Design of large-deformation steady elastoplastic manufacturing processes. Part II: sensitivity analysis and optimization

An optimization algorithm for quasi-steady forming processes is presented that is based upon the computation- ally e cient reference frame formulation. The direct di erentiation method is used to e ciently evaluate the response sensitivities. Select forming response measures and their sensitivities are combined with non-linear programming methods to optimize the process. To illustrate these methods, drawing and rolling processes are optimized. The die shape in a drawing process is designed to minimize the distortion and yield stress variation in the workpiece. The pass heights in a multi-pass rolling process are designed to so that the same degree of camber, and hence the same roll, can be used in each of the passes.