THE OPTIMUM DIE PROFILE FOR THE CYLINDRICAL BENDING OF PLATES

This paper presents a methodology for the design of plate-forming dies in cylindrical bending using optimization techniques to reduce the co st of die production by reducing the trial-and-error procedure conside rably in determining the final die geometry. The plate thickness is di scretized by plane-strain finite-elements. The die is taken to be rigi d and its profile is approximated by Bezier curves the control-point c oordinates of which are the design variables. The die profile is varie d to minimize the difference between the required shape and the shape of the bent plate, considering springback action. The unconstrained op timization problem is solved by the BFGS (Broyden-Fletcher-Goldfarb-Sh anno) method. A numerical example is presented where the optimum die p rofile is obtained for a plate bent into a quarter circle. (C) 1997 El sevier Science S.A.