Crash Optimization of an Automobile Frontal Structure Using Equivalent Static Loads

Abstract

1. Abstract Many commercial automobile industries are seeking to design the automobile structure for improvement of passenger safety as well as reduction of the mass of the automobile. Optimization can be employed to accommodate the crash environment. The automobile crash optimization problem has large nonlinearity in analysis while the analysis is carried out in the time domain. Although the performance of the computer has been significantly improved, automobile crash optimization still needs considerable computational cost. The equivalent static loads (ESLs) method has been developed for such nonlinear dynamic response structural optimization. The ESLs are static loads that generate the same displacement in the linear static analysis as those of the nonlinear dynamic analysis at a certain time step. The ESLs are generated at all the time steps and used as multiple external forces in linear static response structural optimization. Nonlinear analysis and linear static response optimization using ESLs are carried out sequentially until the convergence criteria are satisfied. A new ESLs method is proposed for automobile crash optimization and the proposed method is verified using two practical examples. Crash optimization under a frontal impact performed to minimize the mass, and the thicknesses of the structure are determined to satisfy the relative distance constraints. The side structure of an automobile is optimized under a side impact test. The mass is minimized while the regulation of Insurance Institute for Highway Safety (IIHS) is satisfied. The regulation is the limit of the maximum intrusion that is the relative distance between the B-pillar and the center line of the seat. The resultant designs are discussed from a practical viewpoint. 2. Keywords: Structural optimization, equivalent static loads (ESLs), frontal structure, side impact test, moving deformable barrier (MDB). 3. Introduction Automobile safety regulations have become more stringent in the last decades. Many automobile industries are seeking to design the automobile structure for safety as well as reduction of the automobile mass. It is well-known that the mass of an automobile is one of the important factors for the fuel cost. Automobile structural optimization has been utilized to minimize an objective function such as mass while the conditions for safety are satisfied [1]. Automobile crash optimization generally uses nonlinear dynamic analysis that has large nonlinearity in the time domain. Therefore, optimization techniques for crash optimization should be able to address the nonlinearity in the time domain with an appropriate manner. Automobile industries are trying to utilize a high-fidelity model in structural optimization. An intuitive design based on the designer's experience has been popularly utilized. The conventional optimization paradigm is difficult to use for crash optimization due to extremely high cost. Meta-models are actively used for optimization with approximated functions to save the cost [2-4]. The meta-model approaches vary depending on the sampling method, fitting function or interpolation function, and the optimum solution depends on the selection of a method. When the number of design variables is large, the number of sampling, i.e., the number of nonlinear dynamic analyses can be quite large. The equivalent static loads method (ESLM) has been utilized to save the computational cost as well as to use a gradient-based optimization process. Since the ESLM was introduced by Choi and Park in 1999 [5], it has been applied to various practical examples [6-9]. Two domains such as the analysis domain and the design domain are defined. In the analysis domain, nonlinear dynamic analysis is performed, equivalent static loads (ESLs) are generated by using the displacement output of the analysis domain, and linear static structural optimization is carried out using the ESLs in the design domain. Generally, the finite element (FE) models of the two domains are the same. An FE model for crash analysis may not have boundary conditions; however, an FE model for linear static structural optimization requires boundary conditions. A novel method is proposed to solve this discrepancy by using the inertia relief technique [10] when using the ESLM. The proposed method is validated by solving two practical examples. The two examples are optimizations of a frontal structure and a side structure. Optimization of the frontal structure is carried out under the low speed impact test protocol of the Electronic Code of Federal Regulations (e-CFR) [11]