Numerical simulations of multiple vehicle crashes and multidisciplinary crashworthiness optimization
AbstractIn this study, a fullscale finite element vehicle model of a 1996 Dodge Neon is used in simulating two types of vehicle crashes, offsetfrontal and side impacts. Based on an analysis of the vehicle's internal energy absorption under both impacts, twentyone components are selected and represented by thirteen design variables for the multidisciplinary optimization including the weight, intrusion distance, and energy absorptions. The secondorder polynomials are used in creating the metamodels for the objective and constraint functions. The optimization results show that the weight can be significantly reduced while decreasing the intrusion distance and keeping the original level of energy absorption. With the successfully implemented optimization scheme, a set of nondominated (tradeoff) solutions is obtained and the final design can be selected based on the designer's preference. A simulation of 100 ms offsetfrontal impact using LSDYNA MPP v970 takes approximately 17 hours with 36 processors on an IBM Linux Cluster with Intel Pentium III 1.266 GHz processors and 607.5 GB RAM. A simulation of 100 ms side impact takes approximately 29 hours with the same condition as that of the offsetfrontal simulation. Author(s): H. Fang, K. Solanki, M. F. Horstemeyer 

MethodologyThe fullscale FE vehicle model used in this study has detailed meshes of 328 components that consist of 320,872 nodes and 577,524 elements. Approximately 95% of the elements were shell elements. The total vehicle mass is 1,210 kg. The two FE models are illustrated in Figure 1. The components used in the FE model consist of elastic, piecewise linear elasticplastic, plastic kinematic, honeycomb, viscous, BlatzKo rubber, foam, and rigid body materials. Since a vehicle impact finishes in a short period (in the magnitude of 100 ms), both the energy absorption capacity and absorption rate are important. the energy absorption of all components at 20, 40, and 60 ms were examined, and the components with large energy absorptions in one or both impacts were selected. Some components with large mass but small or no contribution to the energy absorption were also selected for mass reduction. A total of twentyone components were finally selected; they are shown in Figure 2. Figure 3 shows the time histories of energy absorptions of selected components compared to those of the whole vehicle in OFI and SI. In the multidisciplinary optimization, the mass of the selected components is to be minimized, the vehicle's energy absorption at 40 ms in OFI is to be maximized, and the average intrusion distance of the door in SI is to be minimized. The total vehicle's energy absorption at 40 ms in SI is used as a constraint to ensure the optimum design will not reduce the energy absorption at the early stage of SI. The constraints were selected based on the fact that the selected components contributed significantly to the total vehicle's energy absorption and on the concern that changes in these components might have a negative effect on the energy absorption, which in turn might affect other safety parameters such as accelerations. All the impact simulations were performed using LSDYNA MPP v970.^{[1]} The metamodels of the objective and constraint functions for optimization were created with the secondorder polynomials. The multidisciplinary optimization was performed using the objectoriented optimization software HiPPO developed by Fang and Horstemeyer ^{[2]} at CAVS, Mississippi State University. HiPPO incorporates the feasible sequential quadratic programming (FSQP) as the optimization solver developed by Lawrence, et al.^{[3]}  
Material ModelThe basic idea of metamodeling is to construct an approximate model for the true unknown response function using function values at some predefined design points, which are called sampling points and typically determined using design of experiments (DOE) methods. Response Surface Methodology (RSM) is used to construct metamodels for the objective and constraint functions. This DOE method determined the sampling points, where the Taguchi orthogonal array L27 was selected for generating the sampling points.^{[4]} 

Input DataTable 1 gives the initial mass and thickness of the twentyone components selected for analysis. The thickness of the selected components was used as design variables for size optimization. A total of thirteen design variables were needed for the twentyone components due to component symmetry. 

ResultsWith the optimization scheme in this study, a set of tradeoff solutions was obtained for the mass and intrusion distance in side impact. One of the solutions showed that simultaneous reductions of 8.1% and 8.8% could be achieved on the mass and the intrusion distance for side impact, respectively. These reductions are significant considering the fact that the selected components hold for only 8% of the total vehicle's mass. Solutions for further reduction on either of the two objectives are also given Table 2, and the final decision depends on the designer's preference. Figures 4 and 5 compare the engine acceleration and velocity of the original design to one of the selected optimum designs. 

AcknowledgmentsThe authors acknowledge the support of the Center for Advanced Vehicular Systems (CAVS), Mississippi State University, United States of America.  
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