane element has the same external appearance as the ordinary membrane element, it is not able to apply the thickness variation of sheet metal in the blank holder to the contact treatment and the equally distributed blank holding force should be inevitably imposed on sheet metal along the periphery regardless of the contact status. But sheet metal does not contact with the blank holder at the perphery, nor the blank holding force is distributed uniformly along the boundary. To impose the blank holding force properly, the scheme is improved so that the blank holding force at each node imposed on sheet metal is dependent on the calculated thickness derivation and a state of equilibrium with the total blank holding force. The validity of the improved scheme is demonstrated with the simulation of cylindrical and rectangular cup deep drawing.
Planar anisotropy; Modified membrane element; Sheet metal forming; Blank holding force