OPTIMIZATION DESIGN OF METAL PREFORMING WITH AGGREGATE FUNCTION METHOD

This paper addresses the shape optimization formulation for metal preform design problem, as well as the corresponding solution techniques. The metal preform design is an inverse problem in nature and it is stated as a shape optimization problem in the present paper. Different objective functions are discussed from the computational point of view. A mathematical statement of the metal preform design problem is proposed based on the Aggregate Function, with the purpose to convert the ∞-Norm of the shape error into a smooth and differentiable objective function and thus to improve the convergence of the solution of the optimization problem. The flow formulation is adopted for simulation of the metal forming process at high temperatures. With a gradient-based mathematical programming approach, the metal preform design optimization problem can be solved. A numerical example demonstrates the validity of the proposed method.