In a vehicle rollover accident, the strength of the roof structure is an important factor of security in order to reduce the death and injury rates. The National Highway Traffic Safety Administration proposed strength requirements of the roof structure on roof crush resistance in the Federal Motor Vehicle Safety Standard (FMVSS) 216. Recently, there have been many structural optimization studies that design the structure of a vehicle to satisfy this safety regulation. Most previous studies used approximation methods such as the response surface method (RSM) as a crash problem has high non-linearity and difficulty in sensitivity calculation. However, the solution from the RSM may not be accurate and has a limit on the number of design variables. In this research, non-linear dynamic (transient) response optimization using equivalent static loads (ESLs) is proposed to design the structure of a vehicle to satisfy the safety regulation. ESLs for linear response analysis are made to generate the same displacement field as that from non-linear dynamic loads at each time step of non-linear dynamic analysis. A dynamic load is transformed to a set of ESLs. The static loads are used as the multiple loading conditions for linear response optimization, which are not costly in the linear response optimization process. Size optimization using ESLs is performed to reduce the structural mass while the FMVSS 216 regulation is satisfied. The optimum results using ESLs are compared with those from the RSM. As a result, the proposed method is very efficient and derives good solutions. Non-linear analysis is performed using the commercial code LS-DYNA. NASTRAN is used in calculating the ESL and linear response optimization. LS-OPT is utilized for structural optimization using the RSM.

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