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Gradient based topology optimization method is difficult used to optimization of crashworthiness structures due to the expensive computational cost of sensitivity analysis and complex nonlinear behaviors (geometric nonlinearity, material nonlinearity and contact nonlinearity) of structures during a collision. Equivalent static loads (ESLs) method is one of the methods for nonlinear dynamic response optimization. However, this method ignores the material nonlinearity. Thus this paper proposes an improved topology optimization method for crashworthiness structure based on a modified ESLs method. A new calculation of ESLs considering material nonlinearity is proposed. The improved ESLs method is employed to transform the nonlinear dynamic response optimization into a nonlinear static response optimization with multiple load cases. Each element in the design domain is assigned with a design variable.

Based on equivalent static loads method (ESL), a nonlinear dynamic topology optimization is carried out to optimize an automotive body in white (BIW) subjected to representative legislative crash loads, including frontal impact, side barrier impact, roof crush and rear impact. To meet the crashworthiness performances, two evaluation indexes are defined to convert the practical engineering problems into mathematic optimization problems. The strain energy is treated as the stiffness evaluation index of the BIW and the relative displacement is employed as the compliance index of the components and parts.