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In vehicle safety engineering, it is important to determine the severity of occupant injury during a crash. Computer simulations are widely used to study how occupants move in a crash, what they collide during the crash and thus how they are injured. The vehicle motion is typically defined for the occupant simulation by specifying a crash pulse. Many computer models used to analyze occupant kinematics do not calculate both vehicle motion and occupant motion at the same time. This paper presents a framework of response surface methodology for the crash pulse prediction and vehicle structure design optimization. The process is composed of running simulation at DOE sampling data points, generating surrogate models (response surface models), performing sensitivity analysis and structure design optimization for time history data (e.g., crash pulse).

Experiments to obtain the failure loads of spot welds are first reviewed under combined opening and shear loading conditions. A failure criterion is then presented for spot welds under combined opening and shear loading conditions based on the results from the experiments and a lower bound limit load analysis. In order to account for spot welds under more complex loading conditions, another lower bound limit load solution is presented to characterize the failure loads of spot welds under combinations of three forces and three moments. Based on the limit load solution, an engineering failure criterion is proposed with correction factors determined by different spot weld tests. The engineering failure criterion can be used to characterize the failure loads of spot welds with consideration of the effects of sheet thickness, nugget radius and combinations of loads.

A general failure criterion for spot welds is proposed with consideration of the plastic anisotropy and the separation speed for crash applications. A lower bound limit load analysis is conducted to account for the failure loads of spot welds under combinations of three forces and three moments. Based on the limit load solution and the experimental results, an engineering failure criterion is proposed with correction factors determined by different spot weld tests. The engineering failure criterion can be used to characterize the failure loads of spot welds with consideration of the effects of the plastic anisotropy, separation speed, sheet thickness, nugget radius and combinations of loads. Spot weld failure loads under uniaxial and biaxial opening loads and those under combined shear and twisting loads from experiments are shown to be characterized well by the engineering failure criterion.