Abstract
Research and/or Engineering Questions/Objective
The main challenges when optimizing the crash performance of a car part are the high computational cost and the noisy responses. This paper deals with those problems by means of a surrogate-based approach. The crash response of a hybrid glass-fiber reinforced polyamide and steel impact absorbed (steel tube with inner GFRP reinforcement) is optimized by a maximization of its specific energy absorption (SEA) and a minimization of its peak load (PL), which helps to reduce the damage on the occupants.
Methodology
A detailed finite element model of the crash absorber has been verified with experimental impact tests, including damage of the composite material and strain-rate sensitivity of the steel part. The computational model is used to run a surrogate-based global multi-objective optimization strategy, which allows the employment of gradient-based optimization methods on soft, derivable surrogate functions that accurately emulate the response of the finite element model. This avoids the numerical noise present in the FEA analysis and the large computational cost that would be required for each iteration. Two different surrogate-based approaches are tested in order to obtain quality emulations of the responses of SEA and PL in a six-dimensional design space. Variables like thickness of the different parts, cross-section geometry and part offsets are considered. These surrogate approaches are parsed to a Pareto optimization algorithm that produces the optimum sets for this problem.
Results
As a result of the surrogate methods comparative study, polynomial approaches have produced a quality approximation of the SEA function. PL approximation required from a more sophisticated approach due to the nature of the objective function, which is divided in very different regions. A gaussian process (Kriging) and a multi-adaptive regression splines strategies produced quality approaches. The optimum solutions have a much better response than the original design in both SEA and PL, and a Pareto set is obtained to facilitate future design decisions.
Limitations of this study
Not all the possible variations in the design of the absorber’s cross section have been taken into account. Modifications of the inner reinforcement geometric parameters could even lead to better results in both SEA and PL indicators. Besides, the weighted functions method used to obtain the Pareto curves left some blank spaces, which would be captured with a better strategy.
What does the paper offer that is new in the field including in comparison to other work by the authors?
The optimization strategy presented in this paper has never been applied to a hybrid crash absorber with an inner GFRP reinforcement.
Conclusions
A sophisticated optimization strategy has been successfully applied to an ill-conditioned crashworthiness problem with complex objective functions. Results offer guidance to the design of new hybrid crash absorbers.
KEYWORDS – Multi-objective, optimization, surrogate models, crashworthiness, hybrid components.