The aim of this paper is to determine the efficient number of experimental points when using the response surface methodology in crashworthiness problems.

The D-optimality criterion is used as experimental design method. Two application models have been studied, one square tube and one front rail from Saab Automobile AB. Both models were fully parameterized in the preprocessor LS-INGRID but only two design variables were used. The optimization package LS-OPT was used to determine the design of experiments using the D-optimality criterion. Both models were subjected to an impact into a rigid wall and the simulations were carried out using LS-DYNA. A general recommendation is to to use 1.5 times the minimum number of experimental points. A more specialized recommendation is for linear surfaces 1.5, elliptic surfaces 2.2 and for quadratic surfaces 1.6 times the minimum number of experimental points.

The accuracy of different approximating response surfaces is investigated. In the classical response surface methodology (CRSM) the true response function is usually replaced with a low-order polynomial. In Kriging the true response function is replaced with a low-order polynomial and an error correcting function. In this paper the error part of the approximating response surface is obtained from “simple point Kriging” theory. The combined polynomial and error correcting function will be addressed as a Kriging surface approximation.

To be able to use Kriging the spatial correlation or covariance must be known. In this paper the error is assumed to have a normal distribution and the covariance to depend only on one parameter. The maximum-likelihood method is used to find the latter parameter. A weighted least-square procedure is used to determine the trend before simple point Kriging is used for the error function. In CRSM the surface approximation is determined through an ordinary least-square fit. In both cases the D-optimality criterion has been used to distribute the design points.

From this investigation we have found that a low-ordered polynomial assumption should be made with the Kriging approach. We have also concluded that Kriging better than CRSM resolves abrupt changes in the response, e.g. due to buckling, contact or plastic deformation.

Optimization of car structures is of great interest to the automotive industry. This work is concerned with structural optimization of a car body with the intent to increase the crashworthiness properties of the vehicle or decrease weight with the crashworthiness properties unaffected. In this work two different methodologies of constructing an intermediate approximation to the optimization problem are investigated, i.e. classical response surface methodology and Kriging. The major difference between the two methodologies is how the residuals between the true function value and the polynomial surface approximation value at a design point are treated.

Several different optimization problems have been investigated, both analytical problems as well as finite element impact problems.

The major conclusion is that even if the same kind of updating scheme is used both for Kriging and linear classic response surface methodology, Kriging improves the sequential behaviour of the optimization algorithm in the beginning of the optimization process. Problems may occur if a constraint is violated after several iterations and then classic response surface methodology seems to more easily be able to find a design point which satisfies the constraint.

This paper describes the methodology used during the development of an energy absorbing Frontal Underrun Protection device (eaFUP). The aim of this study is to show how different optimisation methods can be used at different stages during the design process. It also shows one approach to derive an optimal design taking several different design alternatives into account, each of which consists of several different materials. The outcome of the optimisation process is three different designs of the eaFUP.

Topology optimization has developed rapidly, primarily with application on linear elastic structures subjected to static loadcases. In its basic form, an approximated optimization problem is formulated using analytical or semi-analytical methods to perform the sensitivity analysis. When an explicit finite element method is used to solve contact–impact problems, the sensitivities cannot easily be found. Hence, the engineer is forced to use numerical derivatives or other approaches. Since each finite element simulation of an impact problem may take days of computing time, the sensitivity-based methods are not a useful approach. Therefore, two alternative formulations for topology optimization are investigated in this work. The fundamental approach is to remove elements or, alternatively, change the element thicknesses based on the internal energy density distribution in the model. There is no automatic shift between the two methods within the existing algorithm. Within this formulation, it is possible to treat nonlinear effects, e.g., contact–impact and plasticity. Since no sensitivities are used, the updated design might be a step in the wrong direction for some finite elements. The load paths within the model will change if elements are removed or the element thicknesses are altered. Therefore, care should be taken with this procedure so that small steps are used, i.e., the change of the model should not be too large between two successive iterations and, therefore, the design parameters should not be altered too much. It is shown in this paper that the proposed method for topology optimization of a nonlinear problem gives similar result as a standard topology optimization procedures for the linear elastic case. Furthermore, the proposed procedures allow for topology optimization of nonlinear problems. The major restriction of the method is that responses in the optimization formulation must be coupled to the thickness updating procedure, e.g., constraint on a nodal displacement, acceleration level that is allowed.