The aim of the present work is to find a stable and effective optimization algorithm that can be used to determine the location and size of drawbeads in sheet metal forming processes. The result from the optimization will be the restraining force that each drawbead applies to the blank. In addition, optimization has been used to determine the physical dimensions of the drawbead.

The study in Paper I is limited to two structures in crashworthiness design, each with two design variables and three responses. The conclusion is that 1.5 times the minimum number of function evaluation should be used to fit the surface approximations. The conclusion of this study gives an indication on how many evaluations that are needed in order to efficiently construct the response surface approximations.

Paper II shows that the optimization algorithm using Space Mapping is well suited for optimization problems in crashworthiness design and in the design of sheet metal forming processes. All optimization applications converged to the correct optimum and the computing time was decreased with a maximum of 63% relative to the traditional RSM optimization.

The Space Mapping algorithm presented in Paper III converged to an optimum value that is lower than the optimum value from the traditional RSM, when the approximated surfaces from the first RSM iteration were used as the coarse model. The Space Mapping algorithm, however, reached a higher value compared to RSM, when surfaces from the third RSM iteration was used as the coarse model. Hence, the Space Mapping algorithm converged to a better objective value compared to RSM with less evaluations.

This thesis has shown that it is possible to apply optimization on the design of sheet metal forming processes. For the problem used in the last paper both the traditional Response Surface Methodology and the Space Mapping technique were successful in avoiding failure due to necking and to decrease the risk of wrinkles. The Response Surface Methodology is robust enough to be used in the industrial tool design process. The Space Mapping technique using linear response surfaces as coarse model needs further research before it can be used efficiently in industry.