Adaptive metamodel-assisted shape optimization for springback in metal forming processes

This paper aims to propose a shape optimization strategy for springback shape in metal forming processes based on the adaptive metamodel of the spatial field that can reduce the computational time and cost. The first stage includes solving metal forming problem using finite element simulation and building of Reduction Order Model of spatial field based on Proper Orthogonal Decomposition. Then, the metamodel of spatial field is built using the combination of Reduction Order Model and Kriging method to replace the expensive high fidelity model. In the second stage, the metamodel of spatial field is used within the iterative optimization procedure to find the optimal design for the final shape after springback in the metal forming processes. This strategy allows reducing computational cost to achieve the optimal design with respect to the approach based on the traditional metamodel. The proposed methodology is illustrated with the U-shape bending from the Numisheet2011 benchmark problem. Two parameters: the blank holder force and the die radius are chosen to optimize the springback effect.