A study on the development of equivalent beam analysis model on pedestrian protection bumper impact

Abstract

This paper presents a dynamically equivalent beam analysis model on pedestrian protection bumper impact instead of a non-linear finite element impact analysis method. Equivalent beam analysis model was developed by substituting the femur and tibia for dynamically equivalent Euler beam. Dynamically equivalent forces of bumper beam, upper stiffener and lower stiffener are found by a finite element analysis results and applied to the Euler beam model of lower legform impactor. This equivalent beam analysis model was used to obtain a bending angle of lower legform impactor by using finite element beam theory. Peak acceleration of the tibia was obtained by developing an approximate acceleration equation. A linear interpolation of non-linear finite element analysis results considering the dimension variation of bumper beam factors affecting the acceleration was used to get an approximate acceleration equation. The accuracy of this simple analysis model was tested by comparing its results with those of the non-linear finite element analysis. Tested bumper beam types were press type beam and roll forming beam used widely in the current car bumpers. The differences of maximum acceleration of the tibia between the two models did not exceed 10% and the bending angle did not exceed 20%. This accuracy is enough to be used in the early stage of bumper beam design to check the bumper pedestrian performance quickly. Use of equivalent beam analysis model is expected to reduce the analysis time with respect to the non-linear finite element analysis significantly.