Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique

The aim of this work is to illustrate how a space mapping technique using surrogate models together with response surfaces can be used for structural optimization of crashworthiness problems. To determine the response surfaces, several functional evaluations must be performed and each evaluation can be computationally demanding. The space mapping technique uses surrogate models, i.e. less costly models, to determine these surfaces and their associated gradients. The full model is used to correct the gradients from the surrogate model for the next iteration. Thus, the space mapping technique makes it possible to reduce the total computing time needed to find the optimal solution. First, two analytical functions and one analytical structural optimization problem are presented to exemplify the idea of space mapping and to compare the efficiency of space mapping to traditional response surface optimization. Secondly, a sub-model of a complete vehicle finite element (FE) model is used to study different objective functions in vehicle crashworthiness optimization. Finally, the space mapping technique is applied to a structural optimization problem of a large industrial FE vehicle model, consisting of 350.000 shell elements and a computing time of 100 h. In this problem the intrusion in the passenger compartment area was reduced by 32% without compromising other crashworthiness parameters.