The potential of using simulation and optimization techniques in the design of sheet metal forming processes has been investigated. Optimization has been used in a variety of sheet metal forming applications. This usage has given ideas and guidelines on how to formulate an optimization problems, how to ensure its rapid convergence and how to reach a feasible process design. Furthermore one method to include the uncertainty and variation in the governing parameters has been evaluated.

For each forming process many formability problems exist which usually are associated with fracture, wrinkling and springback. The aim of a good process design is to avoid these problems. By the use of simulation based design the physical trial- and error iterations can to a large extent be replaced by virtual iterations. When optimization techniques are used in the design process the number of iterations can be very large. In this work effort has been made to develop an optimization method, Space Mapping (SM), which is less computing intensive. It has been shown that SM can drastically reduce the required computing time and that its optimal solution is close to the optimal solution obtained by the more computing intensive Response Surface Methodology (RSM). The drawback of SM is that the method is less robust compared to RSM, and that it requires a better initial design for convergence.

Each industrial sheet metal forming process exhibits a certain degree of stochastic behavior due to uncertainties and variations in material properties, geometry and other process parameters. The forming process must be designed such that it is insensitive to these uncertainties and variations, i.e. the process must be robust. One possibility to consider uncer tainties and variations in a simulation and optimization based design process is to use the Monte Carlo method, in particular in combination with response surfaces as metamodels. It has been shown in this work that a linear response surface can successfully be used to identify the important design variables and to give an estimate of the probabilistic response. It has also been found that quadratic surfaces are required for a more accurate evaluation of the response.

This dissertation addresses the problems and possibilities of using structural optimization in vehicle crashworthiness design. The first part of the thesis gives an introduction to vehicle crashworthiness design. The optimization methods presented are also used to exemplify how structural optimization and robustness analysis can be used in vehicle crashworthiness design.

In the second part of the thesis, five papers are appended, where different optimization methods are evaluated and improved for the usage in vehicle crashworthiness design. These papers concern the optimization methods Response Surface Methodology (RSM), Stochastic Optimization (SO) and Space Mapping (SM).

Each method has its advantages and disadvantages. The Response Surface Methodology is the easiest method to use and the method that most often finds the best design of these three methods. Generally RSM is rather expensive, especially when many design variables are used. Then, SO is an effective alternative because in this method the number of evaluations is independent of the number of design variables, which is not the case for RSM. Space Mapping is the cheapest method, because it needs only one or two evaluations per iteration. However, SM is generally a method to fmd an improved design with fulfilled constraints and sometimes not the absolute optimum solution but to a low cost. Hence, both RSM and SO may produce better designs but at the price of more response evaluations.