In this paper, a die shape optimization method for reduction of stress in explosive deep drawing process is presented by using the reduced basis technique coupled by finite element and design of experiments methods. The primary objective of the proposed method is to reduce the enormous number of design variables required to define the initial die shape. The reduced basis technique is a weighted combination of several basis shapes. The purpose of the method is to find the best combination using the weights for each shape as the design variables. The experimental scheme of Taguchi method is used to build the approximation model and to perform optimization. This method is displayed on the die shape optimization of deep drawing of a trapezoidal cup.
