Optimizing the shape of a bumper beam section considering pedestrian protection

This paper presents a design technique to optimize the shape of a vehicle bumper beam that satisfies both the safety requirements for a front rigid-wall impact and the regulations protecting pedestrians from lower leg injuries caused by bumper impacts. An intermediate response surface modeling (IRSM) technique was introduced to approximate the non-linear force-displacement curves obtained from the front impact analysis of a vehicle bumper. The accuracy of the IRSM model was tested by comparing its results with those of the non-linear finite element analysis. The maximum displacement error between the two models did not exceed 3%. Using pedestrian impact analyses based on the experimental arrangement of the Plackett-Burman design, the approximate functions describing the response values acting on the lower legs were calculated. The shape of the bumper beam was optimized by integrating the IRSM with the force-displacement model and the approximate functions on lower leg impact. The optimization results satisfied safety regulations on the maximum allowable displacement of the vehicle bumper, and also the regulations protecting pedestrians from lower leg injuries caused by bumper impacts.