Optimal Design by Sensivity Analysis in Metal Forming

Abstract

An optimization algorithm is presented to meet various conditions during the design of a given metal forming operation. Metal forming processes described in terms of the flow approach are considered. Shape sensitivity analysis is obtained by the control volume approach, where the design variables are some selected nodal coordinates used to defined
the tool shape. The 80 called direct differentiation method is followed to fonnulate the sensitivity problem. The results from the equilibrium and the sensitivity problems are used to evaluate a cost functional and its gradient in the design space. These values are the input for eac.h iteration of the optimization algorithm, from which the new values of the designed variables are obtained, which minimize the functional, resulting in the optimal shape with respect to the adopted optimization criterion. The conjugate gradient
method and Schittkowski's algorithm are used And compared. Steady state processes are considered. The procedure is illustrated by calculating the optimal design of an extrusion
matrix with respect to different criteria.