This thesis concerns the optimization of structures subjected to impact loading. Major applications can be found in the crashworthiness design of vehicles. There is an industrial interest in using optimization methods in the crashworthiness design process. However, strongly nonlinear responses, including high frequency components, make the Finite Element (FE) simulations computationally demanding. This fact restricts the number of possible optimization methods that can be applied.

In this work two optimization methods have been investigated: Response Surface Methodology (RSM) and Kriging. In both these methods the number of functional evaluations, i.e. here FE simulations, depends at least linearly on the number of design parameters. Thus, the number of design parameters is limited due to the computational effort. One objective of this work has been to reduce the total computational cost of the optimization process, or alternatively the possibility to use more design parameters at the same computational cost. When using RSM and Kriging, the number of functional evaluations in each iteration can be reduced, and/or the convergence of the optimization process can be improved. In many applications, RSM has been used with linear approximating response surfaces for robustness and efficiency reasons. Linear RSM may suffer from iterative oscillations, since the optimal design is often found on the boundary of the feasible design region. This oscillatory behaviour can be reduced if Kriging is used for the approximating response surfaces. However, it has been found that Kriging may have problems in fulfilling the constraints. In the initial design process of a structure very many alternative designs exist. At these early stages topology optimization is a mean of finding a structure that is optimal for the objective at hand. In this work a topology optimization approach is proposed for the design of crashworthiness structures. The resulting structure must still be subjected to an interpretation by engineers and also be improved by further optimization.