Optimal Shape Design for Metal Forming Problems by the Finite Element Method

Abstract

In this work, a method for calculation of the optimal shapes of axisymmetrical converging dies by the finite element method is presented. The shape optimization problem considered in this paper is to find the best shape of the die such that the flow rate will be uniform at the die exit.The optimization problem is to minimize an objective function by varying a part of boundary (ie: the shape of die) subject to constraints imposed by the metal forming problem. In this method, the B‐spline functions allow us to determine the shape of the die, using its control points as design variables. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)