Design sensitivity analysis and optimization for minimizing springback of sheet-formed part

The springback is a manufacturing defect in the stamping process and causes difficulty in product assembly. An impediment to the use of lighter-weight, higher-strength materials in manufacturing is relative lack of understanding about how these materials respond to complex forming processes. The springback can be reduced by using an optimized combination of die, punch, and blank holder shapes together with friction and blank-holding force. An optimized process can be determined using a gradient-based optimization to minimize the springback. For an effective optimization of the stamping process, development of an efficient design sensitivity analysis (DSA) for the springback with respect to these process parameters is crucial. A continuum-based shape and configuration DSA method for the stamping process has been developed using a non-linear shell model. The material derivative is used to develop the continuumbased design sensitivity. The design sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic non-linear analysis with frictional contact, which makes sensitivity calculation very efficient. Numerical implementation of the proposed shape and configuration DSA method is performed using the meshfree method. The accuracy and efficiency of the proposed method are illustrated by minimizing the springback in a benchmark S-rail problem. Copyright q 2007 John Wiley & Sons, Ltd.